Satellite in orbit question

[amine2086]

A satellite is moving around the Earth in a circular orbit with a radial velocity V at a radius R. If the gravitational force of the Earth were to suddenly disappear, then the satellite would

(a) Move with velocity RV tangentially to its circular orbit.
(b) Move with velocity V tangentially to its circular orbit.
(c) Move radially outwards with a velocity RV.
(d) Move radially outwards with a velocity V.

The answer is A but I quite don't get it. If the gravitational force of the earth disappeared, is not the net force on the satellite zero?

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[loveoforganic]

exactly, and it's instantaneous velocity at any given moment is tangential to it's path

 

[sv3]

i dig the tangential thing, but why is velocity RV? and not V?
i got a feeling im missing something here........

 

[G1SG2]

A satellite is moving around the Earth in a circular orbit with a radial velocity V at a radius R. If the gravitational force of the Earth were to suddenly disappear, then the satellite would

(a) Move with velocity RV tangentially to its circular orbit.
(b) Move with velocity V tangentially to its circular orbit.
(c) Move radially outwards with a velocity RV.
(d) Move radially outwards with a velocity V.

The answer is A but I quite don't get it. If the gravitational force of the earth disappeared, is not the net force on the satellite zero?

i dig the tangential thing, but why is velocity RV? and not V?
i got a feeling im missing something here........

The gravitational force is the only force that is causing the satellite to stay in its orbit. Once that force is gone, the satellite will move tangentially to the orbit (remember, it has tangential velocity). Draw a diagram-it doesn't make sense for it to move outwards.Think of swinging a yo-yo over your head (be careful, of course ). Once you stop swinging and let go, it'll fly out in a manner that is tangential to the path of its orbit above your head. Eliminate choices C and D.

Now, you're told that the RADIAL velocity is V. Let's call it W (omega) instead, since it's the angular velocity.

W=V/R. You want the tangential velocity (regular V). So, just multiply by R to get rid of the denominator. V/R*R=V, which is represented by choice A. For this problem, you just need to know that 1) once the centripetal force is gone, the object will move tangential to the orbit, and 2) radial velocity is w=V/R, and you need the tangential velocity V which can be found by multiplying the radial/angular velocity by R. Hope that helps.

 

[DamienPro]

A satellite is moving around the Earth in a circular orbit with a radial velocity V at a radius R. If the gravitational force of the Earth were to suddenly disappear, then the satellite would

(a) Move with velocity RV tangentially to its circular orbit.
(b) Move with velocity V tangentially to its circular orbit.
(c) Move radially outwards with a velocity RV.
(d) Move radially outwards with a velocity V.

The answer is A but I quite don't get it. If the gravitational force of the earth disappeared, is not the net force on the satellite zero?

Correct answer should be B. Answer A would have been right had RV been replaced by RW, where W is the angular velocity. (Note: Radial velocity is perpendicular to the transverse (also called tangential) velocity, although both velocities have the same magnitude of speed.)

 

[G1SG2]

Correct answer should be B. Answer A would have been right had RV been replaced by RW, where W is the angular velocity. (Note: Radial velocity is perpendicular to the transverse (also called tangential) velocity, although both velocities have the same magnitude of speed.)

Hmm, I always thought radial velocity was the angular velocity?

 

[DamienPro]

Hmm, I always thought radial velocity was the angular velocity?

Radial velocity has its speed straight towards or away from an observer, and is often associated with the Doppler effect of a light object. It's something out of the scope of MCAT. I suppose the question here is intended to mean V as angular velocity, otherwise it will really make the answers ambiguous.

 

[odellus]

If a particle is moving in a circular orbit of radius R, it's radial velocity is exactly zero. If an orbiting object has a non-zero value for the radial velocity, it's value for r would change in time, and it would therefore not be a circular orbit. I too found this question on an outside site and it said the correct answer was indeed RV.

This question is junk. None of the answer choices are correct, as the situation it has us envision is impossible.

 

[sv3]

The gravitational force is the only force that is causing the satellite to stay in its orbit. Once that force is gone, the satellite will move tangentially to the orbit (remember, it has tangential velocity). Draw a diagram-it doesn't make sense for it to move outwards.Think of swinging a yo-yo over your head (be careful, of course ). Once you stop swinging and let go, it'll fly out in a manner that is tangential to the path of its orbit above your head. Eliminate choices C and D.

Now, you're told that the RADIAL velocity is V. Let's call it W (omega) instead, since it's the angular velocity.

W=V/R. You want the tangential velocity (regular V). So, just multiply by R to get rid of the denominator. V/R*R=V, which is represented by choice A. For this problem, you just need to know that 1) once the centripetal force is gone, the object will move tangential to the orbit, and 2) radial velocity is w=V/R, and you need the tangential velocity V which can be found by multiplying the radial/angular velocity by R. Hope that helps.

thanks! I dont remember seeing the W=v/r equation when i studied angular momentum and velocity. I have some equations that relate it to inertia and momentum but not this particular one. Hence I would have said the velocity would be just V. Interesting..........

 

[odellus]

If the question and answer were,

"A satellite is moving around the Earth in a circular orbit with an angular velocity ω at a radius R. If the gravitational force of the Earth were to suddenly disappear, then the satellite would

A. Move with velocity Rω tangentially to its circular orbit."

then this would make sense.

 

[Pulsar]

thanks! I dont remember seeing the W=v/r equation when i studied angular momentum and velocity. I have some equations that relate it to inertia and momentum but not this particular one. Hence I would have said the velocity would be just V. Interesting..........

It's because the length of an arc (call it L) subtended by an angle theta is equal to radius * theta.

Differentiate this expression (L = radius * theta) to get dL/dt = R * d(Theta)/dt. dL/dt can be rewritten as v (for velocity) and you can call d(Theta)/dt 'w' (omega, for angular velocity). This gives you v = Rw.

 

[sv3]

It's because the length of an arc (call it L) subtended by an angle theta is equal to radius * theta.

Differentiate this expression (L = radius * theta) to get dL/dt = R * d(Theta)/dt. dL/dt can be rewritten as v (for velocity) and you can call d(Theta)/dt 'w' (omega, for angular velocity). This gives you v = Rw.

Got it, don't like it, but got it. Thanks alot!