## Mass Transfer in binary orbits ?

Im trying to calculate the orbit of a planet rotating a star after "x" amount of mass has been transfered form the planet to the star. I took our own solar system for example and assumed earth was the only planet orbiting the sun.

I used the orbit equilibrium equation :

(GM1M2)/ R = M2 (V)2

where m1 is the mass of the sun and m2 is mass of the earth, v is earth's orbital velocity and r is its orbital radius.

then i added the value x to m1 and subtracted it from m2 ( mass added to the sun and stolen from earth), getting :

(G(M1+x)(M2-x))/ R = (M2-x) (V)2

but V or orbital velocity is simply:

V= [G(M1+x)/R]^1/2

Substituting that back into our equilibrium equation, we get:

(G(M1+x)(M2-x))/ R = (M2-x) ([G(M1+x)/R]^1/2)2

which is simplified to :

G(M1+x)(M2-x)/ R = (M2-x)G(M1+x)/R

As one can see , the terms "R" and "G" can be canceled out from both sides , giving:

(M1+x)(M2-x)= (M2-x)(M1+x)

Which implies that no matter how much mass is transfered from an orbiting body to the body being orbited , the orbital radius WILL NOT change. ONLY the orbital speed would change.

Is this the right conclusion or did I go wrong somewhere ???
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 Tags mass, orbit, planet, transfer

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