An extrasolar planet can be detected by observing the wobble it produces on the

Question

An extrasolar planet can be detected by observing the wobble it produces on the star around which it revolves. Suppose an extrasolar planet of mass revolves around its star of mass . If no external force acts on this simple two-object system, then its CM is stationary. Assume and are in circular orbits with radii and about the system's CM. given that the Ra=1.2x10^9, 1. When viewed from Earth, the distant system appears to wobble over a distance of 2Ra. If astronomers are able to detect angular displacements theta of about 1 milliarcsec (1 arcsec = 1/3600 of a degree), from what distance d (in light-years) can the star's wobble be detected (1 ly= 9.46x10^15 m) ? 2.The star nearest to our Sun is about 4*ly away. Assuming stars are uniformly distributed throughout our region of the Milky Way Galaxy, about how many stars can this technique be applied to in the search for extrasolar planetary systems?

Explanation / Answer

A) Find radius of the star's orbit about the system's CM. (answered)

ra= (mb)(rb)/ma=

B)Now consider a Sun-like star and a single planet with the same characteristics as Jupiter. That is, and the planet has an orbital radius of 7.8×1011 . Determine the radius of the star's orbit about the system's CM. (answered)

*used formula above: ra=1.2x10^9

C)When viewed from Earth, the distant system appears to wobble over a distance of . If astronomers are able to detect angular displacements of about 1 milliarcsec (1/3600 of a degree), from what distance d (in light-years = 9.46E15) can the star's wobble be detected ? (answered)

d = 37 lightyears; I found the answer by using the ArcLength formula:

Arclength=Radius of Arc*theta

D) The star nearest to our Sun is about 4 lightyears away. Assuming stars are uniformly distributed throughout our region of the Milky Way Galaxy, about how many stars can this technique be applied to in the search for extrasolar planetary systems?

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