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

An extrasolar planet can be detected by
observing the wobble it produces on the star around which it revolves. Suppose
an extra solar 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

(b) Now consider a Sun-like star and a
single planet with the same characteristics as Jupiter. That is, mB  =
1.0 X 10-3mA and the planet has an orbital radius of 8.0
X 1011 m. Deter mine the radius rA of the star’
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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 extra solar 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

(b) Now consider a Sun-like star and a
single planet with the same characteristics as Jupiter. That is, mB  =
1.0 X 10-3mA and the planet has an orbital radius of 8.0
X 1011 m. Deter mine 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 =  of a degree), from what distance d (in light-years) can the star’s
wobble be detected (1 ly = 9.46 X 1015m)? (d) 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?

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