Are satellites doing free fall?

Question

I was told that satellites are doing free-fall. But I don't think so, I think, assuming that the satellite is moving at a constant speed in a circular motion, the satellite does not do free-fall motion, because its distance from the earth has not changed, and it has no free-fall. Am i right?

As shown in the figure, the blue straight line is the horizon. This is the horizon without bending. The direction of gravity is parallel and perpendicular to the horizon. The red line is a horizontal straight line. Throw an object horizontally to the left, and the object moves along a parabola under gravity. When the speed tends to infinity, the object moves straight along the red line without free fall.

As shown in the figure, the blue line is the horizon, the horizon is curved, and the red line is concentric with the horizon. Gravity is perpendicular to the horizon. In other words, gravity is along the normal direction of the horizon. Throw objects along and perpendicular to the horizon normal, and the objects move along a "parabola". When the speed is appropriate, the object moves along the red line without free fall.

Any object moving just under the influence of gravity, i.e. without any propulsion, is in free fall. — Not_Einstein, Jan 20 '20 at 23:03
@Not_Einstein I added a detailed explanation to the question. — enbin, Jan 21 '20 at 00:21
@J.Murray The initial velocity of the free-falling body is zero, and the initial velocity of the satellite is not zero. — enbin, Jan 21 '20 at 06:06
@enbinzheng The definition of free fall, if you click on the link in my previous comment, has nothing to do with initial velocities. It is exclusively concerned with what forces are acting on the object. — J. Murray, Jan 21 '20 at 06:11

Thomas Fritsch · Answer 1 · 2020-01-20T22:21:41.107

May be Newton's cannonball-thought-experiment can convince your intuition that there is no principal difference between a body falling down to the earth and a satellite circulating the earth.

Consider a cannon located on top of a high mountain, shooting in horizontal direction. And let's neglegt air resistance.

_{(image from Wikipedia - Newton's cannonball)}

When shooting the cannonball with low speed, it will hit the ground after a short distance at point A.
When shooting the cannonball with higher speed, it will hit the ground after a longer distance at point B.
When shooting the cannonball with really high speed (= 7.9 km/s), it is fast enough to fly around the earth in a circle through point C, and will eventually reach the cannon again from the back. The cannonball is a satellite in a circular orbit.
When shooting the cannonball with even higher speed (> 7.9 km/s), it will again fly around the earth, through point D. The cannonball is a satellite in an elliptical orbit.

In all the above scenarios the cannonball feels only the gravity of the earth, and hence it accelerates towards the center of the earth. Therefore it makes sense in all cases to say "the cannonball is in free fall".

I believe you can't call it a free fall if it's a circular orbit though. — Thinker-101, Oct 10 '22 at 16:57

score 5 · Answer 2 · answered Jan 20 '20 at 21:14

Yes it is doing free fall.

Consider a satellite at some moment in time. Say its velocity at that moment happens to be in the direction of the pole star. If the satellite were not being attracted to the Earth, it would move in a straight line and go off in that direction, moving further and further away from Earth. But, because of the attraction to the Earth, instead of doing that it falls away from that straight line. So it then arrives at some new point in its orbit, and the same happens again: the attraction to the Earth causes its velocity to change direction again. It keeps on doing this. It is not moving closer to the Earth, but it is 'falling' in the sense that its motion is bent towards the Earth as it proceeds on its way, causing the resulting circular (or elliptical) orbit.

If a satellite moves in an elliptical orbit, it will have a free fall. Because the distance between the satellite and the earth has changed. — enbin, Jan 20 '20 at 23:00

score 5 · Answer 3 · answered Jan 21 '20 at 00:56

When people talk about "free fall," what they are referring to is the absence of other forces besides gravity. For example, there are no "normal forces" from the ground holding the object up. This is a correct description of how satellites move.

It is a confusing term for the reasons you bring up. "Free fall" does give a sense that something is moving downwards, and in normal cases of free fall such as skydiving, one must indeed be falling in the intuitive sense. I do think there's a reason why we typically stop calling it "in free fall" and start calling it "in orbit" as the speed of the object approaches orbital velocity.

I think the reason physics text books make a big deal about calling this "free fall" is to point out that there is no force pushing upward to cause an object to stay in its orbit, like a ping pong ball suspended mid-air by a jet of air from a hair dryer below. The only force acting on the satellite is gravity (well, there's a little drag from the gas molecules in space).

