$$\begin{array} { | l | c | c | c | c | } \hline & \text { Mass } & \text { Radius } & \text { Orbital radius } & \text { Orbital period } \ \hline \text { Moon A } & 4.0 \times 10 ^ { 20 } \mathrm {~kg} & \text { unknown } & 2.0 \times 10 ^ { 8 } \mathrm {~m} & 4.0 \times 10 ^ { 6 } \mathrm {~s} \ \hline \text { Moon B } & 1.5 \times 10 ^ { 2 } 0 \mathrm {~kg} & 2.0 \times 10 ^ { 5 } \mathrm {~m} & 3.0 \times 10 ^ { 8 } \mathrm {~m} & \text { unknown } \ \hline \end{array}$$ Mithra is an unknown planet that has two moons,A and B,in circular orbits around it.The table summarizes the hypothetical data about these moons.What is the mass of Mithra? (G = 6.67 × 10^-11 N ∙ m²/kg²) A)1 × 10²² kg B)3 × 10²² kg C)1 × 10²³ kg D)3 × 10²³ kg E)1 × 10²⁴ kg

Question

Quizplus · Accepted Answer

The mass of Mithra can be calculated using the orbital period and radius of either moon, applying the formula for gravitational force and centripetal force. For Moon A, using the formula $T^2 = \frac{4\pi^2r^3}{GM}$, where $T$ is the orbital period, $r$ is the orbital radius, $G$ is the gravitational constant, and $M$ is the mass of Mithra, we can solve for $M$. Plugging in the values for Moon A, $T = 4.0 \times 10^6 \,s$ and $r = 2.0 \times 10^8 \,m$, we find that $M$ is approximately $3 \times 10^{23} \,kg$, which corresponds to choice D.

Mithra Is an Unknown Planet That Has Two Moons,A and |