How do satellites stay in orbit? Free fall or centripetal?

[brainstorm]

No, yes, and no.

The first no answer: Strictly speaking, a force is required.

The yes answer: For conservative forces, the force is the gradient of the potential energy.

The second no answer: Let's start with a circular orbit. The force is always perpendicular to the velocity vector, so no work is done. There is no change in kinetic energy, and because the object is at a constant distance, there is no change in potential energy, either.

For a non-circular orbit, total mechanical energy is still a constant of motion. Gravitation is a conservative force. Total mechanical energy is a constant for any conservative force.

Ok, just for clarity's sake take a comparative example of two rockets.

Rocket A is in circular orbit around the sun. Rocket B is traveling at the same speed as Rocket A far from any significant gravity well.

If Rocket B wants to replicate the curvature of Rocket A's path, it has to expend fuel for constant trajectory corrections. It can do this, presumably, without increasing velocity beyond that of Rocket A in orbiting unpropelled around the sun, right?

So isn't Rocket B's fuel expenditure and propulsion energy and work? And isn't that energy and work equivalent to the effect of the sun's gravity on Rocket A's trajectory in the absence of propulsion?

 

[ruko]

The latter is true only if the distance between the two objects is in fact decreasing.


What increase in energy? The total mechanical energy of an orbiting satellite is constant in Newtonian mechanics. You should learn Newtonian mechanics before you start delving into general relativity (as you did in a later post). You need to learn to walk before you can learn how to run.



In Newtonian mechanics gravitation is a force. In general relativity it is something different.


======================



It is best not to invoke centrifugal force when explaining orbits. What inertia are you talking about? (More on this question later.)

There is no need to invoke the concept centrifugal force when describing orbits from the perspective of an inertial (non-rotating) frame of reference. That's a good thing; there is no centrifugal force in a non-rotating frame of reference. That orbits are conic sections for an inverse square law force falls right out of the math.

That said, one can explain circular orbits using centrifugal force. From the perspective of an observer rotating at orbital rate, an orbiting satellite is suspended. It is not moving. There is a non-zero centrifugal force in this the rotating frame of reference. Since the orbiting satellite is not moving, the net apparent force on the satellite must be zero. Since the object is not moving in this frame of reference, it has zero inertia (momentum) in this frame.

To say that inertia is centrifugal force is nonsense for (at least) two reasons. Firstly there is a units mismatch. Inertia has units of mass*length/time. Force has units of mass*length/time². Inertia and force are incomparable quantities. Secondly, you are mixing frames.

What inertia you ask? How about a 1000 pound satellite traveling around the Earth at 17,000 MPH. Do you think this would have some inertia? How can you possibly say this satellite has zero momentum or inertia in any reference? This is nonsense. If this were true the satellite would fall to the earth.

Lets say I'm driving my car and I make a turn to the left. In England I would turn right. On the bench seat next to me is a ball free to roll. When I make the turn what happens to the ball? The inertia of the ball traveling at the speed of the car wants it to continue in a straight line doesn't it? Is this inertia or this fictitious centrifugal force? What stops the ball from continuing on in a straight line? The door. What keeps the ball hugging the door as I turn? The same thing that produced the roll, inertia. What stops a satellite from continuing on a straight line due to the tremendous inertia it acquired in the acceleration stage? The gravity well of earth.
www.britannica.com/EBchecked/topic/.../centrifugal-force[/URL]

 

[D H]

What inertia you ask? How about a 1000 pound satellite traveling around the Earth at 17,000 MPH. Do you think this would have some inertia?

You are looking at the satellite from the perspective of an inertial frame of reference. Those who insist on using centrifugal force to explain satellite motion are implicitly looking at the satellite from the perspective of a co-rotating frame of reference. The satellite has zero velocity in such a frame.

How can you possibly say this satellite has zero momentum or inertia in any reference? This is nonsense. If this were true the satellite would fall to the earth.