Some things really push the boundaries of these words. It's a little difficult to say whether someone in a squirrel suit is really in free fall. Their motion certainly is more similar to that of a skydiver free falling than it is to, say, a glider flying through the air, but it's some where in the middle ground. Likewise, some vehicles are deemed "sub orbital" because they don't have the velocity to achieve true orbit, but they fly fast enough that the curvature of the earth plays a major factor in their mechanics.

PS. If one says that a satellite in an elliptical orbit is in freefall because its altitude can decrease, that would suggest to me that we also need a term "free rise" to describe the same satellite during the half of the orbit where its altitude is increasing.

So do you think that the motion of a satellite in orbit is a free fall? — enbin, Jan 21 '20 at 01:31
@enbinzheng Yes, as free fall is defined in physics. I think the term is a bit awkward in the case of orbits, but it's what the definition is. I didn't include it in my answer, but one of the interesting implications of free fall is that all components of the object are falling at the same rate, which gives the recognized effect of "floating" that is associated with objects in free fall — Cort Ammon, Jan 21 '20 at 14:58

score 3 · Answer 4 · 2020-01-21T06:24:22.040

A freely falling body is a body which moves in the presence of gravity without any other external force acting on it.

A ball dropped on the surface of the earth is the example that you have in mind. Now let's give some initial tangential velocity to the object (wrt the direction of free fall). Now is this case any different than the ball falling without any horizontal velocity? Not much. It now too follows the definition of free fall (neglecting air resistance).

Now what if the tangential velocity was really large what happens then? The object goes into an elliptical orbit around the earth. Is this case much different than previous case? No. It still follows the definition. So I conclude that an object in orbit around the earth is in free fall.

A thing to note is as follows:

All objects thrown with tangential velocity follow a part of elliptical orbit (the parabolic case is just an approximation).

Elliptical Orbits around earth

Just the difference of a ball from a rocket is that the elliptical orbit of ball passes through earth and the elliptical orbit of rocket goes around it. (Note that circular orbit of your case are a special case of elliptical orbits)

Adrian Howard · Answer 5 · 2020-01-21T03:41:46.763

1

A satellite is falling, it's just also moving forward fast enough that it is always falling around the curve of the Earth. So it is in freefall. If you throw a ball straight out in front of you, you will see it follow a curve as it goes forwards and falls downwards. If you could throw it fast enough, and there were no air resistance, it's forward speed could take it past the horizon as it fell, so that it was always falling toward the curved surface of Earth. When a satellite is in orbit, not firing any thrusters for adjustments, gravity is the only acceleration acting upon it. Therefore, by definition, it IS in free fall. https://en.wikipedia.org/wiki/Free_fall

edited Jan 21 '20 at 03:41

answered Jan 21 '20 at 00:10

Adrian Howard

8,513

I added a detailed explanation to the question. – enbin Jan 21 '20 at 00:45
I made an edit to address your new info. – Adrian Howard Jan 21 '20 at 03:43
The initial velocity of the free-falling body is zero, and the initial velocity of the satellite is not zero. – enbin Jan 21 '20 at 06:11
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If a skydiver jumps out of a flying airplane, is he in free fall? If so, at what point did the airplane have zero velocity? – Adrian Howard Jan 21 '20 at 08:45
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The initial velocity of a freefalling object does not have to be zero, besides velocity is frame of reference dependent, and could have different velocities to different observers. – Adrian Howard Jan 21 '20 at 09:04

score 1 · Answer 6 · answered Jan 21 '20 at 07:10

For an object to be in free fall there must not be any apparent weight.What means is that if you stand on a weighing scale it would give a reading of zero given that it has zero velocity relative to you. In free fall the reading will be zero, you must have seen astronauts floating in space? They would be weight less as they would not "push" the weighing machine.

And for free fall the distance of satellite need not change from the Earth's center (although in reality it does change as the orbits are elliptical but it has nothing to do with weightlessness) the position vector must change and the acceleration i.e the second derivative of the position vector must be equal to the gravitational acceleration not the the second derivative of the magnitude of the distance.

You can consider this analogous to uniform circular motion where the magnitude of velocity does not changes but we still need to pull the rotating object towards center. You can try this yourself. In this case also the magnitude of velocity does not change but the velocity vector does change as the direction of the velocity is continuously changing.

Are satellites doing free fall?

6 Answers6