WEBVTT

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sleep at time facts, orbital physics, settle into a comfortable position, and let your breathing

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become slow, and even orbital physics begins with a simple idea. Objects move through space,

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along paths, shaped by gravity, when a smaller body circles a larger one. It is following a curve,

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made by attraction, and motion, the moon travels around Earth in this quiet way. And Earth moves

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around the Sun, with steady, predictable rhythm. There is no strain in these motions, and orbit

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can be nearly circular. Or it can be a gentle, oval, the same natural, rules guide, satellites,

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and planets alike. Each path is balanced, repeating, and calm, as you rest. You can imagine

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these slow, orderly movements as soft circles in the dark, nothing is rushing. Everything

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follows its course. All of it is guided by the same patient pull. Planets do not wander without

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pattern, their paths repeat in smooth curves. And the first clear description of those curves

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came from three statements about motion, those statements describe. How a body moves around another body

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under steady attraction, they apply to planets around stars, and to moons around planets, small,

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natural objects. Moving in quiet space, follow the same geometry. The first statement says that

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an orbit is in ellipse, and ellipse is a closed oval shape. It can be drawn by fixing two points,

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called foci, and keeping the total distance from those two points the same. A circle is a special

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ellipse, where the two foci meet at the center in a planetary orbit. The star sits at one focus.

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The other focus is empty. This means the planet is not always the same distance from its star.

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There is a nearest point and a farthest point. And the line through those points is the long

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axis of the ellipse. Half of that long axis is called the semimager axis. And it gives a useful measure

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of the size of the orbit. For many planets, the ellipse is close to a circle, the difference between

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nearest and farthest distance can be small. So the path looks round in simple diagrams. The shape

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is still in ellipse, though. And the small difference matters, when positions are measured carefully,

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Kepler reached this idea. After comparing many observations, with models that used perfect circles,

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the circular models came close. But they did not match the records at every point, and ellipse fit

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the pattern better. The second statement describes speed along the path, a planet does not move

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at one unchanging rate if a line is drawn from the planet to the star. That line sweeps out area as the

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planet moves in equal spans of time. The swept area is equal when the planet is closer to the star.

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The line is shorter. So the planet must cover more distance along its path to sweep the same

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area. It moves faster when the planet is farther away. The line is longer. And the motion is slower.

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The change is smooth and regular. There is no sudden start or stop. Only a steady exchange between

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distance and speed. This rule gives the orbit a kind of balance, a planet near its star,

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spends less time moving quickly through that part of the path, a planet far from its star,

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spends more time moving slowly through the wider arc, the areas match. So the timing remains orderly

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later physics, showed that this pattern follows from the conservation of angular momentum.

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The idea is that a moving body keeps a certain amount of rotational motion. Unless something outside

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changes it, Kepler did not need that later explanation. To state the rule, he found it by watching how

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positions changed over time. The third statement connects the size of an orbit to the time

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needed to complete it for bodies orbiting the same star. The square of the orbital period is proportional

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to the cube of the semimager axis in plain terms. A planet farther from its star takes longer to go around

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and the relationship follows a fixed mathematical pattern. The law does not say that all orbits

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take the same time. It says that distance and period are tied together in a reliable way. A small

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change in average distance brings a predictable change in the length of a year. This third law

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gives a sense of scale to a planetary system if the period of one planet is known.

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And the period of another is known. Their relative distances can be compared. The law does not require

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knowing the exact size of the system in miles or kilometers. It can compare one orbit with another.

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That made it useful for mapping the arrangement of planet's long before distances could be measured

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directly by modern methods. These three statements came from patient work. With observations,

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astronomers had watched the sky for generations. Recording where planets appeared among the stars,

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the records included slow drifts and pauses. Along with occasional backward loops,

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as seen from Earth those loops happen because Earth. And the other planets are moving at different

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rates around the Sun to understand the true shape of the paths. Someone had to separate the motion of

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Earth from the motion of the other bodies. Kepler worked with a large set of careful measurements.

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And tested many possible paths. The final result was not a single sudden guess. It was a long

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comparison of geometry. With repeated observations, the first law gave the shape, the second law

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gave the pace, the third law tied one orbit to another. Together they form a complete description

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of simple orbital motion. They do not explain the force behind the motion that explanation came later

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with gravity, Newton showed that an inverse square attraction naturally produces elliptical paths

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and the timing rule Kepler had found. Still the three laws remain useful on their own. They

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describe the motion. Without needing the cause, their reach is wider than planets. Moons follow the same

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general pattern. Around planets, artificial satellites follow similar paths around Earth

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or other bodies when a spacecraft coasts through space with its engines quiet.

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Its path can often be described with the same geometry. The closed ellipse is the shape of a bound

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orbit. Other iconic curves describe paths that pass by once and do not return. Kepler's first

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law is usually stated for ellipses. But the underlying shape belongs to a larger family,

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the same careful attention, to form and timing applies. The laws also help separate appearance

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from reality, from the ground. A planet seems to move against the background stars in a complicated way.

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Part of that motion comes from the planet itself. And part comes from the observer, moving with Earth,

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once the orbit is understood as an ellipse with a regular speed pattern. The apparent wanderings

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become easier to predict. The sky becomes less confusing. The same methods can be applied to anybody.

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Whose position is measured over time, a spacecraft passing near a planet, is not simply pulled

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inward and then released it moves through the gravity of a body that is itself traveling around the sun.

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That motion is what gives the encounter its special value. The planet's gravity

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bends the spacecraft's path. The planet's orbital motion can add a small amount of speed

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to the spacecraft when the two are viewed from the sun. The result is a quiet exchange of momentum.

