A star of mass M (equal to the solar mass) with a planet (much...

A star of mass

M

(equal to the solar mass) with a planet (much smaller than the star) revolves around the star in a circular orbit. The velocity of the star with respect to the center of mass of the star-planet system is shown below: A star of mass M (equal to the solar mass) with a planet (much smaller than the star) revolves around the star in a

A star of mass M (equal to the solar mass) with a planet (much smaller than the star) revolves around the star in a

The radius of the planet's orbit is closest to (1 A. U. Earth-Sun distance)

Options

A $0.004$ A. $U$ .
B $0.008$ A.U.
C $0.004$ A.U.
D $0.12$ A.U.

Correct answer

C. $0.004$ A.U.

Step-by-step solution

\mathrm{T}^{2}=\frac{4 \pi^{2}}{\mathrm{GM}} \mathrm{a}^{2}

\frac{4 \pi^{2}}{\mathrm{GM}}=1

\mathrm{~T}=\mathrm{in}

year

\mathrm{a}=

radius in A.U.

\therefore \mathrm{T}=3

days

=\frac{3}{365}

year

\therefore \mathrm{a}=\left(\frac{3}{365}\right)^{2 / 3}

\mathrm{a}=0.04 \mathrm{A.U}

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