13.72 - One of the brightest comets of the 20th century was Comet Hyakutake, which passed close to the sun in early 1996. The orbital period of this comet is estimated to be about 30,000 years. Find the semi-major axis of this comet's orbit. Compare it to the average sun-Pluto distance and to the distance to Alpha Centauri, the nearest star to the sun, which is 4.3 light-years distant.

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Jarrod RobelLv2

16 Sep 2018

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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 1011 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 1015 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?

(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?