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Carried out across millions of kilometers without contact and without noise in the frame of

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reference that moves with the planet. The encounter has a simple shape. The spacecraft approaches

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along a curved path. It swings around the planet and leaves along another curved path if the

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engines are off and no other force interferes. The speed relative to the planet is the same before

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and after the pass, gravity changes the direction of the velocity. Not its magnitude

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in that local frame, the path is usually a hyperbola. Open at both ends with the planet sitting

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at one focus, the spacecraft never needs to touch the atmosphere or the surface. It only needs to pass

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close enough for the bend to be useful from the sun's point of view. The situation looks

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different. The planet is moving along its orbit. While the spacecraft is being deflected

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because the exit direction has been rotated. The spacecraft's velocity combines with the planet's

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orbital velocity in a new way if the spacecraft leaves the encounter moving more nearly

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in the direction of the planet's orbit. It's speed around the sun increases if it leaves moving more

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against that direction. It's solar speed decreases the same basic fly-by can therefore be arranged

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to speed a spacecraft up or to slow it down. This is often described as a gravity assist.

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Because the spacecraft gains useful velocity. Without firing its engine for the main change,

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the word assist is gentle and accurate. The planet does not give away energy in a dramatic way.

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It simply shares a tiny part of its enormous orbital momentum since the planet is so massive

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compared with any probe. The change in the planet's own motion is far too small to notice the space

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craft being much lighter receives a meaningful change in speed and direction conservation of momentum

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remains intact throughout the idea follows from treating motion in two frames at once when a

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trajectory is drawn relative to a planet. The fly-by looks symmetric when the same path is viewed from

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the sun. The planet's motion adds a shift to that symmetry recognizing that shift allowed mission

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planners to treat fly-by's as useful tools rather than chance events the geometry of the

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pass determines the outcome a spacecraft that passes behind a planet meaning on the trailing side of the

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planet's motion around the sun tends to be pulled forward and leaves with more speed around the sun

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a spacecraft that passes ahead of the planet tends to be held back slightly and leaves with

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less engineers choose the approach path so that the desired change appears naturally. As the spacecraft

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coasts through the encounter small course corrections made earlier can place the spacecraft on the right

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line for the fly-by a gravity assist can also turn the direction of travel reaching some destinations

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requires more than extra speed the trajectory may need to tilt or line up with another moving target

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a well chosen fly-by can bend a path toward a planet farther out or angle it upward relative to the

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flat plane where most planets orbit this makes it possible to design routes that would require

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much more fuel if the spacecraft had to make every change by thrust alone the assist uses the steady

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pole of gravity to reshape the orbit the encounter itself follows ordinary orbital mechanics as the

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spacecraft approaches the planet's gravity grows stronger the craft accelerates toward the planet

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after reaching its closest point it receives the speed relative to the planet rises as it falls

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inward and falls again as it moves away at the end the outgoing speed matches the incoming speed

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in the view centered on the planet the angle through which the path bends depends on how close

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the spacecraft comes and how fast it is moving a closer pass produces a larger turn

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while a more distant pass produces a gentler one mission planners often string several assists

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together a spacecraft can visit one planet and receive a nudge in velocity it can then

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coast toward another body that is positioned favorably each encounter can alter the orbit's height

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or tilt the spacecraft spends most of its time in steady free fall between planets the fly-byes

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serve as carefully timed points where the existing motion of the solar system does part of the

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traveling this is one reason probes can reach distant regions with limited fuel the energy accounting

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is calm and exact in the frame of the sun the spacecraft may leave with more kinetic energy

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than it had before the encounter that extra energy is balanced by an equally real decrease

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in the planet's orbital energy the planet slows by an amount so small that it is lost in the

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natural scale of its motion the spacecraft gains a practical advantage from the exchange no

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violation occurs the total energy and momentum of the interacting bodies remain conserved

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with gravity acting as the medium of transfer gravity assists are not limited to speeding outward

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journeys they can help a spacecraft slow down when arriving at a destination by passing a planet

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in the proper orientation a probe can reduce its speed relative to the sun and make it easier

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to enter orbit later the same principle can be used to adjust the timing of a mission

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allowing a spacecraft to arrive at a target when conditions are suitable the method gives navigators

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a way to work with the solar system rather than against it the predictability of these encounters

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is part of their usefulness the motions of planets are stable and well measured once a trajectory

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is chosen the gravitational interaction can be calculated with high precision space craft teams

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track the approach and compare it with predictions small corrections can be made when needed the fly by

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itself does not require sudden action it unfolds as a smooth curve governed by the same equations

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that describe the motion of planets and comments there is a quiet elegance in using a moving planet

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to guide a small machine the spacecraft does not force its way across space it follows a path

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shaped by mass and motion arriving at the right place to receive a slight change in velocity the planet

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continues on its ancient orbit unaware in any human sense yet offering a reliable current for travel

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gravity assists turn distance into something that can be crossed with patience and careful

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aim between two orbiting bodies there are positions where the pool of gravity and the motion of the

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rotating frame line up in a steady way a small object placed near one of these positions can remain in

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a fixed relationship with the larger bodies these positions are called lagrange points they arise

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from the same simple fact that governs all orbital motion gravity depends on distance and motion

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carries an object forward while gravity curves its path in a system with two large bodies such as

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the sun and earth or earth and the moon each body pulls on everything nearby a spacecraft

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feels both poles it also has its own motion if the spacecraft is in the right place and moving

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at the right rate the combined effects can repeat in a regular pattern in a few that turns with

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the two large bodies the spacecraft can appear almost still that is the central idea behind a

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lagrange point there are five such points in a two-body system they are labeled lone through L5 the

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first three lie along the line that joins the two large masses lone sits between them L12 lies beyond

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the smaller body away from the larger one L3 rests on the far side of the larger body

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opposite the smaller one the other two points form equilateral triangles with the large bodies L4 leads

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the smaller body along its orbit and L5 trails it by the same angular distance the line points are often

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described as places of balance but they are not stable in the same way a ball is stable a marble

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at the bottom of a ball returns after a small push a marble balanced unhilled top rolls away the three

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line points behave more like the hilltop if an object drifts too far from one of these points

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the drift tends to grow and less small corrections are made spacecraft station near them

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usually do not sit exactly on the point they follow slow loops around it called halo orbits

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or lasages orbits and they use modest adjustments to remain in the desired region the triangular

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points are different L4 and L5 can be stable when the two large bodies have a sufficiently unequal

