An extrasolar planet can be detected by observing the wobble itproduces 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 the samecharacteristics as Jupiter. That is, mb = (1.0 x 10^-3)ma and theplanet has an orbital radius of 8.0 x 10^11 meters. Determine theradius ra of the star's orbit about the system's CM.
(c) When viewed from Earth, the distant system appears to wobbleover a distance of 2ra . If astronomers are able to detect angulardisplacements ? of about 1 milliarcsec (1 arcsec = 1/3600 of adegree), from what distance d (in light years) can the star'swobble be detected (1 ly = 9.46 x 10^15 m)?
(d) That star nearest to our Sun is about 4 ly away. Assuming starsare uniformly distributed throughout our region of the Milky WayGalaxy, about how many stars can this technique be applied to inthe search for extrasolar planetary systems?
An extrasolar planet can be detected by observing the wobble itproduces 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 the samecharacteristics as Jupiter. That is, mb = (1.0 x 10^-3)ma and theplanet has an orbital radius of 8.0 x 10^11 meters. Determine theradius ra of the star's orbit about the system's CM.
(c) When viewed from Earth, the distant system appears to wobbleover a distance of 2ra . If astronomers are able to detect angulardisplacements ? of about 1 milliarcsec (1 arcsec = 1/3600 of adegree), from what distance d (in light years) can the star'swobble be detected (1 ly = 9.46 x 10^15 m)?
(d) That star nearest to our Sun is about 4 ly away. Assuming starsare uniformly distributed throughout our region of the Milky WayGalaxy, about how many stars can this technique be applied to inthe search for extrasolar planetary systems?
