# Gravitational Time Dilation

In my calculus class (high school), I'm writing an exploration paper on time dilation, specifically gravitational time dilation. One of the scenarios I'm thinking of looking at is the time dilation an observer experiences on one planet compared to an observer on earth.

I've done a lot of searching for formula's to use, and I'm still unsure of what to works for my scenario. Obviously the earth and my fictional planet would be rotating. I'd appreciate if anyone knows what formula I can use and how I can derive it. Also I'm hoping it involves some integral calculus in it because the more advanced the math is the better for my paper. Thanks!

• "I'd appreciate if anyone knows what formula I can use" As usual the answer is in the wikipedia page (though I appreciate that spotting the one most applicable might not be trivial). As for how you can derive it ... doing it properly even for a very simple case requires rather a lot of math. Jan 13, 2016 at 17:55
• I have one for gravitational time dilation, but it works by putting in the information for one planet then it assumes the observer is very far away. This is fine but won't the gravity on the planet the other observer is on make the time slower on the observers own planet? Jan 13, 2016 at 22:21
• Just have them both compare to flat spacetime. If planet A see the distant clock running 1% fast and planet B see it running 2% fast, then B sees A running fast. This problem doesn't have the symmetry of the SR motional time dilation. Jan 13, 2016 at 23:13