Is Coriolis force weak or strong?

Question

What is the ratio of Coriolios force acting on the Moon (from the point of view of observer on Earth) to the force of Earth gravity acting on the Moon?

Data:
One revolution of Earth: 24 hours
One revolution of Moon: 28 days
One revolution of low-orbit satellite: 85 minutes

Sadly, they forgot to tell me the following data needed to implement Rick's solution:

m = moon's mass
v = velocity of moon as seen in reference frame of rotating earth.
G = universal gravititational constant
M = Earth's mass
r = distance to moon


Looks like I am going to score F on this.

Answer 1

I won't do your homework for you; but you should use these formulas:

Coriolis force acting on the moon:

Fc = 2mωv

where:
m = moon's mass
ω = rate of earth's rotation (in radians/sec)
v = velocity of moon as seen in reference frame of rotating earth.

Gravitational force acting on the moon:

Fg = GMm/r²

where:
G = universal gravititational constant
M = Earth's mass
m = moon's mass
r = distance to moon

The ratio therefore is:

Fc/Fg = (2mωv)/(GMm/r²) = (2ωv)/(GM/r²)

Now use these facts:

v is a combination of the moon's "apparent" velocity due to the earth's rotation, along with its "real" velocity due to its orbit (which is in the opposite direction).

v = v_apparent – v_orbit
= ωr – v_orbit

Furthermore, if you assume the moon's going in a circle, you can use this:

acceleration = v_orbit²/r [formula for circular acceleration]
acceleration = GM/r² [Gravity law & Newton's 2nd]

From which:

v_orbit = sqrt(GM/r)

So:
Fc/Fg = (2ωv)/(GM/r²)
= (2ω(v_apparent – v_orbit))/(GM/r²)
= (2ω(ωr – sqrt(GM/r)))/(GM/r²)

Answer 2

There is no clear information whether this force is stronger at equator or poles. Coriolis effect The Coriolis effect is the apparent deflection of moving objects from a straight path when they are viewed from a rotating frame of reference. The effect is named after Gaspard-Gustave Coriolis, a French scientist who described it in 1835, though the mathematics appeared in the tidal equations of Pierre-Simon Laplace in 1778. One of the most notable examples is the deflection of winds moving along the surface of the Earth to the right of the direction of travel in the Northern hemisphere and to the left of the direction of travel in the Southern hemisphere. This effect is caused by the rotation of the Earth and is responsible for the direction of the rotation of large cyclones: winds around the center of a cyclone rotate counterclockwise on the northern hemisphere and clockwise on the southern hemisphere.

Answer 3

The Coriolis force is proportional to its acceleration. (Not; weak or strong are ambiguous terms)
This type of acceleration happens when a body accelerates on another body.

If you want to compare it to the acceleration of gravity these conditions make it weak.