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Fahad Jan
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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 mb revolves around its star of mass ma . If no external force acts on this simple two-object system, then its CM is stationary. Assume ma and mb are in circular orbits with radii ra and rb about the system's CM.
(a) Show that ra =(mb/ma)rb
(b) Now consider a Sun-like star and a single planet with the same characteristics as Jupiter. That is, mb = (1.0 x 10-3)ma and the planet has an orbital radius of 8.0 x 1011 meters. Determine the radius ra of the star's orbit about the system's CM.
(c) When viewed from Earth, the distant system appears to wobble over a distance of 2ra . If astronomers are able to detect angular displacements ? 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 = 9.46 x 1015 m)?
(d) That 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?
(a) Show that ra =(mb/ma)rb
(b) Now consider a Sun-like star and a single planet with the same characteristics as Jupiter. That is, mb = (1.0 x 10-3)ma and the planet has an orbital radius of 8.0 x 1011 meters. Determine the radius ra of the star's orbit about the system's CM.
(c) When viewed from Earth, the distant system appears to wobble over a distance of 2ra . If astronomers are able to detect angular displacements ? 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 = 9.46 x 1015 m)?
(d) That 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?
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