Elliptical orbit changing as a star's mass increases I'm studying Kepler's Laws, specifically the orbit of the Earth around the Sun. I know that if the Earth was more massive, the orbit would not be significantly affected. If the Sun was more massive, I know the velocity of Earth's orbit around the Sun would increase, but how would the shape of the orbit change? This is a theoretical case, neglecting conservation of mass and assuming the Sun's radius and volume don't change.
 A: If the existing orbit were already circular then any changes like you describe would immediately result in an elliptical orbit. After that the orbit would tend toward a circular orbit. How long that takes depends on the total tidal forces. A rigid body would take longer than a pliable one as tidal forces are exchanged. 
A: Kepler's laws are not correct: 
No area law, no elliptical orbits, nor period. Starting with Newton's mechanical laws, Kepler's area law does not exist. Newton's universal attraction force is radial. $F=F_r$. A side force component, a perpendicular force does not exist $F_p=\frac {m dV_p} {dt}=0$. Then when integrated , we get $V_p=Ct$ . Kepler says $r V_p=area=Ct$. Newtons equation is a prove. Kepler's area law is an estimation.
When using $V_p=Ct$ in the differential form of the energy conservation equation,we get
$r=-4*{t^2}+4 t T-4 \frac {T^2} 6 $ as the equation of celestial motion. This is a spiraled orbit and not an ellipse.
When to the validity of the period law: Newton says period law is valid for circular motion with non accelerated velocity. Kepler says period law is valid even for elliptical orbits with accelerated velocity. High velocity at perihelion low , velocity at aphelion. And no body feel this acceleration?
