What is the relationship between the period of a satellite and its orbital radiu

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Question: What is the relationship between the period of a satellite and its orbital radius?

Options:

Correct Answer: T is proportional to √r

Solution:

The period T of a satellite is proportional to the square root of the orbital radius r, as given by T = 2π√(r^3/GM).

What is the relationship between the period of a satellite and its orbital radius?

What is the relationship between the period of a satellite and its orbital radius?

Step 1: Understand what a satellite's period (T) is. It is the time it takes for the satellite to complete one full orbit around a planet.
Step 2: Know what the orbital radius (r) is. It is the distance from the center of the planet to the satellite.
Step 3: Learn that the relationship between the period and the orbital radius is described by a formula: T = 2π√(r^3/GM).
Step 4: In this formula, G is the gravitational constant and M is the mass of the planet.
Step 5: The formula shows that T (the period) is proportional to the square root of r^3 (the orbital radius cubed).
Step 6: This means that if you increase the orbital radius (r), the period (T) will also increase, but not in a straight line; it follows a square root relationship.

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