Using Kepler's Third Law to find mass

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SUMMARY

This discussion focuses on using Kepler's Third Law to calculate the mass of the fictional planet Snazbort based on its moon Pingdol's orbital characteristics. The orbital period of Pingdol is 7.68 days, and the semimajor axis is 92.53×109 meters. The equation utilized is T2 = 4π2a3/(GM), where T is the orbital period in seconds, G is the gravitational constant, and M is the mass of Snazbort. A critical step in the solution involved converting the orbital period from days to seconds to ensure unit consistency.

PREREQUISITES
  • Understanding of Kepler's Third Law of planetary motion
  • Familiarity with the gravitational constant (G)
  • Ability to convert time units (days to seconds)
  • Basic knowledge of orbital mechanics and elliptical orbits
NEXT STEPS
  • Learn how to apply Kepler's Laws in real-world scenarios
  • Study the gravitational constant (G) and its significance in astrophysics
  • Explore unit conversion techniques for astronomical calculations
  • Investigate the implications of orbital mechanics on satellite design
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Astronomy students, physics enthusiasts, and anyone interested in celestial mechanics and the calculation of planetary masses using orbital data.

Allen L
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Homework Statement


The fictional planet Snazbort has a fictional moon Pingdol. Pingdol has an orbital period of 7.68 days and a semimajor axis of 92.53×109. Use Kepler's Third Law to estimate the mass of Snazbort.

Homework Equations


T^2=4pi^2*a^3/(GM)

where 2a is the length of major axis
T is the time required for it to travel once around its elliptical orbit
G is gravitational constant
M is mass

The Attempt at a Solution


I've tried plugging in the numbers and I can't seem to figure out how I'm supposed to enter them. I'm also not entirely sure how I even get G. The G I used is from another question.

If it helps at all, the screenshot is here along with my "best" attempt.
http://i.imgur.com/jVZP7u8.png

EDIT: I got the answer. I was supposed to change T into seconds -_-
 
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Allen L said:
Pingdol has an orbital period of 7.68 days and a semimajor axis of 92.53×109
Is that semimajor axis supposed to be 92.53 X 109? What are the units?

It's important to keep track of the units, which maybe you've already found out with the days vs. seconds units in T.
 

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