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23 Nov 2019
An extrasolar planet can be detected by observing the wobbleit produces on the star around which it revolves. Suppose anextrasolar planet of mass mb revolves around its star of mass ma .If no external force acts on this simple two-object system, thenits CM is stationary. Assume ma and mb are in circular orbits withradii 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 thesame characteristics as Jupiter. That is, mb = (1.0 x 10-3)ma andthe planet has an orbital radius of 8.0 x 1011 meters. Determinethe radius ra of the star's orbit about the system's CM. (c) When viewed from Earth, the distant system appears towobble over a distance of 2ra . If astronomers are able to detectangular displacements ? of about 1 milliarcsec (1 arcsec = 1/3600of a degree), from what distance d (in light years) canthe star's wobble be detected (1 ly = 9.46 x 1015 m)? (d) That star nearest to our Sun is about 4 ly away. Assumingstars are uniformly distributed throughout our region of the MilkyWay Galaxy, about how many stars can this technique be applied toin the search for extrasolar planetary systems?
An extrasolar planet can be detected by observing the wobbleit produces on the star around which it revolves. Suppose anextrasolar planet of mass mb revolves around its star of mass ma .If no external force acts on this simple two-object system, thenits CM is stationary. Assume ma and mb are in circular orbits withradii 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 thesame characteristics as Jupiter. That is, mb = (1.0 x 10-3)ma andthe planet has an orbital radius of 8.0 x 1011 meters. Determinethe radius ra of the star's orbit about the system's CM.
(c) When viewed from Earth, the distant system appears towobble over a distance of 2ra . If astronomers are able to detectangular displacements ? of about 1 milliarcsec (1 arcsec = 1/3600of a degree), from what distance d (in light years) canthe star's wobble be detected (1 ly = 9.46 x 1015 m)?
(d) That star nearest to our Sun is about 4 ly away. Assumingstars are uniformly distributed throughout our region of the MilkyWay Galaxy, about how many stars can this technique be applied toin the search for extrasolar planetary systems?
28 Jun 2023
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Elin HesselLv2
12 Feb 2019
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