Over 100 planets have so far been detected beyond our solar system.This is accom

Question

Over 100 planets have so far been detected beyond our solar system.This is accomplished by looking for the effect the planet has onthe star. The star is not truly stationary; instead, it and itsplanets orbit around the center of mass of the system. Astronomerscan measure this wobble in the position of a star.

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

f the planet had earth's mass, where would the center of mass ofthe system be located, relative to the center of the star, if theplanet was just as far from the star as the earth is from thesun?

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

Explanation / Answer

Data we need: mass of Jupiter: MJ = 1.8987× 1027 kilograms mass of Sun: MS = 1.98892× 1030 kilograms mass of Earth: ME = 5.9742× 1024 kilograms distance of Jupiter from the sun: DJ = 7.7857x1011m distance of Earth from the sun: DE =1.49598x1011m To compute for the center of mass relative to the center of thestar, set the zero-point or origin at the center of the star. Part A: 5MJDJ = (5MJ + MS)X X = 5MJDJ / (5MJ +MS) (just substitute the values) Part B: MEDE = (ME + MS)X X = MEDE / (ME+MS) (just substitute the values) LAST PART: Because the center of mass is farther from the star, the starwobbles more, making the wobble easier to measure thus also makingthe detection of planets easier.

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