Someone claims Youre heavier at night than during the day b

. Someone claims “You’re heavier at night than during the day, because during the night the Sun’s gravity adds to Earth’s, while during the day it partially cancels it.” Is this claim reasonable? If someone has an apparent weight of exactly 500 N during the day, what is her apparent weight at night?” Note: The Sun’s mass is 2 × 10^30 kg, and it is 1.5 × 10^11 m from the Earth

Solution

Yes the claim is reasonable.

During night,

the apparent weight,

W = G*Me*m/r^2 + G*Ms*m/R^2

where Me = 5.97*10^24 kg

Ms = 2*10^30 kg

r = 6.378*10^6 m

So, Wn = (6.67*10^-11*5.97*10^24/(6.378*10^6)^2 + 6.67*10^-11*2*10^30/(1.5*10^11)^2)*m

So, Wn = 9.795*m

At day, the apparent weight,

Wd = (6.67*10^-11*5.97*10^24/(6.378*10^6)^2 - 6.67*10^-11*2*10^30/(1.5*10^11)^2)*m

= 9.783*m = 500 N

So, m = 500/9.783

So, apparent weight at night = Wn = 9.795*(500/9.783)

So, Wn = 500.6 N <------answer