# Planet orbiting around a star whose mass changes

## Homework Statement

(Assuming all circular orbits)
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Say there is a star with mass M and a planet orbiting that star with a mass m.

The star M then suddenly loses half of its mass. (So now it is M/2)

What is the new radius of orbit of the planet around the star? Warning: Velocity will not be the same!

I'm not sure how to tackle this problem. I know for sure it has to do with angular momentum

## Homework Equations

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L=Iω or r x p angular momentum

## The Attempt at a Solution

conservation of momentum for the planet
from Iωi = Iωf, I got m ri vi = m rf vf , but that doesn't really help

haruspex
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conservation of momentum for the planet
from Iωi = Iωf, I got m ri vi = m rf vf , but that doesn't really help
It helps, but you need another equation. What else will be conserved?
(But I have a concern about the question. It seems to assume the new orbit will be circular. That strikes me as most unlikely.)

It helps, but you need another equation. What else will be conserved?
(But I have a concern about the question. It seems to assume the new orbit will be circular. That strikes me as most unlikely.)
yes, I know it is really not circular but It will be assumed in this probem.

I used f=ma to come up with vi=sqrt(GM/ri) & vf=sqrt(GM/2rf)and plugged in those as V on both sides (with the corresponding r)

I got 2 ri = rf

haruspex
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yes, I know it is really not circular but It will be assumed in this probem.

I used f=ma to come up with vi=sqrt(GM/ri) & vf=sqrt(GM/2rf)and plugged in those as V on both sides (with the corresponding r)

I got 2 ri = rf
Looks ok. The trouble with questions with premisses that defy physical laws is that there may well be different solutions methods, all valid, that produce different answers.

Edit: and gneill has put his finger on just such an alternate answer. As I asked in post #2, what else should be conserved?

Last edited:
gneill
Mentor
I have a feeling that this is a bit of a trick question, and not just because it invokes magic to make mass vanish. Assuming that the planet retains its current orbital speed at the instant half of the star's mass is vanished, I'd look at comparing that speed with the new escape velocity for that location.

PeroK
jbriggs444
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As I read the problem and guess at the author's thoughts, we are to assume that at the same moment half of the star magically vanishes, the planet does not change mass, but magically teleports to a new position with a new velocity, which are both chosen so that angular momentum is conserved and a circular orbit results.

It is strange that one would pose a problem in which angular momentum conservation is paramount using a scenario involving teleportation. Teleportation defies conservation of angular momentum.

Of course, neither linear nor angular momentum are conserved in this problem anyway. The star changes mass. That defies conservation of both quantities in a great number of frames of reference.

haruspex
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2020 Award
As I read the problem and guess at the author's thoughts, we are to assume that at the same moment half of the star magically vanishes, the planet does not change mass, but magically teleports to a new position with a new velocity, which are both chosen so that angular momentum is conserved and a circular orbit results.

haruspex