Question

. (2 points) What will the escape velocity be when the Sun becomes a red giant with a radius 50 times greater and a mass only 0.9 times that of today?

Answer 1

The escape velocity is given by the formula:

v = sqrt(2GM/r)

where v is the escape velocity, G is the gravitational constant, M is the mass of the object (in this case, the Sun), and r is the distance from the center of the object to the point where the escape velocity is being calculated.

When the Sun becomes a red giant with a radius 50 times greater, the new radius (r') will be:

r' = 50 * r

The new mass (M') will be:

M' = 0.9 * M

Substituting these values into the formula, we get:

v' = sqrt(2 * G * (0.9 * M) / (50 * r))

Simplifying:

v' = sqrt(0.036 * GM / r)

So the escape velocity when the Sun becomes a red giant with a radius 50 times greater and a mass only 0.9 times that of today will be about 0.6 times the current escape velocity.