Calculating Density of a Planet Based on Close Orbit Satellite Period

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SUMMARY

The discussion centers on calculating the density of a planet based on the orbital period of a satellite in a close circular orbit. The satellite's orbital period is 1.94 hours, and the key equations involved include T = 2π/ω and GMm/r² = (mv²)/r. It is established that the radius and mass of the planet are not needed directly; instead, a relationship between radius (r) and mass (M) can be derived from the orbital mechanics, which can then be converted into density. The uniform density assumption simplifies the calculations significantly.

PREREQUISITES
  • Understanding of circular orbital mechanics
  • Familiarity with gravitational equations (Newton's law of gravitation)
  • Basic knowledge of angular velocity (ω) and its relation to orbital period (T)
  • Concept of uniform density in planetary science
NEXT STEPS
  • Study the derivation of orbital mechanics equations, particularly T = 2π/ω
  • Research the application of Newton's law of gravitation in planetary density calculations
  • Explore how to express mass in terms of density and volume for spherical objects
  • Learn about the implications of uniform density on planetary structure and formation
USEFUL FOR

Astronomers, astrophysicists, and students studying celestial mechanics or planetary science will benefit from this discussion, particularly those interested in calculating planetary densities from orbital data.

kopinator
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A satellite is in a circular orbit very close to the surface of a spherical planet. The period of the orbit is 1.94 hours. What is density of the planet? Assume that the planet has a uniform density.

density = kg/m^3
T = 2∏/ω = 2∏r/v
GMm/r^2 = (mv^2)/r
v^2 = GM/r
v = rω

So I know I need to find the radius and the mass of the planet in order to find the density. Since I don't have r or v I found ω=8.99E-4. I'm not sure where to go from here.
 
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You don't need the radius or mass (which is a surprising result, I think). Just use r and M, and you will find some relation between those two (based on the orbit). This can be converted into a density afterwards.
 
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