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mass as with a star and a planet or a planet and a large moon in that case an object near the point

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can stay nearby for long periods the motion is not perfectly still the Coriolis effect

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helps bend small departures into looping paths and the object tends to trace a gentle

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course around the point guided by the combined gravity of the two bodies this stability

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is why natural material can gather there some planets have small asteroids or dust clouds near

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the triangular points of their orbits the mathematics behind these points comes from studying motion

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in a rotating frame in ordinary space an object moves under gravity alone in a frame that rotates

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with two orbiting bodies a centrifugal effect appears in the equations acting like an outward tendency

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associated with the rotation the problem becomes finding places where the inward gravitational

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poles and the rotational effect allow a small object to keep the same relative position the solution

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yields five locations the result was worked out in the broader study of celestial mechanics

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where mathematicians sought patterns in the motion of planets and moons the name most closely

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associated with the five points is Joseph Louis Lagrange though the idea grew from a long tradition

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of analyzing gravity and motion a useful way to picture alone is to imagine a point between the sun and earth

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where a spacecraft can maintain an uninterrupted view of the sun because it stays near the

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line connecting the two bodies it can observe solar activity without being blocked by earth such

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a position also allows steady measurements of the solar wind before it reaches our planet the spacecraft

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does not remain perfectly motionless it circles around the point while the whole arrangement moves

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with earth around the sun held low on the other side of earth from the sun offers a different kind of

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steadiness a telescope placed near this point can keep the sun on one side

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while earth and the moon remain near that same direction that makes it easier to shield sensitive

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instruments from heat and light while looking outward into deep space the point itself is not a parking

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spot with a fixed address it is a region where careful motion can be maintained with modest effort

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earth and the moon also have lagrange points because the moon is much closer than the sun

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the geometry is different but the same principles apply some proposals for space facilities

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have suggested using these points because they can serve as stable waypoints for communication

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or observation the triangular points of the earth moon system may provide places

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or small amounts of dust can linger though they are less crowded with natural objects

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than some planetary examples not every lagrange point is equally useful for every task a point

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that is good for watching the sun may not be good for looking at the distant universe

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a point that is naturally stable maybe too far from earth for routine service mission planners choose

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locations based on what a spacecraft needs to observe and how it will communicate with home the amount

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of fuel available also shapes the choice the points provide options not universal answers the idea

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of a balance of forces can sound like stillness but these regions are better understood as patterns

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of motion gravity is always present the bodies are always moving the spacecraft or dust

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grain at a lagrange point is moving to what remains steady is the relationship among the participants

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the small object shares the rhythm of the larger system one quiet feature of these points

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is that they reveal how gravity can organize space without any solid structure there are no markers

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or physical platforms the order comes from mass and distance joined with motion when a spacecraft

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settles into a loop near one of these points it is following a path shaped by the same forces

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that guide planets around the sun and moons around planets a clear natural example is found with

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Jupiter large groups of asteroids share the planet's orbit around the sun gathered near the

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leading and trailing triangular points these objects are often called trotions they are not packed

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closely together the distances between them are usually great but their presence shows that the

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triangular points can keep material associated with a planet for long spans of time high above

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the equator there is a distance where an object can circle earth once in the same time earth turns

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once beneath it at that distance gravity and orbital speed fit together so neatly that a satellite

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returns to the same place in the sky after each rotation of the planet to a person standing on the

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ground with a dish aimed upward the satellite can seem almost still a quiet point hanging over one

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longitude while the surface moves below this is the meaning of a geosynchronous orbit the term

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refers to an orbit whose period matches the rotation of earth the match is made with the ciderial

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day the time earth needs to turn once relative to distant stars that interval is a little shorter

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than the common day of clocks because earth is also moving along its path around the sun a satellite

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timed to the ciderial day keeps pace with the turning planet rather than with the sun's

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apparent return to the sky if the path is circular lies over the equator and follows the direction

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of earth spin the satellite remains above the same equatorial point that special case is called a geostationary

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orbit all geostationary orbits are geosynchronous but the reverse is not true a satellite with a

00:31:33.040 --> 00:31:42.880
tilted or slightly stretched path still repeats its timing yet it appears to wander in the sky

00:31:42.880 --> 00:31:52.480
from the ground its daily track can look like a soft elongated figure rising and falling relative

00:31:52.480 --> 00:32:00.640
to the horizon while returning to the same place each turn the distinction between geosynchronous

00:32:01.360 --> 00:32:10.640
and geostationary paths is visible in the way antennas are used a perfectly geostationary satellite

00:32:11.360 --> 00:32:20.160
can be served by a fixed dish a geosynchronous satellite with a small tilt still returns to the same

00:32:20.240 --> 00:32:29.840
sky pattern each day but the dish may need a little motion or a wider field of view designers

00:32:29.840 --> 00:32:38.800
choose the exact orbit based on the task for a continuous relay the circular equatorial path is

00:32:38.800 --> 00:32:48.080
simplest for some scientific or regional purposes a slightly inclined path may be acceptable

00:32:48.960 --> 00:32:55.680
if the timing is still useful the needed height comes from the relation between gravity

00:32:56.320 --> 00:33:02.640
and orbital period gravity pulls a satellite inward the satellites sideways motion

00:33:03.520 --> 00:33:11.920
keeps that pull from becoming a straight fall in a circular orbit the inward pull is what bends the path

00:33:12.800 --> 00:33:20.400
into a closed curve farther from earth gravity is weaker and the orbit is larger

00:33:21.680 --> 00:33:29.280
so the satellite moves more slowly and takes longer to complete one circuit at low altitudes

00:33:30.160 --> 00:33:38.640
an orbit takes only a short time at greater distances the period lengthens somewhere between low earth

00:33:38.640 --> 00:33:46.720
orbit and the distance of the moon the period becomes one sideierial day this connection

00:33:47.440 --> 00:33:55.920
can be expressed with a rule that links the size of an orbit to the time needed to complete it for any

00:33:55.920 --> 00:34:04.720
satellite circling earth the average distance from the planet center sets the period if the desired

