A satellite is in a circular orbit around the Earth. If its orbital radius is tr
Practice Questions
Q1
A satellite is in a circular orbit around the Earth. If its orbital radius is tripled, how does the orbital speed change?
It triples
It doubles
It remains the same
It is reduced to one-third
Questions & Step-by-Step Solutions
A satellite is in a circular orbit around the Earth. If its orbital radius is tripled, how does the orbital speed change?
Step 1: Understand that the orbital speed of a satellite is given by the formula v = √(GM/R), where G is the gravitational constant, M is the mass of the Earth, and R is the orbital radius.
Step 2: Identify that if the orbital radius R is tripled, it becomes 3R.
Step 3: Substitute 3R into the formula for orbital speed: v = √(GM/(3R)).
Step 4: Simplify the equation: v = √(GM/(3R)) = √(GM/R) * √(1/3).
Step 5: Recognize that √(GM/R) is the original speed v, so we can rewrite it as v/√3.
Step 6: Calculate the new speed: Since √3 is approximately 1.732, the new speed is v/√3, which means the speed is reduced.
Orbital Mechanics – Understanding the relationship between orbital radius and speed in circular orbits.
Gravitational Force – Application of gravitational constant and mass in determining orbital speed.
Mathematical Relationships – Manipulating equations to find how changes in radius affect speed.
