# I am having troubles with the gravitational time dialtion equation.

1. Nov 27, 2009

### zeromodz

Okay, I am just fooling around with the equation

Δt' = Δt * √( 1 - 2GM/RC^2)

To find out the suns gravitational effects on close ojbects
I keep getting a nonreal answer. I can derive the equation to this.

Δt' = Δt * √( 1 - (Schwarzschilds Radius)/R)

The suns Schwarzschilds radius of the sun is is 2954.14m
So if I want to see how much time will change in 30 seconds from 20 meters away I do
30*√(1-2954.14/20)

Then i get a non real answer. What am I doing wrong. Does this equation just have a limit from certain distances or does it just break the laws of physics if an objects time slows down from 20 meters away. If I am not doing anything wrong, could someone give me an equation that works for this stuff.

2. Nov 27, 2009

### clamtrox

Radius is calculated from the center of the sun. So you cannot have radii that are less than what the radius of the sun is, which is something like 700 000 km.

3. Nov 27, 2009

### vin300

R is your distance from the centre of the sun

4. Nov 27, 2009

### zeromodz

So does that mean this equation fails when dealing with black holes? What if the sun were to become really dense and the radius shrinks to a more plausible number like 100 meters. Would this equation still fail?

5. Nov 27, 2009

### hexexpert

The radius won't drop below the Schwarzschild radius nor will another object be able to reach a distance from the Radius less than the S-radius.

6. Nov 27, 2009

### atyy

The time dilation formula you used is for objects hovering outside the event horizon of a black hole. You cannot hover inside the event horizon of a black hole.

7. Nov 28, 2009

### hexexpert

I suspect the black hole should not be treated as a point when close to the S-Radius. Is this correct?