Question

The planet HD80606b features among the two most eccentric planets known to date. The eccentricity of its orbit around a one solar-mass star is 0.934 and it has a period of 111.44 days.

a) What is the energy of its orbit? Express it in Joules and then calculate how long the Sun could power itself were it to use this energy. This planet has a mass of 3.94 Jupiter masses. The Sun’s energy output is 4⋅1026 W.

b) If the orbit of HD80606b were to become circularized at constant angular momentum, what would be the radius of the new, circular orbit? What is the ratio of the energies of the old and new orbit?

Answer 1

we know mass of jupiter = 1.9 *10²⁷ kg

so mass of given planet m = 3* 1.9 *10²⁷ kg

                                      = 5.7 * 10²⁷ kg

time period T = 111.44 days

                   = 0.305 year

we know T² = (4²/GM) a³ where G= gravitational constant

                                                    M = mass of sun

                                                     a = semi major axis