Question

A red supergiant star is ten times more massive than the sun. What would be the likely impact on the motion of Earth if the sun were replaced by this red supergiant?

Answer 1

Force from sun on earth = G m Ms / R^2 = mass * centripetal Acc = m V^2/R
Ms = R V^2 G
so
10Ms = Rn Vn^2 G = 10R V^2 G
so the orbit radius times Velocity squared goes up by 10
If the angular momentum remained the same (no torque)
then
L = m R V so radius * velocity is the same
Rn Vn = R V
Vn = V(R/Rn)
Rn V^2 (R/Rn)^2 = 10 R V^2
R^2 /Rn= 10 R
R/Rn = 10
The earth must be ten times as far away if it is to have the same angular momentum

Answer 2

Otherwise it would simply crash into the much bigger sun