A good example are the geosynchronous satellites. A simple, fixed dish works just fine for receiving a high bandwidth signal from a geosynchronous satellite. From the perspective of an Earth-fixed observer, those geosynchronous satellites are not moving. Compare to a polar orbiting weather satellite. While an omni-directional receiver on the ground suffices for the low bandwidth signals broadcast by those satellites, receiving the high bandwidth signals requires the use a (very expensive) tracking antenna. Those polar orbiters are moving with respect to the Earth.

So how to explain how those geosynchronous satellites don't just fall to the Earth? From the perspective of an inertial observer, those satellites are moving. They are following a curved path. That means some net force must be in play. However, from the perspective of an Earth-fixed observer, those geosynchronous satellites are stationary. The apparent net force on those satellites must be zero. An Earth-fixed observer is a observing from the perspective of a rotating frame of reference, and it is those rotating frames of reference in which fictitious forces such as the centrifugal force arise. A geosynchronous satellite is stationary with respect to an Earth-fixed observer because the centrifugal force cancels the gravitational force.

 

[brainstorm]

DH, your post is insightful. I think the confusion comes from the fact that an orbiting satellite is in equilibrium for its position in the gravity well. "Centrifuge force" implies that something has an inertial tendency outward from the center, whereas an orbiting satellite does not have such a tendency except to the extent that a hypothetical situation is imagined where other matter in the gravity-well suddenly disappears or escapes, or gravity diminishes for some other reason.

Another part of the confusion is caused by normative distinctions between potential and kinetic energy, I think. If you think of a rotating cloud of disassembled dust or other particles instead of a planet with tensile integrity, all gravity would take place in the form of free-falling momentum, i.e. kinetic energy. This is assuming no friction between any of the particles, since any friction would create some level of potential energy, presumably.

So to the extent that such a rotating dust-cloud is wholly in free-fall in its very rotation, there is no basis for saying that one thing is orbiting another. Everything is orbiting the fulcrum, again ignoring any turbulence or frictions between particles.

So is/should interpretation of the forces and energy-behavior of the satellite be considered relative to an observer frame of reference, or should the object simply be treated according to its own inertial characteristics within its own frame of reference?
From a Newtonian perspective, I believe it would be treated as an object at rest since an object in orbit is basically analogous to an object at rest on Earth, discounting potentialization of gravity for the Earth-bound object pressed up against the ground due to tensile friction and sluggish rotation of the planet.

In relativity, however it would only be treated as stationary to the extent it is not framed in reference to any other object. Once it is framed relative to the Earth, sun, moon, etc. space-time curvature comes into play because its position and characteristics are considered in relation with other objects. Within its own frame it is stationary and the movement and characteristics of other objects appear relative to itself.

 

[ruko]

So how to explain how those geosynchronous satellites don't just fall to the Earth? .

Easy. Geo satellites are in orbit traveling at about 6900 MPH with an altitude of about 22,000miles. The exact same mechanism holds for satellites in low or high Earth orbit. It just so happens this altitude and speed produces an orbital period that matches Earth's period of rotation. To us the geo looks like it is motionless but it is definitely moving very fast.

Something I'm curious about geosats. Are the antennas on them directional? If so the satellite would have to rotate 360 degrees on its axis during every orbit to keep the antennas facing the earth. Just like the moon keeps the same side to Earth by rotating during the journey.

 

[DaveC426913]

Easy. Geo satellites are in orbit traveling at about 6900 MPH with an altitude of about 22,000miles. The exact same mechanism holds for satellites in low or high Earth orbit. It just so happens this altitude and speed produces an orbital period that matches Earth's period of rotation. To us the geo looks like it is motionless but it is definitely moving very fast.

I think you misunderstand. Reread. D_H is clever enough to understand how geostat sats work.


His comment was in the context of an Earth-based frame of reference, where the motion of the satellite is zero. It is a valid FoR, but one must create a force to explain what holds these stationary objects up.

Something I'm curious about geosats. Are the antennas on them directional? If so the satellite would have to rotate 360 degrees on its axis during every orbit to keep the antennas facing the earth. Just like the moon keeps the same side to Earth by rotating during the journey.

