# Gravity Equasion?

1. Dec 24, 2004

### Gamish

Gravity Equasion?????

I have a question, after reading about black holes. What is the "gravity equation"? Let me explain. If the earth had a weight of 1000000000 KG, how fast would I accelerate to that object, if I was 1 KM away from it or something? Do you get my point, I don't know all the technical apsects, I am just trying to figure out how massive an object has to be to open up aa black hole.

Thanks in advanced :)

2. Dec 24, 2004

### pervect

Staff Emeritus
You can use Newton's law, F = GmM/r^2, to calculate the force of attraction between two bodies that are far away from each other.

G is the universal gravitational constant, m and M are the two masses, and r is the distance between them.

For strong gravitational fields this equation doesn't work, but I don't think there is any model of gravity "as a force" that will work. The problem is that the geometry of space-time itself becomes distorted near a sufficiently dense mass, so that thinking of gravity as a "force" will not give the correct answer without taking the distortion of the geometry into account.

The event horizon of a black hole occurs at radius [fix] r = 2GM/c^2, called the Schwarzschild radius. Here G is the same universal gravitational constant as it was in Newton's law of gravity, M is the mass of the massive body, and c is the speed of light. For a body as massive as the Earth's sun, the Schwarzschild radius is 1.5km.

Last edited: Dec 25, 2004
3. Dec 24, 2004

### Rob Woodside

Not to be a grinch, but I think you are short a factor of 2 in your Schwarzchild radius.

Galileo's constant acceleration g due to gravity came out nicely from Newton's theory as g = GMp/(Rp^2) where Mp is the mass of a spherical planet of radius Rp. Have a look at Kip Thorne's paper back on black holes or Wheeler & Taylor's book on black holes.

4. Dec 25, 2004

### pervect

Staff Emeritus
You are (of course) quite right about the factor of 2 - I fixed the original post to reflect the correct formula for the Schwarzschild radius.

Merry xmas & a happy new year