Over 500 planets have so far been detected beyond our solar system. This is acco

Question

Over 500 planets have so far been detected beyond our solar system. This is accomplished by looking for the effect the planet has on the star. The star is not truly stationary; instead, it and its planets orbit around the center of mass of the system. Astronomers can measure this wobble in the position of a star.

Part A

For a star with the mass and size of our sun and having a planet with four times the mass of Jupiter, where would the center of mass of this system be located, relative to the center of the star, if the distance from the star to the planet was the same as the distance from Jupiter to our sun?

Part B

If the planet had four times earth's mass, where would the center of mass of the system be located, relative to the center of the star, if the planet was just as far from the star as the earth is from the sun?

Part C

In view of your results in Parts A and B, why is it much easier to detect stars having large planets rather than small ones?

Explanation / Answer

(A) r_cm = (m1 r1 + m2 r2) / (m1 + m2)

r_cm = ( 0 + (1.898 x 10^27)(778.5 x 10^9)) / ((2 x 10^30) + (1.898 x 10^27))

r_cm = 738 x 10^6 m .....Ans

(B) r_cm = ( 0 + (4 x 5.972 x 10^24)(149.6 x 10^9)) / ((2 x 10^30) + (5.972 x 10^24))

r_cm = 1.79 x 10^6 m .....Ans

(C) because of there distinguisable positionof center of mass.

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