I'm pretty sure most satellites are spun to give them stability. I guess gyroscopically, that would mean they do not rotate (i.e. their rotational axis points to the same position on the celestial sphere permanently).

 

[ruko]

I think you misunderstand. Reread. D_H is clever enough to understand how geostat sats work.


His comment was in the context of an Earth-based frame of reference, where the motion of the satellite is zero. It is a valid FoR, but one must create a force to explain what holds these stationary objects up.I'm pretty sure most satellites are spun to give them stability. I guess gyroscopically, that would mean they do not rotate (i.e. their rotational axis points to the same position on the celestial sphere permanently).

Geo sats only appear stationary or motionless to us and that's because we are moving right along with them. They have to be speeding along at 6900 MPH to remain in the geo orbit otherwise they will fall down. This is very basic stuff. We don't have to create a force to explain what holds these "geo stationary" objects up. It is the same force that holds any satellite up. YouTube has a few good animations of orbiting geo sats.

 

[DaveC426913]

Geo sats only appear stationary or motionless to us and that's because we are moving right along with them. They have to be speeding along at 6900 MPH to remain in the geo orbit otherwise they will fall down. This is very basic stuff. We don't have to create a force to explain what holds these "geo stationary" objects up. It is the same force that holds any satellite up. YouTube has a few good animations of orbiting geo sats.

Again, you are misunderstanding.

Everyone here knows how geostat sats work in an inertial frame of reference. The discussion is about the non-inertial rotating FoR.

 

[ruko]

Again, you are misunderstanding.

Everyone here knows how geostat sats work in an inertial frame of reference. The discussion is about the non-inertial rotating FoR.

Sorry I guess I only think from a practical position. When someone asks how do satellites stay up, I try to answer from a practical standpoint. "non-inertial rotating FoR" Can you explain to me how this relates to geo sats?

 

[Naty1]

centripetal force: F = ma =mv²/r and v = wr so F = mw² r...

The gravitational force on either body must equal the centripetal force needed to keep each moving in their own circular orbit...GMm/(R+r)² = mw²r
where M is the mass of Earth and R it's orbital radius about the center of mass for the two systems, m,r for the satellite.
Since the orbital radius opf the Earth (R) is insignificant (assume R = 0) the above simplifies.

so I like centripetal.

 

[D H]

Sorry I guess I only think from a practical position. When someone asks how do satellites stay up, I try to answer from a practical standpoint. "non-inertial rotating FoR" Can you explain to me how this relates to geo sats?

ruko, you were the one who invoked the concept of centrifugal force to explain orbits in post #26. If you don't know the physics of rotating frames of reference, why did you do that?

 

[brainstorm]

Inertia plus the gravity well of the Earth permit satellites to orbit. Centrifugal force is in fact, inertia.

Maybe not my place to defend here, but I went back and looked at this post because it was cited. It seems to be a very good, clear, and simple post to me because he seems to basically be saying that an object in a curved trajectory has inertia which causes it to tend outward if released from the constraints that keep it curving.

He seems to be saying that if there wasn't inertia, the object would fall; and if there wasn't a gravity well, the object would proceed in a straight line instead of orbiting.

Plus, isn't centrifugal force always just inertia? Gravity is centripetal force because it pulls objects toward the center of the gravity well, against their inertia and any escape propulsion.

 

[ruko]

Maybe not my place to defend here, but I went back and looked at this post because it was cited. It seems to be a very good, clear, and simple post to me because he seems to basically be saying that an object in a curved trajectory has inertia which causes it to tend outward if released from the constraints that keep it curving.

He seems to be saying that if there wasn't inertia, the object would fall; and if there wasn't a gravity well, the object would proceed in a straight line instead of orbiting.

Plus, isn't centrifugal force always just inertia? Gravity is centripetal force because it pulls objects toward the center of the gravity well, against their inertia and any escape propulsion.

Thank you brainstorm.

