What would happen to a satellite if its orbit speed doubled?

The radius of orbit will decrease by 1/4, the satellite will come closer to Earth

Explanation:

The orbital speed of any body revolving in an orbit around another boyd is given by:

v (orbital) = √(G · M(central body)/R)

Where G is the gravitation constant.

If the body, e.g satellite is moving around the Earth, then the mass of central body M will also be a constant. Therefore, the only thing on which the orbital velocity will depend on will be Radius of the orbit R.

v ∝ 1/√R

√R ∝ 1/v

Take square:

R ∝ 1/v²

If the velocity of satellite will doubles, then:

R' ∝ 1/ (2v)²

R' ∝ 1/4v²

R' ∝ (1/4)(1/v²)

R' ∝ (1/4)(R)

The radius of orbit will decrease by 1/4, the satellite will come closer to Earth

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