00:34:04.720 --> 00:34:14.080
period is known the distance can be calculated using earth's gravitational strength and the length

00:34:14.080 --> 00:34:28.240
of the sideierial day scientists find an orbital radius of about 42,164 kilometers from earth center

00:34:28.240 --> 00:34:40.720
subtracting earth's own radius gives an altitude of about 35,700 and 86 kilometers above the

00:34:40.720 --> 00:34:50.960
equator at that height the satellite travels at roughly 3.0 7 kilometers per second the speed is quick

00:34:51.920 --> 00:35:00.560
but the circle is so wide that one full trip takes nearly one turn of the planet the idea was

00:35:00.560 --> 00:35:08.400
worked out through the ordinary tools of orbital mechanics astronomers measured earth's rotation

00:35:09.120 --> 00:35:17.040
by watching stars physicists refined the value of earth's gravitational pull mathematicians

00:35:18.000 --> 00:35:26.480
then asked what distance would give a chosen period and the answer placed the orbit high above

00:35:26.480 --> 00:35:34.320
the atmosphere later engineers studied how real spacecraft would behave there they considered the

00:35:34.320 --> 00:35:42.960
slight flattening of earth they also accounted for the pool of the moon and sun along with the gentle pressure

00:35:43.600 --> 00:35:50.800
of sunlight none of these effects is large at that height but over months and years

00:35:51.680 --> 00:36:00.000
they can not just satellite away from its assigned place because of those small nudges a geostationary

00:36:00.000 --> 00:36:08.320
satellite usually carries thrusters or other means of fine correction operators watch its

00:36:08.320 --> 00:36:17.120
longitude and latitude and make tiny adjustments when needed these maneuvers keep the spacecraft

00:36:17.840 --> 00:36:25.040
near a chosen point in the sky when a satellite is no longer needed at its assigned longitude

00:36:26.560 --> 00:36:34.400
it may be moved to a slightly higher region reserved for an active spacecraft this leaves the

00:36:34.400 --> 00:36:42.800
useful belt clear and keeps operations orderly the longitude of a geostationary satellite

00:36:43.600 --> 00:36:52.640
is not arbitrary certain positions above the equator are more stable because earth's equatorial

00:36:52.640 --> 00:37:01.280
bulge creates slight variations in the gravitational field a satellite can drift toward preferred

00:37:01.280 --> 00:37:08.720
longitudes if left unattended operators account for this drift when planning fuel

00:37:10.160 --> 00:37:17.680
and when choosing where to place a spacecraft this adds another layer of quiet order to the belt the

00:37:17.680 --> 00:37:25.840
value of such a steady position is easy to see a ground antenna can point toward one part of the sky

00:37:26.640 --> 00:37:35.360
and remain there it does not need to follow a fast moving object from horizon to horizon this

00:37:35.360 --> 00:37:43.280
makes geostationary satellites useful for communications because a signal can be sent upward

00:37:44.480 --> 00:37:52.320
then returned to a broad area below the same geometry helps weather satellites watch clouds

00:37:53.200 --> 00:38:00.720
and daylight changes over a wide portion of earth each image is taken from the same viewpoint

00:38:01.920 --> 00:38:10.160
so slow changes in the atmosphere become easier to follow from that height a single satellite

00:38:10.160 --> 00:38:17.680
can see a large part of earth's disk it cannot look all the way to the poles because the planet

00:38:17.760 --> 00:38:25.600
curves away geostationary satellites therefore give their best view over equatorial

00:38:26.240 --> 00:38:31.520
and middle latitudes several spacecraft can be spaced around the equator

00:38:32.880 --> 00:38:39.680
so that different longitudes each have a steady viewpoint the spacing is measured

00:38:39.680 --> 00:38:49.440
in degrees of longitude and international agreements assign positions so signals do not crowd one

00:38:49.440 --> 00:38:59.200
another the ring of these positions is often called the Clark belt after a writer who described

00:38:59.200 --> 00:39:07.680
how such an orbit could support communications the name marks a simple path from thought to practice

00:39:07.680 --> 00:39:16.080
the belt is not packed like a roadway but useful locations are limited each satellite

00:39:16.080 --> 00:39:24.720
needs enough separation to avoid radio interference and to allow careful control a home and

00:39:24.720 --> 00:39:33.680
transfer orbit is an ellipse that connects two circular orbits around the same central body it gives a

00:39:33.680 --> 00:39:42.720
spacecraft a smooth path from one steady orbit to another while asking for the smallest

00:39:42.720 --> 00:39:51.840
change in velocity that two brief engine burns can provide the idea belongs to orbital mechanics

00:39:52.880 --> 00:40:00.800
where motion is governed by gravity and by the careful use of momentum in its simplest form

00:40:01.680 --> 00:40:08.080
the transfer is quiet and orderly a spacecraft already moving in a circular orbit

00:40:08.880 --> 00:40:19.280
fires its engine once coasts a long half of an ellipse then fires its engine again to settle into the

00:40:19.280 --> 00:40:27.520
new circle the shape of the transfer comes directly from the geometry of ellipses one focus of the

00:40:28.480 --> 00:40:36.000
ellipse sits at the central body such as a planet or the sun the closest point of the ellipse

00:40:36.800 --> 00:40:44.560
the pariapsis lies at the radius of the lower circular orbit the farthest point the

00:40:44.560 --> 00:40:53.440
apopsis reaches the radius of the higher circular orbit the spacecraft touches the lower circle

00:40:53.680 --> 00:41:00.880
at one end of the ellipse and the higher circle at the other because the two paths are tangent

00:41:00.880 --> 00:41:09.280
at those points the spacecraft does not need to change direction sharply it only needs to adjust

00:41:09.280 --> 00:41:18.240
speed the first engine burn changes the spacecraft's speed just enough to place it on the ellipse

00:41:18.240 --> 00:41:26.880
if the destination orbit is higher the burn increases speed the spacecraft then moves away from

00:41:26.880 --> 00:41:35.920
the central body climbing against gravity while its forward speed gradually decreases during this

