Question

The first extra-solar planet around a main sequence star (i.e., not a neutron star or white dwarf) was found around the star 51 Pegasi in 1995. The large planet causes a measureable motion of the star around the center of mass of the system. Pegasi 51's orbital motion had a period of 4 days indicating a very large planet very close to the star. A large planet of mass M around a small star of mass 4M. The distance between planet and star is L. Both the planet and star will orbit around the center of mass of the system (marked by the red X).
Required:
Where is the center of mass of the star-planet system?

Answer 1

Answer:

   $r_{cm}$= 1/5 L

Explanation:

To find the center of mass of the system let's use

        $r_{cm} = \frac{1}{M}$ ∑ r_i x_i

where m is the total mass of the system

let's apply this expression to our case

       

Let's set the reference frame on the star

         $r_{cm} = \frac{1}{M +4M} ( 4M 0 + M L)$

         r_{cm} = $\frac{1}{5}$ L

         $r_{cm}$= 1/5 L

Hey, the breast center is 1/5 of the distance between the star and the planet.