How Small Must Earth's Mass Be Compressed to Form a Black Hole?

[ticels]

a black hole is an object so heavy that neither matter nor even light can secape the influence of its gravitational field. Since no light can scape from it, it appears black. Suppose a mass apporxmiately the size of the Earth's mass 5.56x10^24 kg is packed into a small unifrom sphere of radius r.

*Use speed of light c=3.0x10^8 and Universal Gravitation G
*Escape speed must be the speed of light
*Relative equation
g=sq(G/r2); F=GMm/r^2; escape velocity=sq(2GM/r)

1) based on Newtonian mechanics, determine the limiting radius r0 where this mass (approximately the size of the Earth's mass) becomes a black hole. Answer in units of m.

2)Using Newtonian mechanics, how much would a mass of 4.26μg weigh at the surface of this super-dense sphere? Answer in units of N.

thx for help in advance.

 

[Mentia]

Hey hey. This is a pretty cool problem I think. What you're doing is calculating the Schwartzchild radius. You can get more info on that from Wikipedia: http://en.wikipedia.org/wiki/Schwarzschild_radius

Basically, you set the escape velocity to be the speed of light and then solve for "r".

You plug in c for the velocity, the given mass for M, and G for G and voila you've got the Schwartzchild radius.

For the 2nd problem, now that you have "r", you can solve for F from Newton's law of universal gravitation: F=GMm/r^2