What is the relationship between the orbital radius and the period of a satellite in a circular orbit?
Practice Questions
1 question
Q1
What is the relationship between the orbital radius and the period of a satellite in a circular orbit?
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 (T ∝ √r).
Questions & Step-by-step Solutions
1 item
Q
Q: What is the relationship between the orbital radius and the period of a satellite in a circular orbit?
Solution: The period T of a satellite is proportional to the square root of the orbital radius r (T ∝ √r).
Steps: 5
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 not direct. Instead, it involves a mathematical relationship.
Step 4: The relationship can be expressed as T ∝ √r, which means that the period T is proportional to the square root of the orbital radius r.
Step 5: This means if you increase the orbital radius, the period will increase, but not in a straight line. It increases more slowly because of the square root.
