The period of a planet or satellite increases with distance...

The period of a planet or satellite increases with distance to the $3 / 2$ power. How does the orbital speed depend on distance? Does increasing the distance increase or decrease the orbital speed?

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Key Concepts

Proportional Reasoning in Orbital Mechanics

Proportional reasoning in orbital mechanics involves understanding how changes in one quantity affect another through mathematical relationships. In this case, if the period increases with distance to the 3/2 power, the orbital speed, computed as distance divided by period, decreases proportionally with the square root of distance. This inverse relationship is key to comprehending how orbital speed diminishes as the orbital radius increases.

Orbital Speed

Orbital speed is the rate at which an object travels along its orbit. It is determined by dividing the distance traveled in one complete orbit (the circumference) by the orbital period. Since the orbital period increases with distance, the speed varies inversely with the period, fundamentally linking the distance of an orbit to the speed required to maintain it.

Kepler's Third Law

Kepler's Third Law states that the square of a planet's orbital period is proportional to the cube of its semi-major axis (or distance from the central body). This principle underpins the relationship between the period of an orbit and its size, providing insight into how orbital characteristics change with distance.

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