For orbits of greater altitude, is the period of revolution of satellite longer or shorter?

Question:

For orbits of greater altitude, is the period of revolution of satellite longer or shorter?

Kepler's Third Law:

Kepler's third law of planetary motion describes the proportionality between the square of the period of revolution and the semi-major axis radius of revolution. This law can be used in analyzing whether the relations among the altitude, period or revolution and the orbit of the satellite.

Answer and Explanation:

The orbital speed of a satellite can be represented using Kepler's third law of planetary motion. This law is given by

{eq}\displaystyle \begin{align} T^2 & \propto r^3\\ T^2 &= kr^3 \end{align} {/eq}

where {eq}T {/eq} is orbital period, {eq}r {/eq} is the semi-major axis of revolution or the radius of revolution, and {eq}k {/eq} is the proportionality constant.


Since the period is directly proportional,then orbits of greater altitude means that the distance between the planet and the satellite is greater. This requires the satellite to travel at lesser speed to avoid crashing. With greater orbit and lesser speed, we can say that the period of revolution would longer.


Learn more about this topic:

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Kepler's Three Laws of Planetary Motion

from Basics of Astronomy

Chapter 22 / Lesson 12
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