Calculating Mars's Orbital Period Using Kepler's Third Law

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SUMMARY

The discussion centers on calculating Mars's orbital period using Kepler's Third Law, specifically the equation T² = 4π²r³/GM. The user initially calculated Mars's orbital period as 1.88 years, which was incorrect. It was clarified that Mars's orbital radius is 1.52 times that of Earth's, not the diameter, leading to the correct understanding that Mars's year is approximately 687 Earth days, or about 1.88 Earth years.

PREREQUISITES
  • Understanding of Kepler's Third Law of planetary motion
  • Familiarity with the equation T² = 4π²r³/GM
  • Knowledge of astronomical units, particularly Earth's orbital radius
  • Basic algebra for manipulating equations
NEXT STEPS
  • Study the derivation and applications of Kepler's Third Law
  • Learn about the calculation of orbital periods for other planets
  • Explore the significance of astronomical units in planetary science
  • Investigate the differences between diameter and radius in orbital mechanics
USEFUL FOR

Astronomy students, educators, and anyone interested in celestial mechanics and the calculation of planetary orbits.

Lance WIlliam
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Homework Statement



Mars's orbit has a diameter 1.52 times that of Earth's orbit.
How long does it take Mars to orbit the Sun?
in years.


Homework Equations



I tried using T^2=4(pi)^2r^3/GM

I got 1.88years...but its wrong...

The Attempt at a Solution

 
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Lance WIlliam said:

Homework Statement



Mars's orbit has a diameter 1.52 times that of Earth's orbit.
How long does it take Mars to orbit the Sun?
in years.


Homework Equations



I tried using T^2=4(pi)^2r^3/GM

I got 1.88years...but its wrong...

The Attempt at a Solution

What makes you think it's wrong?

Mars' year is 687 Earth days...
 
With these things it would help if you showed your work so people can see exactly where you went wrong.

I think its the radius that is 1.52 times that of Earth's not the diameter. As Dave points out, you're correct.
 
Last edited:
Thankyou I got it..."masteringphysics" always wants answers in the craziest of ways...
 

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