Question

A planet has been discovered around a Sun-like star with an estimated mass of 54.3 times the Earth\'s mass and an estimated radius of 15.1 times the Earth\'s radius. It has been hypothesized that the planet has abundant hydrogen in its atmosphere. In order for the planet to maintain a hydrogen atmosphere for a significant amount of time, the planet\'s temperature must be less than some maximum temperature. Recall that the mass of Earth is 5.97 × 1024 kg and the radius of Earth is 6.37 × 106 m. The universal gravitational constant is 6.67 × 10-11 N·m2/kg2. The mass of a hydrogen atom is 1.67 × 10-27 kg. Boltzmann\'s constant is 1.38 × 10-23 J/K. What is the maximum temperature Tm of the atmosphere? Assume that the hydrogen will be retained by the planet only if the RMS speed of the atoms is less than 20% of the escape velocity. Recall that the RMS speed is given by Vmrs = square root ( 3kT / m)

Answer 1