Why don't Mercury and Venus have moons?

This colorful view of Mercury was produced by using images from the color base map imaging campaign during MESSENGERís primary mission. These colors are not what Mercury would look like to the human eye, but rather the colors enhance the chemical, mineralogical, and physical differences between the rocks that make up the planetís surface. Image credit: NASA / Johns Hopkins University Applied Physics Laboratory / Carnegie Institution of Washington.

Most likely Mercury and Venus have no moons because they are too close to the Sun.

Any moon with too great a distance from these planets would be in an unstable orbit and it would be captured by the Sun. If they were too close to these planets they would be destroyed by tidal gravitational forces. The zones where moons around these planets could be stable over billions of years is probably so narrow that no body was ever captured into orbit, or created in situ, when the planets were first being accreted.

What are the specifics? Lets do the calculation of forces!

Mercury: How far from Mercury would a satellite be at which point the gravity force of the sun equals that of mercury?

G(Mp)m/rs^2 = G(Ms)m/R^2

were M is the masss of the sun, m is the mass of the satellite, rs is the distance of the satellite from the center of mercury and R is the distance from Mercury to the sun. The value for the satellite mass, m, cancils, as does the constant of gravity, G, so for R = 35 million km, Ms = 2x10^30 kg, Mp = 3.3x10^23 kg, we get with some algebra that rs = 14,000 km.

The tidal limit for the satellite, which is the point at which the tidal gravity force of Mercury shatters the satellite, is given by the formula R = 1.26 x Rm (Rho m/Rho M)^1/3 where Rho m is the satellites density and Rho M is the planets density. For a satellite made of mercury material the densities are the same so the tidal radius is 1.26 x Mercury's radius of 2440 km, or 3070 kilometers.

So the roughly stable orbit range for such a satellite is between 3000 km and 14,000 km from the center of Mercury, or between 600 and 11,000 km from its surface. For Venus, the same calculation woud give a significantly wider orbit range from 7600 km to 162,000 km from the planet's center, or 1600 to 156,000 km from its surface.

Clearly, Venus is a far more promissing place to stuff one or more moons, so it is a puzzle why it has none, unless the catastrophic impact that tilted Venus's rotation axis also stripped off any primordial, orbiting moons.

Return to Dr. Odenwald's FAQ page at the Astronomy Cafe Blog.