Interesting. It makes me wonder how low a density a planet could have and still have enough gravitation to hold together.
Zero. One of the first calc III equations we had to solve was a gas cloud of infinite size but finite mass...
Inside a star system, you would calculate a planet's roche lobe, which for a planet is basically going to be its hill sphere, roughly given by
r = R * (M2
/ (3 * M1
Setting WASP-17b's mass to 1, the parent star's mass is ~2,600
r = R * (1 / 7800)1/3
Or a bit over .05 times the radius. Not surprising since the parent star's mass is only slightly more than our Sun's, anyway.
Semiminor axis being roughly .05 AU, that gives a hill sphere radius of approximately 375,000 kilometers, or about three times the planet's radius.
However, the planet is far larger than any possible stable orbit around it. It is probably losing mass fairly rapidly, in astronomical terms.