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You are standing on Earth’s surface during a total eclipse, and both the Moon and the...

You are standing on Earth’s surface during a total eclipse, and both the Moon and the Sun are directly overhead. What fraction is your weight decreased due to their combined tidal gravitational force?

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Answer #1

I can imagin myself here standing on earth surface when both Moon and sun are over my head.
Obviously a fraction of my weight will decrease due to both Moon and Sun's Gravitational force on me.

First talk about Moon-
Distance between earth and moon is- 384,400km or 384400000 meters.
and radius of earth is - 6371km or 6371000meters
so distace between me and moon would be: 384400000-6371000= 378029000 meters
mass of the moon- 7.34767309 × 1022
Force on me due to moon given by Newton's gravitational law:

   {m is mass of man(Me)}
  
(DO NOT CONFUSE m with meter)

force due to Sun:
Mass of the sun:
distance between sun and earth:
distance between me and sun:

force due to Sun on me:


Net force on me = Force on me due to earth -(force on me due to sun+force on me due to moon}
=
=
  
So The decrease in weight is negligible. Although it is computed on long calculations that the decrease weight in such a cases is approx 0.0000017%

  
  

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