You Are the Science Officer on a Visit to a Distant

Multiple Choice

You are the science officer on a visit to a distant solar system. Prior to landing on a planet you measure its diameter to be $1.8 \times 10 ^ { 7 } \mathrm {~m}$ You have previously determined that the planet orbits $2.9$ $\times 10 ^ { 11 }$ m from its star with a period of 402 earth days. Once on the surface you find that the acceleration due to gravity is 19.5 \mathrm{~m} / \mathrm{s}^{2} . What are the masses of (a) the planet and (b) the star? $( G =$ $\left. 6.67 \times 10 ^ { - 11 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { kg } ^ { 2 } \right)$

A) $\text { (a) } 2.4 \mathrm{~kg} \times 10^{25} \mathrm{~kg} \text {, (b) } 7.1 \mathrm{~kg} \times 10^{30} \mathrm{~kg}$
B) $\text { (a) } 2.4 \mathrm{~kg} \times 10^{25} \mathrm{~kg} \text {, (b) } 1.2 \mathrm{~kg} \times 10^{31} \mathrm{~kg}$
C) $\text { (a) } 4.3 \mathrm{~kg} \times 10^{25} \mathrm{~kg} \text {, (b) } 1.2 \mathrm{~kg} \times 10^{31} \mathrm{~kg}$
D) (a) $4.3 \mathrm{~kg} \times 1025 \mathrm{~kg}$
(b) $7.1 \mathrm{~kg} \times 10^{30} \mathrm{~kg}$