- #1

Zman

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I used the ‘gravitational time dilation’ equation to see how the clock rate varies with distance from the center of an object. I got the opposite result to what I was expecting.From Wikipedia;

Gravitational time dilation outside a non-rotating sphere

**t0**is the proper time between events A and B for a slow-ticking observer within the gravitational field,

**tf**is the coordinate time between events A and B for a fast-ticking observer at an arbitrarily large distance from the massive object (this assumes the fast-ticking observer is using Schwarzschild coordinates, a coordinate system where a clock at infinite distance from the massive sphere would tick at one second per second of coordinate time, while closer clocks would tick at less than that rate),

**r**is the radial coordinate of the observer (

**which is analogous to the classical distance from the center of the object**, but is actually a Schwarzschild coordinate),

**rs**is the Schwarzschild radius.I was interested to find out how the radius

**r**varies with the time ratio

**t0**/

**tf**for a given mass.

I plugged in

**t0**/

**tf = 1/10**

This is effectively asking what is r when the fast clock is running 10 times faster than the slow clock.

The answer is

**r = rs**X 100/99Then I asked what is r when the fast clock is running 2 times faster than the slow clock.

I plugged in

**t0**/

**tf = ½**expecting a smaller radius

I got the answer

**r =**

**rs**X 4/3 which is a bigger radius than the previous case.Clocks tick more slowly at the center than higher up. The higher up (the greater the radius) the faster a clock ticks relative to the center clock.Looking to clear up my confusion