What is the relationship between the period of a satellite and its orbital radius?
Practice Questions
1 question
Q1
What is the relationship between the period of a satellite and its orbital radius?
T is directly proportional to r
T is inversely proportional to r
T is proportional to r^2
T is proportional to √r
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).
Questions & Step-by-step Solutions
1 item
Q
Q: What is the relationship between the period of a satellite and its orbital radius?
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).
Steps: 6
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.
