Gravitational Pull: Sun vs. Earth's on Moon

[acvessey]

Hi. I'm totally new to this forum because I am not seeing what I would refer to as 'logic' on wiki.
I'll make this one easy for someone! Can anyone direct me to a website which might clearly explain the following statement:
"The Sun's gravitational pull on the Moon is over twice as great as the Earth's pull on the Moon": copied from: http://en.wikipedia.org/wiki/Orbit_of_the_Moon
Surely a low density and relatively small (distant) attractor such as our Sun, have a lesser pull than a high density, relatively large (close) object such as our Earth on our Moon? otherwise the Moon would not be in Earth's orbit but rather, falling out of our orbit and toward the sun. Isn't that why the Moon has a huge tidal effect on our oceans but the Sun has bugger-all? Doesn't a rock and feather fall toward an attractor at the same rate in a vacuum!
Cheers.
Tony V

 

[D H]

Do the math. The Sun is 333000 times as massive as is the Earth, and is 389 times further from the Moon that is the Earth. 333000/389^2 = 2.2.

 

[jtbell]

Or look up the masses of the sun, moon and earth, and the distances between the Earth and sun (which is the same as the average distance between the moon and the sun) and between the Earth and moon, and calculate the gravitational forces using Newton's law of gravitation.

 

[K^2]

otherwise the Moon would not be in Earth's orbit but rather, falling out of our orbit and toward the sun.

The moon is traveling at 30km/s ±1km/s around the Sun. The 30km/s is what prevents both the Earth and the Moon from falling onto the Sun. The ±1km/s is due to orbit around the Earth.

The way to look at it is that you can consider the Earth-Moon system going around the Sun from a rotating frame in which Earth remains fixed (ignoring elipticity of the orbit). In that rotating frame, centrifugal force acts on both Earth and Moon and keeps both from falling onto the Sun. In addition to that, the Moon is going around in circles around Earth with gravity providing centripetal force for that motion. There is, of course, also the Coriolis effect, which will alter the Moon's orbital period slightly.

 

[Drakkith]

Surely a low density and relatively small (distant) attractor such as our Sun, have a lesser pull than a high density, relatively large (close) object such as our Earth on our Moon? otherwise the Moon would not be in Earth's orbit but rather, falling out of our orbit and toward the sun. Isn't that why the Moon has a huge tidal effect on our oceans but the Sun has bugger-all? Doesn't a rock and feather fall toward an attractor at the same rate in a vacuum!
Cheers.
Tony V

Imagine you are in free fall towards the Earth. (We are going to ignore things like friction from air and such) You have a ball that you let go along side you. Both you and the ball fall at the same rate. If you could fall for a long enough period of time you would see that you and the ball start to move towards each other thanks to your mutual gravity.

The same effect occurs with the Earth and Moon. Both are in free fall around the Sun thanks to its gravity, and both are also attracted to each other, forming another orbital system.