These questions concern a planet orbiting the star hd209548 which has a mass mstar = 1.05 times that of the sun. several years ago, a planet was discovered orbiting around this star with an orbital period of only 3.524 days. the plane of the planet's orbit around hd209548 is edge-on to our line of sight. for this problem, you may assume the planet is in a circular orbit (in reality this is a good approximation, since the eccentricity of the planet's orbit is only 0.08) and that the planet's mass is much smaller than the mass of the star. a) find the planet's average distance (semi-major axis) from the star hd209548. express your answer in meters. b) at what distance from the centre of the star is the centre of mass of the star-planet system located if the planet has a mass mp = 0.5 times that of jupiter (mj)? 1.0mj? c) what is the orbital velocity of the star around the centre of mass of the star-planet system for the cases given above? d) write an equation for the orbital velocity of the star in terms of the planet mass the observed velocity of the star is 86 m/s. what is the mass of the planet? express your answer in jupiter masses. (if you cannot do this problem, you may assume mp mj for the remaining problems. if you do, state this assumption clearly in your answers.) e) explain in a few sentences why, according to the theory of our solar system, we would not expect a planet of that size so close to the star. f) the plane of the planet's orbit around hd209548 is nearly edge-on to our line of sight. we know this because we see a transit of the planet in front of the star. the duration of time in which the planet is in front of the star is 2.88 hours. use this fact to estimate the radius of the star. (hint: draw a diagram. you may also need to calculate the planet's orbital velocity around the star.) (this problem is quite tricky. if you cannot do it, you may assume rstar = ro for the remaining problems. if you do, state this assumption clearly in your answers.) g) during the transit, the light from the star drops by 1.7%. assume that this star has the same luminosity as the sun, and that it is equally bright over its surface as seen from earth. use this information and your answer from above to estimate that the radius of the planet. h) based on your estimate of its radius, what is the planet's average density? compare this with the terrestrial and jovian planets in our solar system