Why doesn’t sun pull moon towards it?
Seriously. why doesn’t that happen? Well there are a few things we should know before knowing the answer.
Well the key things we should know is that
Earth and Moon go around the sun together, as if they are one single body.
When three bodies interact due to gravitation, their motion is determined by position relative to what is known as the Hill Sphere of each.
Hill Roche sphere
For a moon to be retained by a planet the moon must have an orbit that lies within the planets Hill sphere. In other terms the Hill sphere approximates the gravitational sphere of influence of a smaller body by the gravitational pull from a more massive body.
The radius of the Hill Sphere is given by
Below is an image showing the Hill sphere of earth and sun.
Here the points L1,L2,L3,L4 and L5 are so called Lagrange points of the bodies.
Lagrange points are positions in an orbital configuration of two large bodies where a small object affected only by gravity can maintain a stable position relative to the two large bodies.
Now the answer to the question.
In the Earth example,
The Earth (5.97×1024 kg) orbits the Sun (1.99×1030 kg) at a distance of 149.6 million km.
The Hill sphere for Earth thus extends out to about 1.5 million km (0.01 AU). The Moon’s orbit, at a distance of 0.384 million km from Earth, is comfortably within the gravitational sphere of influence of Earth and it is therefore not at risk of being pulled into an independent orbit around the Sun.