Astronomy/What is the logic behind the Hill Sphere?
According to Wikipedia, Hill Sphere is : the volume of space around an object where the gravity of that object dominates over the gravity of a more massive but distant object around which the first object orbits.
True as this may be, it just mathematically supports a phenomenon that has been observed but it does not give reason or logic as to why does this happen in the first place. I mean why should the gravity of a less massive object dominate the gravity of a more massive one?
I wasn't aware of the Hill Sphere until recently when I was trying to visualize the orbits of different celestial bodies. The Hill Sphere comes closest to explaining why the moon orbits the Earth, more than it orbits the Sun and why the Earth orbits the sun, more than it orbits the center of our galaxy. By this logic all celestial bodies within the Gravitational pull of the center of our galaxy should directly be orbiting the center.
My argument is that if the Hill sphere of the Sun is as large as the solar system itself, any object within this sphere should be orbiting the sun. Why was the moon caught into the earth's gravitational pull in the first place when it had a much stronger pull from the sun?
The answer to this would also eventually clarify why the earth orbits around the sun and not the center of the milky way.
First of all, the gravity of a less massive object can dominate the gravity of a more massive one if the distance of the latter is great enough. Bear in mind the force of gravitational attraction varies inversely as the square of the distance.
Second, in terms of the Earth-Moon system, the force of the Sunís gravity on the Moon is more than twice the force of Earthís gravity on the Moon. This was first noted by science writer Isaac Asimov in his book 'The Collapsing Universe' and why he coined the term "double planet".
At the same time, things aren't so simple as Asimov led readers to believe, since the Hill sphere must also be factored in - as you noted. The same wikipedia article you citd also shows the Earthís Hill sphere has a radius of about 1.5 million kilometers, while the Moonís orbital radius of 400,000 km keeps it well within the Earthís Hill sphere. From this perspective, the Moon orbits the Earth more than it orbits the Sun.
But in technical terms asserting the supremacy of one orbital dynamic over the other is wrong- since both are valid.
The Sun is pulling on *both* the Earth and the Moon and since both the Earth and Moon are roughly the same distance from the Sun the force acceleration due to the Sunís gravity on the Moon and the Earth is about the same. That means the Sunís gravity is important in keeping the Earth and Moon together orbiting the Sun, but doesnít affect the Earth and Moon as a system. The Moon is still gravitationally bound to the Earth.
It turns out that Asimov's scenario would only actually come into play if you moved the Earth and Moon to about 40 million km from the Sun ó closer to the Sun than Mercury. Then if you re-calculated the Hill sphere of the Earth it would be 400,000 km, or equal to the moonís distance from the Earth now. That means the Moon could be stripped from the Earth by the Sun, so then you could say (as Asimov implied) that the Moon orbits the Sun and not the Earth.
Now, note that extrapolating this Hill sphere concept to the galaxy and universe as a whole is not advised since these do not really exhibit true Keplerian orbits. The galaxy revolves more as a disc though Keplerian estimates can be used as *approximations*. As for the universe, given the complex issues of galactic cluster dynamics I wouldn't being to speculate how it would work in those generalized terms.
Bottom line is that the Hill sphere concept is useful for planetary systems and moons, possibly in the solar system too, but not really applicable in more expansive scales such as you suggest.