Change in orbit when mass is doubled

In summary, the satellite 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.
  • #1
Muu9
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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?
 
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  • #2
Muu9 said:
What do you guys think?
I think you should do the maths!
 
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  • #3
Muu9 said:
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.
 
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  • #4
Drakkith said:
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.
 
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  • #5
Filip Larsen said:
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.
 
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  • #6
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.
 
  • #7
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.
 

1. How does doubling the mass affect the orbit of an object?

When the mass of an object is doubled, its orbit will also change. This is due to the fact that the gravitational force between two objects is directly proportional to their masses. Therefore, when the mass is doubled, the force of gravity between the two objects will also double, resulting in a change in the orbit of the object.

2. Will the change in orbit be significant if the mass is doubled?

Yes, the change in orbit will be significant if the mass is doubled. This is because the gravitational force between two objects is an inverse-square law, meaning that it decreases as the distance between the objects increases. Therefore, even a small change in mass can result in a significant change in the orbit of an object.

3. How does the distance between the two objects affect the change in orbit when mass is doubled?

The distance between two objects also plays a role in the change in orbit when mass is doubled. The gravitational force between two objects decreases as the distance between them increases, so if the distance remains the same, the change in orbit will be greater. However, if the distance between the objects increases, the change in orbit will be less significant.

4. Can the change in orbit be reversed by halving the mass?

Yes, the change in orbit can be reversed by halving the mass. This is because the gravitational force is directly proportional to the mass, so halving the mass will also halve the force of gravity between the two objects. As a result, the orbit of the object will return to its original state.

5. Are there any other factors that can affect the change in orbit when mass is doubled?

Yes, there are other factors that can affect the change in orbit when mass is doubled. These include the mass and distance of other objects in the system, as well as external forces such as atmospheric drag. These factors can alter the gravitational force and therefore impact the change in orbit when the mass is doubled.

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