One of the great discoveries in astronomy in the past decade is the detection of planets outside the solar system. Since 1996, 100planets have been detected orbiting stars other than the Sun. As the planets themselves cannot be seen directly, telescopes can detect the small periodic motion of the star as the star and planet orbit around their common center of mass. Both the period of this motion and the variation in the speed of the star over the course of time can be decided observationally. The mass of the star is found from its observed luminance and from the theory of stellar structure. Iota Dracon is is the eighth brightest star in the constellation Draco. Observations show that a planet, with an orbital period of 1.50 y, is orbiting this star. The mass of IotaDraconis is 1.05MSun.
a) Estimation the size (in AU) of the semi main axis of this planet's orbit.
b) The radial speed of the star is observed to vary by627 m/s. Utilize conservation of momentum to find the mass of the planet. Suppose the orbit is circular, we are observing the orbit edge-on, and no other planets orbit IotaDraconis. Express the mass as a multiple of the mass of Jupiter.