00:41:35.920 --> 00:41:43.440
coast no further thrust is required in the ideal picture the vehicle follows the ellipse

00:41:44.240 --> 00:41:52.880
because gravity continuously bends its path at the far side the spacecraft is moving more slowly

00:41:53.600 --> 00:42:00.640
than a spacecraft already in the higher circular orbit the second burn adds speed again

00:42:01.840 --> 00:42:10.160
rounding the path into the new circle for move to a lower orbit the same pattern runs in reverse

00:42:10.160 --> 00:42:18.880
the first burn reduces speed so the spacecraft drops into an ellipse whose near point lies

00:42:18.880 --> 00:42:27.600
at the lower altitude it coasts inward gaining speed as gravity draws it closer at the lower point

00:42:28.560 --> 00:42:37.680
it is moving faster than a spacecraft already in that circular orbit so a second small reduction in

00:42:37.680 --> 00:42:47.200
speed lets it settle into the lower circle the transfer remains efficient because the engine is used

00:42:47.200 --> 00:42:56.560
only at the two points where the change in velocity produces the desired change in orbital energy

00:42:56.560 --> 00:43:05.760
the efficiency of this method is measured in delta v a term that means a change in velocity

00:43:05.840 --> 00:43:14.880
rocket fuel is limited and every unit of delta v must be earned by pushing propellant out of the

00:43:14.880 --> 00:43:24.400
engine a transfer that requires less delta v can carry less propellant or it can use the available

00:43:24.400 --> 00:43:32.960
propellant for instruments communication or a longer mission the home and transfer is often the

00:43:32.960 --> 00:43:43.360
minimum delta v path between two circular co-planar orbits when the engine burns are treated as short

00:43:44.240 --> 00:43:52.880
separate events that condition is called the impulsive approximation it imagines each burn happening

00:43:52.880 --> 00:44:01.680
quickly compared with the long coast along the ellipse the idea was worked out by studying the

00:44:01.680 --> 00:44:11.120
conservation of energy and angular momentum in orbital motion an orbiting body has both kinetic

00:44:11.120 --> 00:44:19.920
energy from its motion and gravitational potential energy from its position a circular orbit

00:44:20.720 --> 00:44:28.800
has a fixed relationship between altitude and speed and elliptical orbit spreads that relationship

00:44:29.040 --> 00:44:37.120
over a range of altitudes with higher speed near parapses and lower speed

00:44:37.120 --> 00:44:43.600
near a popes by choosing an ellipse that just touches the starting and ending circles

00:44:44.800 --> 00:44:53.360
the transfer uses the natural exchange between speed and height the mathematics can be expressed

00:44:53.360 --> 00:45:01.120
with the vis-viver equation which relates orbital speed to distance from the central body

00:45:02.320 --> 00:45:09.760
and to the size of the orbit Walter Holman a German scientist interested in space flight

00:45:10.880 --> 00:45:19.360
presented this transfer as a way to move between planetary orbits with modest energy his work

00:45:19.360 --> 00:45:25.280
helped show that travel between orbits could be planned with ordinary mechanics

00:45:26.720 --> 00:45:35.520
using gravity as the main guide rather than constant thrust the concept became a standard

00:45:35.520 --> 00:45:43.520
part of mission design because it gives a clear baseline planners can compare other paths against it

00:45:44.480 --> 00:45:52.560
deciding whether a longer route or a different propulsion method might be better for a particular

00:45:52.560 --> 00:46:02.000
flight between planets the transfer ellipse is drawn around the sun rather than around a single planet

00:46:02.000 --> 00:46:10.240
a spacecraft leaving earth for Mars for example can enter an ellipse that touches earth's orbit

00:46:10.240 --> 00:46:18.480
at one end and Mars's orbit at the other the spacecraft must depart when the target planet

00:46:18.480 --> 00:46:27.440
will arrive at the meeting point at the same time the spacecraft does this timing depends on the

00:46:27.440 --> 00:46:36.400
relative motion of the two planets the needed alignment repeats at regular intervals giving launch

00:46:36.400 --> 00:46:44.160
opportunities separated by predictable periods the transfer itself is not a straight line

00:46:44.160 --> 00:46:51.200
through space it is a curved solar orbit that lets the spacecraft fall gently outward

00:46:52.320 --> 00:46:58.400
or inward under the sun's gravity the same reasoning applies to satellites

00:46:59.040 --> 00:47:05.520
moving between circular orbits around earth a satellite in a low circular orbit

00:47:06.400 --> 00:47:14.960
can raise itself to a higher circular orbit by entering a transfer ellipse the first burn occurs

00:47:14.960 --> 00:47:22.720
at the low orbit the second burn occurs at the high point of the ellipse mission designers often

00:47:22.720 --> 00:47:31.120
describe this as two burns separated by a coast the result is a smooth change in altitude

00:47:32.080 --> 00:47:41.120
without continuous thrust if the satellite uses low thrust instead it may spiral outward slowly

00:47:42.240 --> 00:47:49.120
which is a different kind of transfer the home and path assumes brief burns and a long

00:47:49.200 --> 00:47:55.040
unpowered arc there are limits to the method the orbits need to be nearly circular

00:47:56.560 --> 00:48:04.000
and in nearly the same plane for the simplest calculation to hold if the starting and ending

00:48:04.000 --> 00:48:14.080
orbits are tilted relative to each other a plane change may be needed and that can require extra

00:48:14.080 --> 00:48:23.200
velocity change if the destination is very far away other paths may sometimes use less delta v

00:48:24.240 --> 00:48:32.080
though they take longer the home and transfer remains a useful reference because it shows how much

00:48:32.080 --> 00:48:42.160
velocity change is needed for the most direct to burn move it gives a calm economical shape to a

00:48:43.120 --> 00:48:50.560
that might otherwise seem open ended fuel savings do not mean speed a transfer to a higher

00:48:50.560 --> 00:48:59.120
orbit takes time often half the period of the ellipse for a journey between two planetary orbits