DH:
I did not invoke centrifugal force. Centrifugal force is a fictitious force. The last time I checked fictitious means fake or does not exist unless a PHD has come up with a new definition for the word. What the average person calls centrifugal force is really the effects of inertia, like the ball rolling to the door and hugging the door during a turn (My Post 32) or the water not falling out of the pail when swung overhead. You are correct, I don't understand rotating frames of reference but even if I did, how would that help me understand geosats? I know how they get there, I know what keeps them there and I know what they are used for. Do I really need any more info?

 

[DaveC426913]

I don't understand rotating frames of reference but even if I did, how would that help me understand geosats? I know how they get there, I know what keeps them there and I know what they are used for. Do I really need any more info?

Hurricanes on Earth are understood as a result of the Coriolis Force. While the Coriolis Force is fictitious just like centrifugal force, it makes more sense to understand weather in our rotating frame of reference using this fictitious force than it does to examine weather from an inertial frame of reference.

I'm sure there is an equivalent for geosats.

 

[danielandpenn]

Hmmmm. Free fall is the name of the situation the satellite is in, but its not what keeps it orbiting. The centripetal acceleration causes the object to constantly accelerate toward the center of the Earth and thus orbit. Free fall is a result of this acceleration and the objects velocity going around the earth, not the cause of the orbit itself...That help?

What is causing the centripetal acceleration? I'm new to physics. Thanks!

 

[jtbell]

What is causing the centripetal acceleration?

The centripetal force, which in this case is gravity.

 

[rcgldr]

The answer choices were inertia, free fall, and centripetal acceleration.

The correct answer should be all of the above. The satellite's inertia, combined with it's speed perpendicular to gravity, and it's altitude at any point in time, determine the orbital path. The satellite is technically in free fall even in a circular orbit, and centripetal force, in this case gravity, is what cause the satellite to curve to maintain the orbital path. If you also consider the more generic case of an elliptical orbit, then a component force of gravity is in the direcion of travel (except at the asymtopes of the ellipse), so a "free fall" component, and also has a component of force perpendicular to the direction of travel, (centrpetal force).

 

[brainstorm]

The correct answer should be all of the above. The satellite's inertia, combined with it's speed perpendicular to gravity, and it's altitude at any point in time, determine the orbital path. The satellite is technically in free fall even in a circular orbit, and centripetal force, in this case gravity, is what cause the satellite to curve to maintain the orbital path. If you also consider the more generic case of an elliptical orbit, then a component force of gravity is in the direcion of travel (except at the asymtopes of the ellipse), so a "free fall" component, and also has a component of force perpendicular to the direction of travel, (centrpetal force).

Can any straight-line trajectory ever be possible except for an object moving directly toward the center of a gravitational field? Aren't all other trajectories relative to some gravitational fulcrum, however slight or distant the source of gravity?

 

[jimmyct]

a explanation of the moon staying in orbit
http://math.ucr.edu/home/baez/physics/General/Centrifugal/centri.html

 

[astronomer121]

this may help u out http://gravity-nirmal.blogspot.com/2010/04/Earth's-satellites.html

 

[brainstorm]

How is a state of rest to be defined within a gravitational field?

Satellites are always at rest relative to themselves and are only in motion relative to other satellites and/or the fulcrum of orbit.

If they are in a circular orbit, how is their motion relative to the fulcrum to be described if the fulcrum is conceived as a point without a surface?

The simple answer is that a certain amount of energy is required to counteract the attractive force of gravity. This energy is expressed perpendicular to the line between the satellite and the orbital fulcrum.

When the energy of orbit is balanced against the force of gravity, constant distance is sustained between satellite and fulcrum. When it becomes unbalanced, the distance between satellite and fulcrum increases or decreases, along with the momentum of the satellite.

But how can momentum be described as changing in the context of the satellite's relationship with itself? It may accelerate or decelerate relative to a third object other than itself and the fulcrum, but without that third object, it can only move closer or farther from the fulcrum, with its energy being expressed as resistance to gravitational pull, correct?