If the radius of the orbit of a satellite is doubled, what happens to its orbita

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Question: If the radius of the orbit of a satellite is doubled, what happens to its orbital speed?

Options:

Correct Answer: It decreases by a factor of √2

Solution:

The orbital speed v is given by v = √(GM/r). If r is doubled, v decreases by a factor of √2.

If the radius of the orbit of a satellite is doubled, what happens to its orbital speed?

If the radius of the orbit of a satellite is doubled, what happens to its orbital speed?

Correct Answer: Orbital speed decreases by a factor of √2.

Step 1: Understand that the orbital speed of a satellite is determined by the formula v = √(GM/r), where G is the gravitational constant, M is the mass of the planet, and r is the radius of the orbit.
Step 2: Identify what happens when the radius r is doubled. If r becomes 2r, we will substitute this into the formula.
Step 3: Substitute 2r into the formula: v = √(GM/(2r)).
Step 4: Simplify the equation: v = √(GM/r) * √(1/2).
Step 5: Recognize that √(1/2) is the same as 1/√2, which means the new speed is v = (1/√2) * √(GM/r).
Step 6: Conclude that the orbital speed decreases by a factor of √2 when the radius is doubled.

Orbital Mechanics – Understanding the relationship between orbital radius and speed of a satellite.
Gravitational Force – The role of gravitational force in determining orbital speed.
Mathematical Relationships – Applying the formula for orbital speed and understanding how changes in radius affect speed.