Formation of the Solar System (Astrophysics Homework Help)

AI Thread Summary
The discussion centers on calculating the temperature difference between the regions where Venus and Jupiter formed, based on their distances from the Sun. The formula used is T = k/R², which indicates that temperature inversely correlates with the square of the distance. The initial calculation suggested Venus is 55.2 times hotter than Jupiter, but this was identified as incorrect. The correct approach involves using the inverse square root relationship for temperature comparison. The final conclusion emphasizes the need for accurate application of the inverse square law in astrophysical calculations.
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Homework Statement



Formation of the Solar System

The distance of Venus is about 0.7 AU, and the orbital radius of Jupiter is about 5.2 AUs. How many times hotter is the region where Venus formed compared to the region where Jupiter formed? Enter numbers and decimal point only. Round off to the nearest tenth.

Homework Equations


The Attempt at a Solution




The temperature of a region of the solar system depends on how close it is to the sun, according to the inverse square law:

T = k/R²

where "k" is some constant. So:

Tvenus / Tjupiter = (k/Rvenus²) / (k/Rjupiter²)
= (Rjupiter / Rvenus)²
= (5.2 AU / 0.7 AU)²

I arrived at Venus' region being 55.2 times hotter than Jupiter region and it is wrong.

Thank you in advance for your help.
 
Physics news on Phys.org
It's not

T = k/R2

It's inverse square root.
 
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