I Change in orbit when mass is doubled

[Muu9]

TL;DR Summary

What happens to the once-circular orbit of a satellite when it's planet's mass suddenly doubles?

A satellite is orbiting a planet in a circular orbit. The planet's mass doubles instantly. What happens to the orbit of the satellite?

I think it would move to an elliptical orbit with major axis equal to the old radius and a minor axis equal to either 1/2 or sqrt(2)/2 times the old radius. I'm leaning toward the latter. What do you guys think?

 

[PeroK]

What do you guys think?

I think you should do the maths!

 

[Drakkith]

I think it would move to an elliptical orbit with major axis equal to the old radius and a minor axis equal to either 1/2 or sqrt(2)/2 times the old radius. I'm leaning toward the latter. What do you guys think?

Nothing would happen*. An object's orbital velocity is independent of its mass.

*As long as we are treating the star as not being affected by the planet's gravity.

Edit: Whoops, I misunderstood the question. The satellite's orbit would obviously change. Exactly how I'm uncertain at the moment.

 

[Filip Larsen]

Nothing would happen*. An object's orbital velocity is independent of its mass.

But here it is clearly stated it is the massive object that is doubling mass. And technical all mass changes would in principle have some effect, but since the satellite is not given mass I assume the OP question aim for a simple solution that does not involve reduced mass.

 

[Drakkith]

But here it is clearly stated it is the massive object that is doubling mass. And technical all mass changes would in principle have some effect, but since the satellite is not given mass I assume the OP question aim for a simple solution that does not involve reduced mass.

Oh wow, how did I misunderstand the question so badly?? I've edited my post.

 

[Drakkith]

Playing around in Universe Sandbox gave me the following:

1. An object orbiting Earth in a circular orbit at distance of 220,450 km. Semi-major axis, semi-minor axis, pericenter, and apocenter are all 220,450 km.
2. Doubling Earth's mass leaves the apocenter the same but changes the pericenter to 73,820 km, semi-major axis to 147,135 km, and semi-minor axis to 127,592 km.

Dividing the old values by $\sqrt{2}$ or $2\sqrt{2}$ doesn't perfectly equal any of the new values, but they are close, so I don't know if its a rounding error or if the square root of two just doesn't come into play here.

 

[Filip Larsen]

The OP hasn't returned with some math yet, but in case a hint is needed allow me to recommend the vis-viva equation which pretty much is the go to equation for most problems involving speed and radial position for two-body orbits.