User:Mark Widmer/sandbox

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

Draft for additions to Hill_sphere New sections:

Hill sphere of the Sun

The Sun has a Hill sphere as well, though the formulas listed earlier are not applicable since the Sun does not orbit a compact object. Two considerations that determine the Sun's Hill sphere are (1) that the Sun orbits the center of mass of the extended distribution of objects that makes up the galaxy, and (2) the nearest star, Alpha xxx, can affect the orbits of objects far enough from the Sun, even though the Sun does not orbit Alpha xxx.

? Calculation/estimate of Sun's Hill radius due to Alpha Centauri?

Hill sphere of objects that orbit Earth

The Moon -- added to article

Artificial satellites in low-Earth orbit

Satellites in low-Earth orbit are too close to Earth to have smaller objects orbiting it. For a satellite of mass 1000 kg orbiting Earth at an altitude of, say, 400 km, the Hill radius is calculated to be only 26 cm, much smaller than the typical size of such a satellite. Moreover, as both the Hill radius and the size of the object (of fixed density) increase in proportion to the cube root of the mass, an object at this altitude will always be larger than its Hill radius no matter what its mass, and therefore be unable to have satellites of its own.

A spherical object with a density greater than about 14 g/cc would be compact enough to be smaller than its Hill sphere.