Celestia Forums

Is it possible for there to be large moons in orbit around 51 Pegasi-type planets or would the proximity of the star disallow such an orbit?

I've heard about the Hill radius but I've never found a formula for calculating it (or numerical solution e.g. Newton-Raphson process if an algebraic solution isn't available).

If the primary planet is less than 1/150 of the mass of the parent star, you can estimate the Hill radius as:

H = a*(Mp/[3*Ms])^1/3

where a is the semimajor axis of the planet's orbit, Mp is the mass of the planet, Ms is the mass of the star. The stable limit for satellite orbits lies at something between 1/3 and 1/2 of H, depending on the nature of the orbit.
The problem with satellites of hot Jupiters is not whether they can occupy a stable orbit, but whether they can occupy a stable orbit for any great length of time. A giant planet close to its star spins down relatively quickly (less than a million years) until it becomes a synchronous rotator. So all its moons end up orbiting faster than the planet rotates, and tidal drag draws them towards the planet (just as is happening with Phobos at present) until they impact or disintegrate into a ring system.
A detailed discussion of this is given in Stability of Satellites Around Close-in Extrasolar Giant Planets, by Barnes and O'Brien. Among other things, they predict that nothing with a mass > 2e-6 Earth masses will have survived around 51 Peg.

Grant

Thanks for that link the formulae are very useful...

Using the equations they give there and the radius given in Celestia, I get the maximum mass of 55 Cancri b satellites as 9.4e-4 Earth masses. 625km radius (assuming earth density) isn't too bad... that's somewhere between Dione and Rhea...