Question

M moon = 7.35 times 10 to the 25 grams

M sun = 1.989 times 10 to the 33 grams
D earth-moon = 384,000 kilometers
D earth-sun = 1.50 times ten to the 8 kilometers

Using the above data to determine the ratio of the tidal force on you due to the Sun over the tidal force on you due to the Moon.

Answer 1

Fs/Fm = 176.8

Step-by-step explanation:

The tidal force due to a planet on earth can be given by Newton's Law of Gravitation:

F = Gm₁m₂/r²

where,

F = Tidal Force = ?

G = Gravitational Constant

m₁ = mass of 1st planet

m₂ = mass of 2nd planet

r = distance between the planets

FOR TIDAL FORCE DUE TO SUN:

m₁ = Mass of Earth

m₂ = Mass of Sun = 1.989 x 10³³ g

r = distance between earth and sun = 1.5 x 10⁸ km

F = Fs

Therefore,

Fs = Gm₁(1.989 x 10³³ g)/(1.5 x 10⁸ km)²

Fs = Gm₁(1.989 x 10³³ g)/(2.25 x 10¹⁶ km²)

Fs = Gm₁(8.84 x 10¹⁶ g/km²) ----- equation 1

FOR TIDAL FORCE DUE TO MOON:

m₁ = Mass of Earth

m₂ = Mass of Moon = 7.35 x 10²⁵ g

r = distance between earth and moon = 3.84 x 10⁵ km

F = Fm

Therefore,

Fm = Gm₁(7.35 x 10²⁵ g)/(3.84 x 10⁵ km)²

Fm = Gm₁(7.35 x 10²⁵ g)/(14.74 x 10¹⁰ km²)

Fm = Gm₁(5 x 10¹⁴ g/km²) ----- equation 2

Dividing equation 1 by equation 2 we get:

Fs/Fm = Gm₁(8.84 x 10¹⁶ g/km²)/Gm₁(5 x 10¹⁴ g/km²)

Fs/Fm = 176.8