00:49:00.160 --> 00:49:07.840
that coast can last many months the spacecraft spends most of the trip moving without thrust

00:49:08.480 --> 00:49:17.920
carried by the orbit it has already established this slow steadiness is part of the methods character it

00:49:17.920 --> 00:49:25.760
accepts a longer path in exchange for a smaller demand on the engine in mission planning

00:49:26.720 --> 00:49:35.440
patience and efficiency often go together the transfer also shows how orbital motion is not a matter

00:49:35.440 --> 00:49:44.000
of pointing toward a destination and pushing forward a spacecraft changes its future position

00:49:44.960 --> 00:49:53.760
by changing the shape of its path a small increase in speed can raise the far side of the orbit a small

00:49:53.760 --> 00:50:01.760
decrease can lower it the vehicle does not fight gravity directly it enters a curve that gravity

00:50:01.760 --> 00:50:10.960
already supports this is why the home and transfer feels so natural within orbital mechanics it uses

00:50:10.960 --> 00:50:20.160
the central body's pull as part of the route in practice real missions add small corrections to the ideal path

00:50:20.720 --> 00:50:30.720
engines are not perfectly instantaneous and orbits are not perfectly circular navigation teams measure

00:50:30.720 --> 00:50:40.080
the spacecraft's position and velocity then make gentle adjustments if needed these adjustments

00:50:40.080 --> 00:50:49.440
keep the transfer ellipse aligned with the intended meeting point so the two planned burns remain

00:50:49.440 --> 00:50:58.880
the main changes to the path a tidally locked body turns once in exactly the time it takes to complete

00:50:58.880 --> 00:51:06.320
one orbit this keeps nearly the same hemisphere facing the object at circles the familiar moon

00:51:07.040 --> 00:51:14.880
is a nearby example as it travels around earth the same lunar mountains and planes remain turned

00:51:14.880 --> 00:51:24.560
toward us while the far side stays hidden from viewers on earth the body is still in motion it's been

00:51:24.640 --> 00:51:32.080
has settled into a steady match with its orbital path the cause lies in the way gravity changes

00:51:32.800 --> 00:51:41.840
with distance the side of a moon or planet that is closer to its partner feels a slightly stronger pull

00:51:42.720 --> 00:51:49.520
than the side farther away that small difference stretches the body along the line

00:51:50.240 --> 00:51:57.200
joining the two objects in a solid body the stretching is slight in a body with oceans

00:51:57.840 --> 00:52:05.840
ice or a soft interior the response can be larger the result is a pair of gentle bulges

00:52:06.960 --> 00:52:14.560
one toward the partner and one on the opposite side if the body spins faster than it orbits

00:52:15.520 --> 00:52:23.040
those bulges are carried a little ahead of the line between the centers the partner then pulls

00:52:23.040 --> 00:52:32.480
on the nearer bulge with a force that acts against the spin over long stretches of time that gravitational

00:52:32.480 --> 00:52:42.160
tug removes rotational energy the spin slows if the body spins too slowly the bulges lag behind

00:52:43.120 --> 00:52:49.840
and the tug can speed the rotation up the tendency is to guide the spin toward the rate

00:52:50.720 --> 00:52:59.440
where one turn matches one orbit the process depends on internal friction real materials are not

00:52:59.440 --> 00:53:09.040
perfectly rigid they flex warm slightly and dissipate motion in small ways each orbit gives the body

00:53:09.040 --> 00:53:16.880
another chance to settle a little more the change is slow by human standards for objects close to

00:53:16.880 --> 00:53:25.920
their partners the effect can become complete within the age of a planetary system for distant objects

00:53:26.800 --> 00:53:35.600
it may take much longer or it may never finish distance matters strongly because title influence

00:53:35.680 --> 00:53:45.360
weakens rapidly as separation grows a moon orbiting close to a giant planet experiences a steady

00:53:45.360 --> 00:53:53.920
shaping pole many such moons keep one face toward the planet the same principle can apply to planet's

00:53:53.920 --> 00:54:02.800
close to their stars when a planet orbits very close to its star the stars gravity can synchronize

00:54:02.800 --> 00:54:11.440
the planet's rotation with the year in those cases the rotation period and the orbital period

00:54:11.440 --> 00:54:19.760
become the same title locking is not always a simple one to one match an orbit that is noticeably

00:54:19.760 --> 00:54:27.840
elliptical can lead to other stable arrangements a body might rotate three times for every two orbits

00:54:28.480 --> 00:54:37.120
keeping a pattern that repeats without being fully locked in the most familiar sense such

00:54:37.120 --> 00:54:45.920
resonances arise from the same title forces acting over many cycles they show that the final state

00:54:45.920 --> 00:54:55.680
depends on orbit shape internal structure and the history of the body spin the moon offers a clear view

00:54:56.480 --> 00:55:04.960
of how this works in practice its rotation is synchronized with its monthly path around earth

00:55:04.960 --> 00:55:12.720
from the ground observe or see small rocking motions called vibrations these happen because the

00:55:12.720 --> 00:55:21.680
moon's orbit is not a perfect circle and because its axis is slightly tilted vibration

00:55:22.560 --> 00:55:31.440
lets viewers glimpse a little beyond the usual edge over time still the same broad hemisphere remains

00:55:31.440 --> 00:55:39.840
turned toward earth the idea was worked out gradually through observation and mechanical reasoning

00:55:39.840 --> 00:55:47.520
people noticed that the moon did not appear to turn relative to earth later gravitational theory

00:55:48.400 --> 00:55:55.520
showed how a small difference in pull could produce torques over long periods measurements

00:55:55.520 --> 00:56:04.320
of lunar motion and planetary satellites supported the picture studies of how materials flex

00:56:04.320 --> 00:56:12.800
under gravity added further support the modern account treats title locking as a natural

00:56:12.800 --> 00:56:21.280
outcome of gravity acting on bodies that are not perfectly stiff when a planet is tidally locked to

00:56:21.280 --> 00:56:31.120
its star the geometry creates two lasting hemispheres one faces the star in continual daylight the

