Two wheels roll side-by-side without sliding, at the same speed. The radius of wheel 2 is one-half (1/2) the radius of wheel 1. The angular velocity of wheel 2 is:

w'=(1/2)w

Explanation:

In order to calculate the angular velocity of the second wheel, you use the following formula:

     (1)

v: speed of the wheel 1 = speed of the wheel 2

r: radius of the wheel 1

For the second wheel you have:

r'=2r

You replace this value of r' in the following equation:

The angular velocity of the second wheel is one half of the angular velocity of the first wheel

The key is the proximity of the Moon to the Earth compared to the Sun.

Explanation:

 The Moon is closer to the Earth than to the Sun, and the formula for the gravitational force contains in the denominator the square of the distance in between the interacting objects. Such is going to be translated into a much larger denominator for the case of the Sun, than for the case of the Earth. A larger value in the denominators will produce a much smaller force

The gravitational influence of the Sun can also be observed in more subtle orbit displacements for example during Sun eclipses when the moon is clearly in between the sun and the Earth.