How Does a Star's Mass Loss Affect Satellite Orbit Distances?

[bon]

Homework Statement

A satellite is in circular orbit of radius R about a star of mass M . The star
suddenly undergoes an explosion in which one percent of its mass is blown spherically
symmetrically to a large distance. What are the new nearest and furthest distances of
the satellite’s orbit around the star?

Homework Equations

The Attempt at a Solution

Am i right in thinking that both the angular momentum and energy of the star decrease..the new J = 0.99mrv and the new KE = 1/2 (0.99m)v^2? Same PE?

 

[ehild]

Why should either the KE or the angular momentum of the satellite change? Did any force do any work on it? Or the force field ceased to be central?

ehild

 

[bon]

Why should either the KE or the angular momentum of the satellite change? Did any force do any work on it? Or the force field ceased to be central?

ehild

it's mass changed! - i.e. the total PE and KE of remaining satellite + parts blown away is unchanged, yes..but surely the KE of the remaining bit of satellite decreases as its mass is less...?

Otherwise there would be no max/min distances that it asks us to calculate..

 

[ehild]

Read the text more carefully.

"The star suddenly undergoes an explosion in which one percent of its mass is blown spherically symmetrically to a large distance."

ehild

 

[rdl]

I would approach this problem by using the principles of orbital mechanics and conservation of energy and momentum. The sudden explosion of the star would cause a decrease in its mass, leading to a decrease in the gravitational force between the star and the satellite. This would result in a decrease in the satellite's orbital velocity and a change in its orbit.

To calculate the new orbit, I would use the equation for gravitational force, F = Gm1m2/r^2, where m1 and m2 are the masses of the star and satellite, respectively, and r is the distance between them. Since the mass of the star has decreased by 1%, the new force would be 0.99 times the original force.

Next, I would use the equation for centripetal force, F = mv^2/r, to calculate the new orbital velocity of the satellite. Since the force has decreased, the velocity would also decrease by the same factor of 0.99.

Using the equation for orbital period, T = 2πr/v, I would calculate the new orbital period of the satellite. This would remain the same as the original orbital period, since the mass of the satellite has not changed.

Finally, I would use Kepler's third law, T^2 ∝ r^3, to calculate the new orbital radius. The new orbital radius would be the distance at which the new orbital period and the new force are in equilibrium. This would give me the new nearest and furthest distances of the satellite's orbit around the star.

In summary, the new nearest and furthest distances of the satellite's orbit around the star would decrease by a factor of 0.99 due to the decrease in the gravitational force between the two objects. This decrease would be reflected in the decrease in the satellite's orbital velocity and the new equilibrium distance calculated using Kepler's third law.