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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