A 50-kg satellite circles the Earth in an orbit with a period of 120 min. What minimum energy is required to change the orbit to another circular orbit with a period of 180 min? (Earth: radius = 6.4 × 10⁶ m, mass = 6.0 × 10²⁴ kg) A) 2.9 × 10⁸ J B) 3.5 × 10⁸ J C) 4.1 × 10⁸ J D) 4.7 × 10⁸ J E) 5.9 × 10⁸ J

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Quizplus · Accepted Answer

The minimum energy required to change the orbit can be calculated using the formula for the total energy of a satellite in orbit, which is $E = -\frac{GMm}{2r}$, where $G$ is the gravitational constant, $M$ is the mass of the Earth, $m$ is the mass of the satellite, and $r$ is the radius of the orbit. The radius of the orbit can be related to the period $T$ by the third Kepler's law, which states $T^2 \propto r^3$. The energy difference between the two orbits is needed, which involves calculating the total energy for each orbit and finding the difference. The correct calculation based on these principles results in an energy change of approximately $2.9 \times 10^{18}$ J.

A 50-Kg Satellite Circles the Earth in an Orbit with a Period