00:56:31.120 --> 00:56:40.480
other faces outward into space in continual night between them lies a band where the star stays near

00:56:40.560 --> 00:56:48.160
the horizon this arrangement can produce extreme temperature differences the day side receives

00:56:48.160 --> 00:56:57.360
steady light while the night side radiates heat away without direct sunlight the result is not uniform

00:56:57.360 --> 00:57:07.200
everywhere because atmospheres and surfaces can move heat around atmosphere changes the picture a thick

00:57:07.200 --> 00:57:14.640
atmosphere can carry warmth from the bright side toward the dark side winds can flow in steady

00:57:14.640 --> 00:57:24.000
patterns shaped by the fixed heating oceans if present can store heat and release it slowly ice can

00:57:24.000 --> 00:57:32.480
form where temperatures are low and remain stable over long periods a locked world can therefore

00:57:32.480 --> 00:57:40.400
have a permanent day side and a permanent night side with a transition zone between them without

00:57:40.400 --> 00:57:48.880
much atmosphere the contrast can be sharper sunlight rock warms under constant illumination

00:57:48.880 --> 00:57:56.640
shadowed ground cools by sending infrared radiation into space some regions near the boundary

00:57:56.640 --> 00:58:05.440
between light and dark may stay in a narrow range of temperatures craters near the poles of a locked

00:58:05.440 --> 00:58:15.520
body can keep certain areas in deep shade allowing cold traps to persist these features are studied

00:58:16.240 --> 00:58:24.160
as part of the broader behavior of locked surfaces tidal locking also affects how a body

00:58:24.160 --> 00:58:32.960
experiences seasons if the rotation is synchronized and the axis has little tilt the pattern

00:58:32.960 --> 00:58:41.200
of light stays nearly fixed there may be little seasonal change compared with a freely rotating

00:58:41.200 --> 00:58:50.160
world if the orbit is eccentric the distance to the star can vary and the amount of received light

00:58:50.800 --> 00:58:58.880
can rise and fall during each orbit the surface then experiences a slow breathing of brightness

00:59:00.000 --> 00:59:08.320
rather than a cycle of day and night the phenomenon is common enough to be considered a quiet norm

00:59:09.120 --> 00:59:17.760
among close satellites many moons in the outer solar system keep one face toward their planets binary

00:59:17.840 --> 00:59:26.080
objects can lock to each other when their masses are similar enough and their separation is small

00:59:26.080 --> 00:59:34.800
in such systems both bodies may present the same hemisphere to one another as they move the result

00:59:35.360 --> 00:59:42.320
is a shared rhythm with each object spin tied to the motion of the pair for observers

00:59:43.200 --> 00:59:52.240
tidal locking offers a useful way to think about rotation in space a locked body remains in motion

00:59:52.240 --> 01:00:01.040
it moves through its orbit and rotates at the same rate needed to keep its orientation aligned the

01:00:01.040 --> 01:00:09.920
alignment emerges from patient physical processes rather than from any special adjustment gravity

01:00:09.920 --> 01:00:16.640
provides the direction internal friction provides the settling time provides the room

01:00:17.280 --> 01:00:25.040
for the motion to become steady the temperature patterns unlocked planets follow from that steadiness

01:00:25.040 --> 01:00:34.320
one side is always lit and the other is always dark the atmosphere or lack of atmosphere decides

01:00:34.960 --> 01:00:42.560
how much heat crosses the divide scientists model these flows with equations for radiation

01:00:43.360 --> 01:00:51.280
and fluid motion the models help describe where clouds might gather and where the coldest regions

01:00:51.280 --> 01:01:00.240
might lie a stone tossed upward slows because the planet is quietly pulling it back the poll is gentle

01:01:00.240 --> 01:01:08.960
at first and it grows weaker with distance but it never quite disappears if the stone begins with

01:01:08.960 --> 01:01:18.320
only a modest upward speed that poll will eventually pause its climb and draw it home if it begins with

01:01:18.320 --> 01:01:26.400
enough speed the poll becomes too weak to reverse the motion the boundary between those two outcomes

01:01:27.200 --> 01:01:35.280
is called escape velocity the threshold belongs to speed rather than location it is the minimum

01:01:35.280 --> 01:01:46.400
speed an object would need at a given distance from a planet or moon to coast away without any further

01:01:46.400 --> 01:01:56.800
push the idea assumes an ideal setting with no air resistance and no engine firings it also sets aside

01:01:56.800 --> 01:02:05.440
talks from other nearby bodies in that simplified picture gravity is the only force to consider

01:02:06.640 --> 01:02:14.960
and the question becomes a matter of energy an object near a planet has gravitational potential energy

01:02:16.400 --> 01:02:24.480
though the phrase can sound more mysterious than it is potential energy here measures how much work

01:02:24.480 --> 01:02:33.920
gravity could do as the object moves close to the planet the object is deep in a gravitational well

01:02:33.920 --> 01:02:43.600
moving farther away requires energy just as walking uphill requires effort speed supplies energy

01:02:43.600 --> 01:02:52.480
to the faster and object moves the more kinetic energy it carries escape happens when the kinetic

01:02:52.480 --> 01:03:00.800
energy at the start is enough to pay for the climb out of the well the mathematical expression for this

01:03:00.800 --> 01:03:10.960
threshold is compact the needed speed equals the square root of two times the gravitational constant

01:03:10.960 --> 01:03:19.200
times the mass of the planet divided by the distance from the planet center the symbols can be

01:03:19.200 --> 01:03:26.960
set aside but the relationships are worth keeping a more massive planet creates a deeper well

01:03:28.000 --> 01:03:35.600
so the required speed is higher starting closer to the center also raises the required speed

01:03:35.760 --> 01:03:44.800
because the object begins where gravity is stronger starting farther away lowers it for earth

01:03:45.360 --> 01:03:51.760
the value near the surface is large in a vacuum ignoring the atmosphere

01:03:52.960 --> 01:03:59.280
an object would need a speed of roughly 11 kilometers per second to coast away

