User:Mark Widmer/sandbox

Sandbox. Mark Widmer (talk) 01:17, 5 August 2021 (UTC)

Draft for additions to Hill_sphere New sections:

Hill sphere and L1 Lagrange point

(Might go in intro or main section)

Hill sphere of the Sun

The formulas listed earlier are not applicable to calculating a Hill radius for the Sun, even though the Sun must have a Hill sphere owing to the presence of other stars in the galaxy that will significantly perturb the orbit of any object that is far enough away.

It is reasonable to consider two phenomena that could determine the Sun's Hill radius. One is the effect of the galaxy as a whole, as the Sun orbits the galactic center every xxx years. However, the distribution of the matter in the galaxy is such that the net gravitational force on the Sun is not inversely proportional to the distance from the galaxy's center. An inverse-square dependence is assumed in deriving the above formulas for the Hill radius.

Rather than considering the effect of the galaxy as a whole on objects orbiting the Sun, one can consider the effect of individual stars. In particular, that of the nearby Alpha Centauri star system. However, as the Sun and Alpha Centauri are not in bound orbits about each other, the earlier Hill radius formulas do not apply.

In the absence of a simple calculation, one can use the farthest distance to objects known to orbit the Sun to at least get a minimum value for the Hill radius. The Kuiper belt is known to extend out to about 50 AU from the Sun, while the hypothetical Oort cloud is theorized to extend as far as 50,000 AU, or 0.8 light years, away. The Oort cloud, if it exists, would establish the Sun's Hill radius as being at least ~20% of the distance to Alpha Centauri.

Hill sphere of objects that orbit Earth

The Moon -- added to article

Artificial satellites in low-Earth orbit -- added to article