Background formula for this problem:

where F = force of gravity.

For a given mass, the radius of the sphere to which it must be compressed to be a black whole is its Schwartzschild Radius.

The work energy principle (work done on a particle by a gravitiational force is equal to the change in the kinetic energy of the particle) means that:

R is radius of object in question.

r is a random distance from the center of gravity

v = velocity of particle as it goes from r to the dist. R (and of course initial velocity is the initial velocity at distance r).

------------------------(Now the Problem)------------------------

*To find the escape velocity, 2 quantities are equated: the work done in moving a particle of mass m from the distance R out to infinity, and the kinetic energy gained by the particle in letting it fall from infinity with initial velocity = 0. The final velocity is called the escape velocity.

To deduce of a mass M object .....

^Solve the above for R and we can have v=c (speed of light), and the m will cancel out. R = Schwartzschild Radius of the object M.

PART A

Show that

PART B

Calculate for both the sun/earth.

Sun = Mass

Earth = Mass

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I'm not sure how to start Part A. How do I start?

Could I just do something like this?

(As x goes to infinity, the r in the denominator makes the first fraction above zero?) But this doesn't get me close to the part a proof.

Sorry if it seems confusing, it's a long problem, ask if you need help reading instructions, etc.