Relative velocity=relative momentum?

In summary, the speed of light is constant in all reference frames according to the special theory of relativity. Therefore, even if a solar sail is traveling at a high speed away from a radiation source, the radiation hitting it would still appear to be hitting it at the speed of light. However, the momentum supplied by the photons would be affected by the relativistic Doppler effect and would be approximately one quarter of what it would be if the sail was at rest relative to the source.
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Assume a solar sail was traveling at a high speed (say .866c) away from the radiation source. The radiation hitting it is of course traveling at c. But according to the special theory of relativity it would appear on the sail that the radiation is hitting the sail at c speed (since the speed of light is constant in all reference frames). Thus would a photon supply the same momentum push when the sail is traveling away from the source at .866c as it would if the sail was merely at rest (or with a much lower speed) relative to the source?
 
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  • #2
Thus would a photon supply the same momentum push when the sail is traveling away from the source at .866c as it would if the sail was merely at rest (or with a much lower speed) relative to the source?
No, momentum changes due to the relativistic Doppler effect. In your example, it would be ~1/4 of the momentum measured by an observer at rest wrt the source.
 

1. What is relative velocity?

Relative velocity refers to the velocity of an object in relation to another object. It takes into account the motion of both objects and is typically measured as the rate of change of distance between the two objects.

2. How is relative velocity calculated?

Relative velocity can be calculated by subtracting the velocity of one object from the velocity of the other object. This results in a vector quantity that represents the speed and direction of the relative motion between the two objects.

3. What is relative momentum?

Relative momentum is a measure of the amount of motion an object has in relation to another object. It takes into account the mass and velocity of both objects and is calculated using the formula p = mv, where p is momentum, m is mass, and v is velocity.

4. How is relative momentum related to relative velocity?

Relative momentum and relative velocity are closely related as they both involve the motion of two objects in relation to each other. The relative velocity between two objects can be used to calculate the relative momentum of those objects.

5. Why is understanding relative velocity and relative momentum important in science?

Understanding relative velocity and relative momentum is crucial in many areas of science, including physics, astronomy, and engineering. It allows scientists to accurately describe the motion of objects in relation to each other and make predictions about their future movements. It also helps in understanding the behavior of objects in different reference frames and can be applied in various real-world scenarios, such as space travel and collisions between objects.

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