Solve the problem.
-The orbit of a satellite has a period of $T = 1436.8$ minutes. Calculate the semimajor axis of the satellite. (Earth's mass $= 5.975 \times 10 ^ { 24 } \mathrm {~kg}$ and $\mathrm { G } = 6.6720 \times 10 ^ { - 11 } \mathrm { Nm } ^ { 2 } \mathrm {~kg} ^ { - 2 }$ ).
A) $2.751 \times 10 ^ { 6 } \mathrm {~km}$
B) $2751 \mathrm {~km}$
C) $4.217 \times 10 ^ { 7 } \mathrm {~km}$
D) $42,170 \mathrm {~km}$

Question

Quizplus · Accepted Answer

The semimajor axis $a$ can be calculated using Kepler's third law: $T^2 = \frac{4\pi^2}{GM}a^3$. Solving for $a$ gives $a = \left(\frac{GMT^2}{4\pi^2}\right)^{1/3}$. Substituting the given values, $a$ is approximately $42,170 \mathrm{~km}$.

Solve the Problem T=1436.8T = 1436.8T=1436.8 Minutes Calculate the Semimajor Axis of the Satellite

Solve the Problem $T = 1436.8$ Minutes Calculate the Semimajor Axis of the Satellite