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)
4v
4 v
12v
1 half v
2v
2 v
14v
The correct answer is: 1 half v
The correct answer is 2v.
To determine the velocity of a satellite when its orbital radius is changed, we can use the principle of conservation of angular momentum. According to this principle, the product of the orbital radius and the linear velocity remains constant as long as no external forces act on the satellite.
Let's call the initial orbital radius r and the initial velocity v. Therefore, the initial angular momentum is given by (r * v).
Now let's consider when the satellite's orbital radius is changed to 4r. To maintain the conservation of angular momentum, the new angular momentum should be the same as the initial angular momentum. So, we have:
Initial Angular Momentum = New Angular Momentum
(r * v) = (4r * v_new)
To find the new velocity (v_new), we can rearrange the equation:
v_new = (r * v) / (4r)
Simplifying the equation, we find:
v_new = v / 4
Therefore, the velocity of the satellite when its orbital radius is changed to 4r is 1/4 of the initial velocity. So the correct answer is:
1 half v