# What happens when the velocity of a revolving satellite/body changes?

Dear Experts,

I have certain doubts regarding bodies moving around a particular planet, in a orbit.

1. What will happen if the satellite/the body accelerates internally?

The equation for mechanical energy of a satellite is,
TE = KE + PE
= 1/2 m v^2 + (-GMm / (R + h)

(R= radius of the planet, M = Mass of the planet, h = height of the orbit above the surface of the planet)

Will the following happen?
If the satellite/body accelerates,v increases. If energy conservation has to work, in order to keep the total energy constant, The increase in the KE part must be compensated by a decrease in PE part. For that to happen the magnitude of (GMm / (R+h) ) should go up...Since all the other parameters are constants, the only thing that can change is h and h must decrease. Which means that the body/satellite will come closer to the planet, and if this acceleration continues, the satellite/ body will collide with the planet eventually.

2. What happens if the satellite is accelerated externally, or if the velocity of the satellite is increased by some external agent?

In this case, is it correct to assume that there neednt be energy conservation, as the body is acted upon by an external agent.

TE = KE + PE
= 1/2 m v^2 + (-GMm / (R + h)

If i increase v , TE must go up.

The total energy of an orbit is also given by

TE = - GMm / 2(R) Where R is the radius of the orbit.

Therefore , higher the value of R, lesser the magnitude of (GMm/2R) , lesser the negative value, Greater the amount of energy. Therefore it is sufficient to believe that father orbits have higher energy.
If we increase the velocity of the body/ satellite with external interaction, the body must settle down in a higher radius orbit. And if i further increase it, there must be a point where it escapes the earths 's gravitational field.

But i find it hard to visualize the the scenarios in outer space, that is, in both cases,the satellite/ body speeds up, but the trajectory it follows is different.

I request the resourceful people here at PhysicsForums to kindly see illuminate me regarding this and point out to me the areas in which my concept is flawed or not well constructed. Thank You

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I would also be glad to recieve some help about how to analyze the motion of the satellite/body subsequent to external interaction.

That is,
1. what will happen if I hit the satellite or the body with some other object towards the center of the orbit.
2. What will happen if i hit the satellite or body with some other object away from the orbit, outward.

mfb
Mentor
1. What will happen if the satellite/the body accelerates internally?
What do you mean with "internally"?
If the satellite/body accelerates,v increases.
That depends on the direction of acceleration.

If energy conservation has to work, in order to keep the total energy constant, The increase in the KE part must be compensated by a decrease in PE part.
If a satellite increases its velocity from falling towards the planet: sure. It can collide with the planet, depending on the trajectory.

The total energy of an orbit is also given by

TE = - GMm / 2(R) Where R is the radius of the orbit.
I guess it should be (2R). This is valid for circular orbits only.

Two increases in velocity are in fact the usual way to reach a higher orbit. Note that the final orbit has a lower velocity than the initial orbit. You have to accelerate forwards to get a "slower" orbit. This is one of the weird features of orbital mechanics.

That is,
1. what will happen if I hit the satellite or the body with some other object towards the center of the orbit.
2. What will happen if i hit the satellite or body with some other object away from the orbit, outward.
The same as with thrusters: the orbit changes. In which way, depends on the initial orbit and the point where you hit it.

By accelerating internally i mean, without external interference, that is by means of some propulsion. If the satellite shoots some mass out in opposite direction.

And in case of changing the velocity by an external agent, is it possible to apply law of energy conservation, as the system is not isolated. When we supply energy from outside, by some means, there will obviously be an increase in the energy of the body. Is it correct to think that the body will readjust to keep the total energy back to the previous value?

About the direction of acceleration, i would like to know what will happen if the acceleration is tangential to the orbit, and forward. In case of circular orbit, no component of the acceleration will be along the direction of gravitational pull...In such a situation how will the body / satellite behave...

A circular orbit is only possible when the orbital speed is carefully matched to the orbital radius. As soon as the satellite changes its velocity - in direction or in magnitude - this condition is no longer true, so the orbit becomes elliptic (or ceases to be closed in extreme cases). You can figure out the parameters of the ellipse by applying conservation of total energy and angular momentum with the new velocity.

A.T.
When we supply energy from outside, by some means, there will obviously be an increase in the energy of the body. Is it correct to think that the body will readjust to keep the total energy back to the previous value?
Why would that happen? Where would the energy go to?

About the direction of acceleration, i would like to know what will happen if the acceleration is tangential to the orbit, and forward.
It goes into an elliptical orbit. If the acceleration is continuous, it will spiral outwards, eventually escaping.

mfb
Mentor

By accelerating internally i mean, without external interference, that is by means of some propulsion. If the satellite shoots some mass out in opposite direction.

And in case of changing the velocity by an external agent, is it possible to apply law of energy conservation, as the system is not isolated. When we supply energy from outside, by some means, there will obviously be an increase in the energy of the body. Is it correct to think that the body will readjust to keep the total energy back to the previous value?
That does not match the descriptions you used in post 1.

There are two cases, and I'll avoid "internally" and "externally", I think those words are just adding confusion:

- the satellite changes its speed (note the difference between speed and velocity) due to the gravitational attraction: this always happens if and only if it changes its distance to the object. Energy conservation is useful to study this.

- the satellite fires its thrusters, collides with objects or similar: it can change its velocity at will, and energy conservation is not very useful here.

I thank all you experts on helping me regarding this concept. I really appreciate it.