Planet around HD209458

HD209458 is a star which is similar to the Sun and is 150 light years away in the constellation Pegasus. It was discovered in november 1999 from the displacement of spectral lines (see fig.) that the radial velocity of the star varied perodically with a period of 3,52 d and an amplitude of 82 m/s. This must be due to a rather large body orbiting the star and pulling on it. Using the measurements one may calculate the orbit and the mass of this invisible body. Because the astronomers did not know the angle of the orbital plane with respect to the line of sight, they could only estimate   these parameters.

Some days later it was discovered that the luminosity of the star decreased 1,7 % at 3,52 d intervals. It seems very reasonable to suppose that the line of sight lies in the orbital plane of the invisible body, and that the body passes in front of the star and partially eclipses it. From the decrease in the luminosity and the radius of the star (which is known from its spectral type), it is easy to calculate the radius of the body. It is found to be 1,6 times the radius of Jupiter, while the mass turns out to be 0,63 Jupiter masses. This gives a density of only 200 kg/m3, and shows that it must be a large gas planet.

 

  1. Calculate the orbital radius and velocity of the planet assuming that  HD209458 has the same mass as the Sun. Compare with the value of the parameters in the simulation, and run the simulation. Observe the velocity of the star (which is given with respect to the center of mass). Does it agree with the numbers on the figure above?

  2. Use conservation of momentum and calculate the velocity of the star towards us at the moment when the planet goes straight away from us. Does your answer agree with the figure and the simulation?