# Seasons and General Relativity

*Most recent answer: 04/07/2013*

Q:

Gravitational time dilation teaches us that a clock (time) goes faster as it is further away from a source of gravitation. Does this imply that time changes as the earth moves further from or closes to the sun (i.e. Winter or summer)?
If this is true, is it possible to measure or calculate this seasonal difference in time?

- Yves Muyters (age 24)

Antwerp, Belgium

- Yves Muyters (age 24)

Antwerp, Belgium

A:

First a simple old-fashioned point: the seasons do not correpond to how close the Earth is to the Sun. If they did, the seasons would be the same in the north and south hemispheres, rather than opposite. The distance changes have a real effect on the seasonal changes but less important than the changes in the orientation of the tilted spinning Earth toward the sun.

The small fractional changes are easy to calculate: gD/c

Mike W.

The small fractional changes are easy to calculate: gD/c

^{2}, where g is the gravitational field, D is the distance change, and c is the speed of light. I tried a quick calculation of the change in clock rate (as compared with some distant clock) as the Earth changes its distance from the Sun and got about a fractional change of 3*10^{-12}. That's well above the accuracy of modern standard clocks, around one part in 10^{14}per day. I don't know if it's been measured, however, since a comparison of any two clocks on Earth wouldn't show the effect. It could be measured using clocks in separate orbit around the Sun, but I haven't found a description of that having been done.Mike W.

*(published on 04/07/2013)*