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 4r?(1 point)
Responses
2v
2 v
14v
1 fourth v
12v
1 half v
4v
4 v
2v
If the satellite is moved to an orbital radius of 4r, the velocity can be determined using the principle of conservation of angular momentum. Angular momentum is conserved when the product of the object's moment of inertia (mass times the square of the orbital radius) and its angular velocity (velocity divided by the orbital radius) remains constant.
So, we have:
m * r * v = m * (4r) * v'
where v' represents the new velocity.
Simplifying the equation:
r * v = 4r * v'
Dividing both sides by r and simplifying:
v = 4v'
Therefore, the velocity of the satellite if it is moved to an orbital radius of 4r is 4v.