What is the Orbital Period of an Asteroid with a Temperature of 200 K?

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SUMMARY

The orbital period of an asteroid with an equilibrium temperature of 200 K can be calculated using Kepler's Third Law, which relates the orbital period to the semi-major axis of the orbit. Given the solar constant of 1370 W/m² and Earth's radius of 637 km, the total power entering Earth's atmosphere can be determined, along with the power absorbed without an atmosphere and the surface temperature of the asteroid. The relationship between the asteroid's radius, mass, and temperature is crucial for deriving the orbital period accurately.

PREREQUISITES
  • Understanding of Kepler's Third Law of planetary motion
  • Familiarity with the solar constant and its implications
  • Knowledge of thermal equilibrium and blackbody radiation
  • Basic principles of circular orbits and gravitational forces
NEXT STEPS
  • Study Kepler's Third Law in detail to understand its application to asteroids
  • Learn about blackbody radiation and how it relates to temperature and power absorption
  • Research the calculations for total power entering and absorbed by planetary atmospheres
  • Explore the effects of albedo on temperature and energy absorption in celestial bodies
USEFUL FOR

Astronomy students, astrophysicists, and anyone interested in celestial mechanics and the thermal properties of asteroids.

rodrigues
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Homework Statement


Hi everyone,

was hoping someone could help me to answer a question:

an ateroid has an equilibrium temperature measured as 200 K. What is the object's orbital period around the Sun?


That is the exact wording of that particular question and that's why I am a little stumped.. it also says to base it upon your considerations in question #4, which reads

assuming the Earth's radius is 637 km, the solar constant is 1370 w/m2, and our planetary albedo is 0.31, then:
(a) determine total power entering Earth's atmosphere
(b) the total power that would be asborbed in the absence of an atmosphere
© surface temperature assuming it radiated into space all the energy it absorbed

Homework Equations





The Attempt at a Solution

 
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I guess you have to just find a relationship btw the variables caracterising the asteroid knowing it is in circular orbit of radius R and that the asteroid is a ball of radius r, mass m and its temperature is 200K.
 

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