# Q & A: Earth's acceleration and gravity

Q:
The fact that the Earth revolves around the sun must create a "centrifical force" that pulls objects outward away from the sun. This would mean an object is lighter at night than it is during the day. At night this initia would pull the object away from Earth and in the day it would push it toward Earth. Has this phenomenon been named, measuerd, or calculated?
- Robert Clymer (age 51)
Los Angeles, CA US
A:
This effect is certainly calculable, which we'll proceed to do.

First, you should realize that the main part of the effect you're discussing doesn't exist. Yes, the earth is accelerating toward the sun, which would create a gravity-like "centrifugal force" away from the sun, as observed in the earth-frame. However, there is of course a gravitational force toward the sun, and these effects cancel. The simplest expression of that cancellation is Einstein's equivalence principle- that phenomena in free fall in a uniform gravitational field are indistinguishable from those in free fall in the absence of the field.

Along the lines you point to, the acceleration toward the sun is a little bigger for the part of the earth farther from the sun, because it's going farther in the same length of time than the part near the sun.  That means that (in the earth frame) there's a small net outward force on the outer (night) part and a small net force toward the sun on the inward (day) side. (Again, we're using the earth frame.)  Both point up from the earth. So they don't cause a day-night difference.

All that's left are little deviations from uniformity in the field. The day part of the earth is closer and thus pulled toward the sun a little extra hard- an upward effect. The night part is farther away and thus pulled a little more weakly- again giving an upward force. These are the effects that give rise to the tides (along with similar and somewhat stronger effects from the moon). So, on average over a month to eliminate the moon tides,  you weigh a little less in the middle of the night and at noon than you do in the morning and the evening.

Of course the tides are very easily observed. Although moon tides are stronger than sun tides, the latter are strong enough to make a big difference. At some points in the month they add to the moon tides and at others they subtract.

Mike W.

(published on 11/25/2012)