Special Relativistic force problem.

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SUMMARY

The discussion focuses on a special relativistic force problem involving a spherical dust grain in the Earth's orbit around the sun. The radiation flux from the sun is given as 10^6 erg/cm²·sec at a radius of 1 AU, with the grain having an internal density of 2 g/cm³. The participant is attempting to equate the forces from radiation and gravity, but is uncertain about the approach, particularly regarding the use of 3-vector momentum as suggested by their teacher. The key conclusion is that while the forces can be set equal, the complexity of the problem may require a deeper understanding of relativistic effects.

PREREQUISITES
  • Understanding of Newtonian gravity
  • Familiarity with radiation flux and its dependence on distance (1/R²)
  • Knowledge of 3-vector momentum in physics
  • Basic concepts of special relativity
NEXT STEPS
  • Study the derivation of forces from radiation pressure in classical mechanics
  • Learn about the implications of special relativity on momentum and force
  • Explore the relationship between radiation flux and gravitational forces in astrophysics
  • Investigate advanced topics in relativistic dynamics and their applications
USEFUL FOR

Physics students, particularly those in upper-level courses focusing on special relativity and astrophysics, as well as educators looking to clarify concepts related to force and momentum in relativistic contexts.

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Homework Statement



At the radius of the Earth’s orbit around the sun (1.5 *10^13cm = 1AU), the flux of radiation from the sun is 10^6 erg/<br /> cm^2·sec . Now consider a spherical dust grain of radius r with internal density
\rho = 2g/cm^3, 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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