Extra Solar Planet Detection by the Doppler Detection method The following slides are a summary of the classroom presentation annotating the Doppler Detection Equations from the Exoplanets.Org web site. There are seven points made in the following presentation. Know them!

Please be able to explain how each of the following seven steps are made beginning with the observation of a wobble and ending with an estimate of the planet’s mass.

1.Many separate measurements of a star’s velocity are made over a long period of time.

2. If the star “wobbles” then it has an unseen companion causing the wobble. It may be a planet or a low-mass star.

3. The period of the wobble equals the orbital period of the unseen companion.

4. Using Kepler’s 3’rd law the semi-major axis r of the unseen companion’s orbit can be calculated from the period of its orbit.

5. Using the equation for the orbital velocity, the unseen companion’s orbital velocity v PL can be calculated from its orbital semi-major axis.

6. Using the conservation of momentum principle, the mass of the unseen companion M PL can be estimated from the planet’s orbital velocity, the mass of the star and the star’s observed maximum velocity, K

7. The estimated mass is only a lower limit for the mass because the orbital inclination i is unknown. The planet’s mass may be larger.

Summary of Steps in the Doppler Detection method 1.Many separate measurements of a star’s velocity are made over a long period of time. 2.If the star “wobbles” then it has an unseen companion causing the wobble. It may be a planet or a low-mass star. 3. The period P of the wobble equals the orbital period of the unseen companion. 4.Using Kepler’s 3’rd law the semi-major axis r of the unseen companion’s orbit can be calculated from the period of its orbit. 5.Using the equation for the orbital velocity, the unseen companion’s orbital velocity v PL can be calculated from its orbital semi-major axis. 6.Using the conservation of momentum principle, the mass of the unseen companion M PL can be estimated from the planet’s orbital velocity, the mass of the star and the star’s observed maximum velocity, K 7.The estimated mass is only a lower limit for the mass because the orbital inclination i is unknown and cannot be determined from the Earth. The planet’s mass may be larger.