Mass of Planet X in Solar Masses

Click For Summary
SUMMARY

The mass of Planet X can be calculated using Newton's form of Kepler's Third Law, where the orbital period (P) is 30 days and the semi-major axis (a) is 0.012 AU (15 times the diameter of Planet X, which is 0.0008 AU). The formula M = a^3 / P^2 is applied, leading to the conclusion that the mass of Planet X in solar masses is derived from these values. The discussion highlights the importance of accurately applying Kepler's laws to determine planetary masses.

PREREQUISITES
  • Understanding of Newton's form of Kepler's Third Law
  • Basic knowledge of astronomical units (AU)
  • Familiarity with orbital mechanics
  • Ability to perform algebraic calculations involving powers and proportions
NEXT STEPS
  • Study the derivation and applications of Kepler's Laws in celestial mechanics
  • Learn about the significance of astronomical units (AU) in planetary science
  • Explore the methods for calculating planetary masses using observational data
  • Investigate the role of satellite orbits in determining the characteristics of celestial bodies
USEFUL FOR

Astronomy students, astrophysicists, and anyone interested in celestial mechanics and the calculation of planetary masses.

srivens
Messages
2
Reaction score
0
Planet X is observed to have a small moon. This moon is observed to orbit the planet once per month at a distance of 15 Planet X diameters. What is the mass of Planet X in solar masses? [Hint: Use Newton's form of Kepler's Third Law: P2 is proportional to a3/M, where M is the mass of Planet X (assuming that the mass of the moon is negligible in comparison).]

the diameter of planet X is .0008 au as derived from previous problems. so 15 planet x diameters would be .012

So this would be a correct?
And p would be 30 days?

so the mass would be M = .012^3/30^2?

If this is correct am i missing something because i cannot come up with the correct anwer.
 
Last edited:
Physics news on Phys.org
figured it out... thanks anyway
 

Similar threads

Replies
4
Views
2K
Replies
2
Views
3K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 2 ·
Replies
2
Views
3K
  • · Replies 7 ·
Replies
7
Views
3K
  • · Replies 7 ·
Replies
7
Views
3K
Replies
8
Views
2K
Replies
1
Views
1K
  • · Replies 7 ·
Replies
7
Views
4K
  • · Replies 21 ·
Replies
21
Views
6K