Can anyone help?
It's just part A, part B i can figure out even without looking at the rest of the question.
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
--------------------
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.