EvC Forum: Sun-Earth-Moon Gravity

Let's plug values^[1] in the formula gasby quotes in Message 13:

G*M*m
--------- = F
d*d

G = universal gravitational constant
M = mass of one object in Kg
m = mass of the other object
d = distance between them in Meters
F = force in Newton

G = 6.674210^-11 Nm²kg^-2
M = 5.974210²⁴ kg (mass of Earth)
m = 7.34767310²² kg (mass of Moon)
d = 405,696 km = 4.0569610⁸ m (Perigee)

For the Earth and Moon this gives:

F = (6.674210^-11 x 5.974210²⁴ x 7.34767310²²) / (4.0569610⁸ x 4.0569610⁸) N
F = 2.910³⁷ / 1.610¹⁷ N [approx.]
F = 1.810²⁰ N [approx.]

For the Sun and Earth:

m = 1.98843510³⁰ kg (mass of Sun)
d = 147,098,074 km = 1.4709807410¹¹ m (Perihelion)

F = (6.674210^-11 x 5.974210²⁴ x 1.98843510³⁰) / (1.4709807410¹¹ x 1.4709807410¹¹) N
F = 7.910⁴⁴ / 2.210²² N [approx.]
F = 3.610²² N [approx.]

For the Sun and Moon:

M = 1.98843510³⁰ kg (mass of Sun)
m = 7.34767310²² kg (mass of Moon)
d = 147,098,074 km = 1.4709807410¹¹ m (Perihelion - approximately the same as for Earth)

F = (6.674210^-11 x 1.98843510³⁰ x 7.34767310²²) / (1.4709807410¹¹ x 1.4709807410¹¹) N
F = 9.810⁴² / 2.210²² N [approx.]
F = 4.510²⁰ N [approx.]

So we have:

Earth-Moon attraction = 1.810²⁰ N
Earth-Sun attraction = 3.610²² N
Sun-Moon attraction = 4.510²⁰ N

As Coragyps worked out (with much less pain!

) in Message 15 the Earth-Sun attraction is about 100 times bigger than either of the others and the Earth-Moon attraction is two to three times bigger than the Sun-Moon attraction.

Never underestimate the power of the inverse square law

^[1] All values taken from Wikipedia.

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