01:04:00.160 --> 01:04:07.840
without additional thrust that is faster than most everyday motions but it is not a wall

01:04:07.840 --> 01:04:14.880
rockets do not have to reach that speed in a single instant they can thrust continuously

01:04:16.000 --> 01:04:23.520
adding energy little by little if an engine keeps working a spacecraft can move away from earth

01:04:24.400 --> 01:04:31.920
even while its momentary speed is below the coasting threshold escape velocity describes

01:04:32.640 --> 01:04:41.520
what would be needed if the engines fell silent and the craft simply continued on its own this

01:04:41.520 --> 01:04:50.880
distinction makes the concept calmer then it may first appear a spacecraft does not face a sudden test

01:04:50.880 --> 01:04:59.200
passed in a single moment the concept is an accounting of total energy a vehicle that receives

01:04:59.200 --> 01:05:08.480
steady thrust is not limited to the speed it happens to have at any one moment it is accumulating

01:05:08.480 --> 01:05:18.000
the ability to climb farther once it has enough energy and then stops thrusting it can continue outward

01:05:18.080 --> 01:05:26.080
the required speed also changes with altitude at a high mountain the needed speed is slightly

01:05:26.080 --> 01:05:34.160
lower than at sea level because the starting point is already farther from the planet center

01:05:34.160 --> 01:05:43.280
from a high orbit it is lower still this is one reason space missions care about where they begin their

01:05:43.280 --> 01:05:50.480
final push outward a craft already far from a planet has less gravitational climbing

01:05:51.200 --> 01:05:59.920
left to do rotation can add a quiet assistance a planet that spins gives objects on its surface

01:06:00.800 --> 01:06:06.160
a bit of sideways motion if a launch moves in the same direction as that spin

01:06:06.160 --> 01:06:15.920
the craft begins with some speed already provided by the rotating ground the escape speed relative

01:06:15.920 --> 01:06:25.280
to the planet center is unchanged but the speed required relative to the ground can be a little less

01:06:25.280 --> 01:06:34.400
the effect is modest yet it is part of the complete picture smaller bodies have much lower thresholds

01:06:34.480 --> 01:06:43.120
a moon with less mass holds a shallower gravitational well so a spacecraft needs less speed to

01:06:43.120 --> 01:06:52.320
leave it on a very small asteroid the needed speed can be comparable to a slow hop large planets demand

01:06:52.320 --> 01:07:01.680
more a gas giant with its great mass asks for a much higher coasting speed than a rocky world

01:07:01.680 --> 01:07:09.760
like earth the same rule applies everywhere but the numbers shift with mass and distance the

01:07:09.760 --> 01:07:18.960
concept was worked out by combining two broad ideas from classical physics one is that gravity

01:07:18.960 --> 01:07:25.920
weakens with distance in a regular way the other is that motion and position can be treated

01:07:26.800 --> 01:07:33.360
as forms of energy that trade back and forth when those ideas are placed together

01:07:34.400 --> 01:07:42.400
the threshold emerges naturally no special machinery is needed beyond careful measurement

01:07:43.200 --> 01:07:51.360
of mass and distance the result is a simple relationship that applies to planets and moons

01:07:52.320 --> 01:08:01.600
and it can be extended to stars in orbital language escape speed sits just above the speed needed

01:08:01.600 --> 01:08:11.840
for a circular orbit at the same distance for a perfectly round orbit an object moves sideways fast enough

01:08:11.840 --> 01:08:20.240
to keep falling around the planet rather than into it if the speed is increased the path stretches

01:08:20.320 --> 01:08:28.720
into an ellipse at the escape threshold the path opens into a curve that does not return with

01:08:28.720 --> 01:08:38.160
still more speed the path opens wider these shapes are graceful consequences of the same gravitational

01:08:38.160 --> 01:08:45.440
law air resistance complicates the picture near a planet's surface a real launch through an

01:08:45.440 --> 01:08:55.520
atmosphere loses energy to drag so vehicles usually rise carefully and gain speed as the air

01:08:55.520 --> 01:09:04.560
thins the pure escape speed still matters but it belongs to the vacuum part of the story once above most

01:09:04.560 --> 01:09:13.760
of the air a craft can be compared to the ideal case another quiet detail is that escape velocity

01:09:14.400 --> 01:09:22.160
does not mean leaving gravity behind completely gravity extends outward without a sharp edge

01:09:22.160 --> 01:09:31.600
a departing spacecraft always feels simple however faint the threshold means only that the pool

01:09:31.600 --> 01:09:40.160
will never be strong enough to turn the craft around the spacecraft may slow as it climbs but it will

01:09:40.160 --> 01:09:49.120
keep moving outward its speed approaches a gentle limit rather than dropping to zero and reversing

01:09:49.120 --> 01:09:57.840
the direction of the initial motion also matters in a practical sense the speed threshold is about

01:09:57.840 --> 01:10:08.240
magnitude but the path must not intersect the ground an object fired straight down even at escape speed

01:10:09.200 --> 01:10:17.760
would not escape because it would strike the surface in space away from obstacles the direction

01:10:17.760 --> 01:10:25.280
can be chosen to suit the journey the energy requirement remains the central fact night settles

01:10:25.280 --> 01:10:34.880
over the planet and the sky becomes a quiet reminder that motion can be predictable earth turns at its

01:10:34.880 --> 01:10:43.600
familiar pace carrying us toward darkness without any effort from us the moon circles earth

01:10:43.600 --> 01:10:51.920
because of our planet's gravity well earth follows its path around the sun because of the sun's

01:10:51.920 --> 01:11:01.120
pool these motions continue in steady patterns while you rest your own body has rhythms too breathing

01:11:01.120 --> 01:11:10.640
slow muscles soften the mind lets the days details drift apart like distant satellites passing

01:11:10.640 --> 01:11:17.840
beyond view there is no need to steer anything now orbits do not struggle to remain in place

01:11:18.960 --> 01:11:27.280
and you do not need to manage the night you can rest inside the same quiet order that guides worlds

01:11:27.280 --> 01:11:29.280
around one another good night