Question
A satellite orbiting Earth at an orbital radius r has a velocity v. Which represents the velocity if the satellite is moved to an orbital radius of 5r?
Responses:
a) 1/5 v
b) 1/ to the square root of 5 v
c) 5v
d) to the square root of 5 v
Responses:
a) 1/5 v
b) 1/ to the square root of 5 v
c) 5v
d) to the square root of 5 v
Answers
GPT 3.5
To answer this question, we can use the principle of conservation of angular momentum. According to this principle, the angular momentum of a satellite remains constant as long as no external torque acts upon it.
The angular momentum (L) of a satellite is given by the equation L = mvr, where m is the mass of the satellite, v is its velocity, and r is its orbital radius.
If we move the satellite to an orbital radius of 5r, the new angular momentum (L') can be calculated using the same equation: L' = m(v')5r, where v' is the new velocity.
Since angular momentum is conserved, we can equate L and L': mvr = m(v')5r
Simplifying the equation, we get: v = 5v'
So, the new velocity (v') is equal to (1/5) v.
Therefore, the correct answer is option a) 1/5 v.
The angular momentum (L) of a satellite is given by the equation L = mvr, where m is the mass of the satellite, v is its velocity, and r is its orbital radius.
If we move the satellite to an orbital radius of 5r, the new angular momentum (L') can be calculated using the same equation: L' = m(v')5r, where v' is the new velocity.
Since angular momentum is conserved, we can equate L and L': mvr = m(v')5r
Simplifying the equation, we get: v = 5v'
So, the new velocity (v') is equal to (1/5) v.
Therefore, the correct answer is option a) 1/5 v.