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Q & A: Effect of sun and moon on one's weight during the day

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Most recent answer: 07/31/2020
Q:
Sun's gravitational pull on earth bound objects is about 0.0006 of earth's gravity. So if a mass at noon on the equator weighs exactly 200 lb, (sun's gravity opposed to earth's gravity) will it weigh more at midnight, when the sun's gravitational pull is "in line" with the earth's gravity?
- Henry Hall (age 66)
Elkins Park, PA, US
A:

Hello Henry,

There is very little difference in your weight at noon or midnight due to gravity effects of the sun.   Think of what a scale measures. It measures the force that is needed to keep you "at rest" on Earth, meaning accelerating along with the earth as the earth orbits the sun, always accelerating toward the sun.   So at noon the earth's acceleration is pushing you up, adding to your weight. If the sun's gravitational field were uniform, that would be exactly the amount of extra weight needed to make up for the sun's upward pull on you. In other words, in a uniform field you, the earth, and the scale would all be accelerating together and so the field would produce no noticeable effects on the combination. That's called the equivalence principle. So the fairly big effect you're thinking of just doesn't happen.

Now the sun's field isn't quite uniform, since it gets stronger closer to the sun. That means that at noon, it's pulling you toward it just a little more than the extra upward push you get from the earth. So yes, your weight is a tiny bit less at noon due to the sun's pull. What about at midnight? You're now farther from the sun, so it's downward pull isn't quite enough to make up for the earth being pulled out from under you toward the sun. So you also weigh a little less at midnight. You weigh a little more at dawn and sunset, because the direction toward the center of the sun has just a little in common with the direction toward the center of the earth, so the sun then is pulling you "down" a bit. These effects, the same ones that cause tides, amount to much less than 0.0006 of your net weight.

A more technical explanation is that any effects due to an external gravitational field must be of a quadrupole shape rather than a dipole shape.  I recommend you take a look at the Wiki article 

  for a pretty good discussion of tidal effects.

LeeH and Mike W.


(published on 07/18/2015)

Follow-Up #1: different moon tides

Q:
How can you say that the moon�S gravitation is a .0006 factor on your weight when gravitation is a function of distance squared and when the moon is pulling up on you, it�s much much closer to you than when the distance is away from you�it varies. What does the math say when it�s a solar eclipse, vs the middle of the night with the moon on the other side of the world in a universe where the earth�s axis was vertical and all orbits were co planar?
- Brad (age 47)
MD
A:

Again, it's only how much the moon's pull is changing near the earth that matters, not the average pull. These changes are stronger the closer you are to the moon. in fact, that tidal effect goes as 1/distance3 rather than 1/distance. So the effect is very slightly larger when you're on the same side as the moon than when you're on the opposite side. Since the earth's size is small compared to the distance to the moon, the effects are the same to much better than the one-digit acuracy we gave.

Mike W.


(published on 07/31/2020)

Follow-up on this answer.