Temperature of a planet a distance from sun

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SUMMARY

The discussion focuses on estimating the temperature of a planet located 130 billion km from the Sun, with a diameter of 1700 km. The participants utilize the heat balance equation and Wien's displacement law, specifically the formula λ = b/T, where b = 2.9 x 10^-3. The correct temperature estimation equation is identified as Tp = Ts((Rs/D^2)^(0.5)), although it is noted that this equation has unit inconsistencies. The luminosity of the planet can be calculated using L_{planet} = 4π L_{sun} (d_{sun}^2/d_{planet}^2).

PREREQUISITES
  • Understanding of Wien's displacement law and its application
  • Familiarity with the heat balance equation in astrophysics
  • Knowledge of albedo and its impact on planetary temperature
  • Basic concepts of luminosity and distance relationships in astronomy
NEXT STEPS
  • Research the application of Wien's displacement law in astrophysical contexts
  • Learn about the heat balance equation and its derivation
  • Explore the concept of albedo and its effects on planetary climates
  • Investigate luminosity calculations for celestial bodies
USEFUL FOR

Astronomy students, astrophysicists, and anyone interested in planetary science and temperature estimation methods.

tetris11
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Homework Statement


Hi,
A spinning shiny red-appearing planet at 130 billion km from the sun, has a diameter of 1700km.
Estimate temperature of planet using simple heat balance equation.
Estimate also the temperature obtained by Wien displacement law.


Homework Equations


I've been given no equations, but I know that shiny planets have an Albedo =1, and the wavelength or red = 650nm, which is useful for the Wien law [tex]\lambda[/tex]=b/T, where T is kelvin and b = 2.9x10^-3

Temp of sun = 5800k
Rad of sun = 6.96x10^8

The Attempt at a Solution


I don't know what equation there is to use! I've looked on the internet and gotten this eq.

Tp = Ts((Rs/D^2)^(0.5))

where Tp is temperature of planet, Ts of sun, Rs radius of sun, D distance to planet.
help!
 
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