talkingaway wrote: ↑
Wed Feb 10, 2021 5:14 pm
Volante wrote: ↑
Wed Feb 10, 2021 12:26 pm
alietr wrote: ↑
Wed Feb 10, 2021 11:50 am
Airplane Sun Moon.PNG
That just raises further questions!
I'm wondering if they meant, "Which of these directly overhead would reduce your weight the most compared to being directly underneath?" which would be the moon.
But would it? If the sun's pulling you with x newtons of force upwards when it's above, then it's pulling you down x newtons when it's below, for a difference of 2x. Same for the moon, so it just depends on which x is bigger - and I think like you calculated before, it's bigger by a factor on the order of hundreds.
I'm temporarily assuming a geocentric view of the world, and perfectly circular orbits. And that all three bodies are fundamentally point masses. Maybe I'm missing something in the geometry of the situation?
Not the geometry, but that the formula for gravitational force squares the distance.
The airplane already has zero effect so nuts to the airplane. Meanwhile, while the sun does has a massive effect, it's so far away, adding 8,000^2 to the divisor is more negligible since you're already squaring 92,000,000 on top of that.
The moon, however, is at a distance of 238,900 miles and adding 8,000 to that is a significant change, making a force of = 0.002464 N (newtons) or a change of .000167 N
Just to confirm my hypothesis, doing a farther sun calculation I get .47078. I recalculated the closer to .47086 because WA rounds to four sig figs for final solution (.4709 - .4708 wouldn't cut it, that could be anywhere from .00001 to .00019, and .000167 is between those), giving a delta change of .00008 N.
So standing on the earth, the moon pulls you away from the earth more when it is directly overhead than pulls you toward the earth if it is directly opposite.