Calculating Eccentricity of Planet's Orbit After Star Explosion

[thesaruman]

Homework Statement

A planet is in a circular orbit about a star that explodes, shedding 2% of its mass in an expanding spherical shell. Find the eccentricity of the new orbit of the planet, which otherwise is not affected by the shell.

Homework Equations

\sqrt{1-\varepsilon^2} = \frac{b}{a}, where b and a are the minor and major half-axis, and \varepsilon is the eccentricity; \rho (1 + \varepsilon \cos(\varphi)) = a(1-\varepsilon^2) (Kepler's orbit); A = \frac{L \tau}{2 m} (area law), where A is the area of the orbit, L is the angular momentum of the system, and \tau is the period of it.

The Attempt at a Solution

I have a bold hypothesis: the constant of the problem is the planet. If I it would be possible to change the coordinate system as centered on the planet, and if the Kepler's law keep inaltered, I could treat the star before and after the explosion as planets, and use the third law to stablish a relationship between their orbits. Is this possible?

 

[mgb_phys]

Has the position of centre of mass of the star changed by ejecting a spherical shell of material?

 

[thesaruman]

Has the position of centre of mass of the star changed by ejecting a spherical shell of material?

No, it didn't change; I understand what you mean. Ok I will think about how establish a relation between the old and the new eccentricity using the fact that the mass of the planet is constant; I truly believe that the solution resides in considering this.