Special Relativistic force problem.

In summary, the problem involves calculating the force on a spherical dust grain of a certain radius and density located at a certain distance from the sun, taking into account the radiation flux from the sun and ignoring the gravity of the Earth. The solution involves setting the forces equal and solving for the 3-vector momentum. There may be other methods to solve the problem, but it is not clear which is the correct one.
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Homework Statement



At the radius of the Earth’s orbit around the sun ([itex]1.5 *10^13[/itex]cm = 1AU), the flux of radiation from the sun is [itex] 10^6 erg/
cm^2·sec[/itex] . Now consider a spherical dust grain of radius r with internal density
[itex]\rho = 2g/cm^3[/itex], at some distance R from the sun. Assume that the grain is at rest with respect to the sun. Use the fact that radiation flux falls with distance from a source as 1/R2 Ignore the gravity of the Earth in this problem, but not the gravity of the Sun. Use Newtonian gravity and ignore general relativistic

Homework Equations



I won't both writing them out but we can easily derive the force from the flux & gravity effects on the particle.

Now here is where things get a bit sticky for me. I want to just set these forces equal and solve as per the usual, but I am assuming that the problem must be trickier than that considering this an upper level course.

My teacher suggested that we set both equal to the 3-vector momentum and go from there, but I derived the same results doing this as I did just setting the two equations equal.

Where am I going wrong here? Or am I solving this the correct way?
 
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And the problem is ... ?
 

Related to Special Relativistic force problem.

1. What is the Special Relativistic Force Problem?

The Special Relativistic Force Problem is a concept in physics that arises when trying to reconcile the principles of special relativity with classical Newtonian mechanics. It deals with the question of how forces are affected by the relative motion between two objects.

2. How does special relativity affect the concept of force?

Special relativity states that the laws of physics should be the same for all observers in uniform motion. This means that the concept of force, which is based on Newton's laws of motion, must also be consistent for all observers, regardless of their relative motion. However, this leads to some paradoxes and inconsistencies, giving rise to the Special Relativistic Force Problem.

3. Can the Special Relativistic Force Problem be resolved?

There is currently no universally accepted solution to the Special Relativistic Force Problem. Some scientists propose modifications to Newton's laws of motion, while others suggest that the concept of force itself may need to be redefined in the context of special relativity. Further research and experimentation are needed to fully understand and resolve this problem.

4. How does the Special Relativistic Force Problem relate to Einstein's theory of relativity?

The Special Relativistic Force Problem is a specific aspect of Einstein's theory of special relativity. It highlights the discrepancies between classical mechanics, which is based on Galilean relativity, and special relativity, which takes into account the speed of light as a constant and the relativity of simultaneity.

5. Why is the Special Relativistic Force Problem important?

The Special Relativistic Force Problem is important because it challenges our understanding of the fundamental principles of physics and forces us to question the validity of classical mechanics in the context of special relativity. Resolving this problem could lead to a deeper understanding of the nature of forces and their role in the universe.

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