MadSci Network: Astronomy

Re: Is the distance between the Sun and Earth changing?

Date: Sat Nov 11 13:09:07 2000
Posted By: Benjamin Monreal, Grad student, Physics, MIT
Area of science: Astronomy
ID: 971695883.As

Hello Jerry,
Yep---the Earth does experience tidal friction from the Sun, and this helps slow its rotation (as well as the Sun's rotation) and causes the Earth to increase the size of its orbit. Rather, it should, although the effect seems to be too small to measure.

Tidal friction is much more visible in the case of the Moon. Tides have dissipated all of the Moon's rotational energy; that's why the same side is always facing us. The Moon is also slowing down the Earth's rotation; ten million years ago, there were 400 days in a year since the Earth was spinning faster. Eventually, the Earth will also lock phase with the Moon, and days will be 50 times longer. (A month and a day will be exactly the same length.) The reason that the Moon has to move away is that the Earth/Moon system has to conserve angular momentum. Some of the system's original angular momentum was in the monthly orbit of the Moon, and some was in the daily rotation of the Earth. As the angular momentum of the Earth drops, you have to add angular momentum to the Moon's orbit, which means the Moon has to move away.

The effect due to the sun is much much smaller; firstly, tides due to the Sun are smaller. Secondly, the Earth's daily rotation is a vanishingly small part of the angular momentum of the Sun/Earth system. I did a quick calculation: the Earth's rotation contributes one ten-millionth to the angular momentum of the Earth-Sun system. In the future, when the Earth is rotating 1/50th as fast, it will contribute two billionths. That gives you an idea of how much the length of the year might change when the Earth has stopped rotating altogether, I-don't-know-how-many billions of years from now; in order to stop the Earth's rotation, you have to increase its orbital momentum by a few billionths. Since the year-length is only known to one part in a billion anyway, we'll never see this effect on human timescales. (This is a very coarse calculation, I know! But scientists get a lot of mileage out of "order of magnitude" thinking.)

Good question, thanks. Hope this helps! If you want to do some calculations yourself, you can get numbers from

-Ben Monreal

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