Calculate Time Difference: Relativity Equation for Sun and Earth Masses

[kajak]

Hey everyone,

This is my 1st post here. I need help in finding an equation. I read the time moves slower for larger objects that smaller ones. For example a day form the sun’s point of view could be equal to let's say a month in earth’s view. So if I have the mass of Earth and the sun’s mass how can I calculate the exact difference in time? I.e.: 1 sun day equals how many human days. I hope o asked in a clear way. I’m not asking how many times the Earth rotates in 1 sun rotation. Thanks in advance

 

[Tzemach]

Time moves more slowly in a gravitational field, but the difference between the Sun and Earth gravitational fields is not that great. Gravity depends on density and distance from the centre of gravity so the sun although far larger than the Earth does not experience a time frame that is greatly different to that on Earth.

 

[kajak]

well i am aware of that. i gave the Earth and the sun as examples. i need the equation to calculate larger sizes.

 

[yogi]

It has nothing to do with size - clocks run slower in a stronger gravitational potential - if you placed a clock "A" close to an object the size of the Earth that had a much larger density than the earth, the clock "A" would run slower than a clock "B" placed near the surface of the Sun.

 

[Tzemach]

In order to understand this you have to examine the behaviour of gravity which is inversely proportional to the distance from the centre of gravity. In other words a clock at sea level and a clock at the top of a tall building will measure time at different rates, even though they are both on Earth. Even your feet experience more gravity than does your head.

Try this example which I hope will help you to understand how a gravity field operates. The mass of the Earth is 81.3 times greater than the Moon, so we might expect the Earth’s gravity to be 81.3 times greater than that of the moon. Gravity weakens as we move away from the centre of gravity. This means that on the surface of the moon, we are 1,738 km from its centre of gravity but on the Earth’s surface, we are 6,371 km from the centre of gravity. This distance is 3.666 times greater on Earth, so to compare surface gravity we need to divide Earth’s 81.3 times greater gravitational potential by 3.666(squared) or 13.44. The result is that Earth’s gravity is only 6.05 times greater than the moon’s despite its mass being 81.3 times greater.