Calculating Mass of Asteroid Given Moon's Size, Distance, and Orbit

  • Thread starter Thread starter GingerBread27
  • Start date Start date
  • Tags Tags
    Asteroid Mass
Click For Summary
SUMMARY

The discussion focuses on calculating the mass of an asteroid based on the size and orbit of its moon, specifically a moon that is 1.6 km wide and orbits 148 km from the asteroid's center with a period of 21 hours. The user attempted to apply Kepler's Law of Periods using the formula (T^2) = (4π^2/(GM))(r^3) but encountered errors due to unit conversion. The correct approach emphasizes the importance of converting kilometers to meters for accurate calculations.

PREREQUISITES
  • Understanding of Kepler's Laws, specifically the Law of Periods
  • Knowledge of centripetal acceleration and gravitational force
  • Ability to perform unit conversions, particularly from kilometers to meters
  • Familiarity with basic physics equations related to orbital mechanics
NEXT STEPS
  • Study Kepler's Laws in detail, focusing on the Law of Periods
  • Learn about gravitational force calculations using Newton's law of universal gravitation
  • Practice unit conversion techniques, especially in physics contexts
  • Explore centripetal acceleration and its relationship with orbital motion
USEFUL FOR

Astronomy students, physicists, and anyone interested in celestial mechanics and orbital calculations will benefit from this discussion.

GingerBread27
Messages
108
Reaction score
0
Assume an asteroid's moon is 1.6 km wide, and 148 km from the center of the asteroid, which is 55 km long. The moon's orbit is circular with a period of 21 h.

Whatis the mass of the asteroid?

Ok This has to do with Kepler's Laws and I don't really understand Kepler's Law. I tried using the Law Of Periods so I did (75600 s)^2=((4pi^2)/(GM))*(148 km)^3. I get the wrong answer so I don't know what I did wrong. Any ideas?
 
Physics news on Phys.org
It's a circular orbit. Use what you know about centripetal acceleration and gravity.
 
GingerBread27 said:
Ok This has to do with Kepler's Laws and I don't really understand Kepler's Law. I tried using the Law Of Periods so I did (75600 s)^2=((4pi^2)/(GM))*(148 km)^3. I get the wrong answer so I don't know what I did wrong. Any ideas?
Of course there is nothing wrong with using Kepler's law! (Which is equivalent to what I suggested.) Be careful with units---convert km to m.
 

Similar threads

Asteroid Gravity: Keplers 3rd Law
  • · Replies 18 ·
Replies
18
Views
5K
Asteroid Orbits: Finding r with Kepler's Laws
  • · Replies 3 ·
Replies
3
Views
2K
What is the orbital period of an asteroid between Earth and Jupiter?
  • · Replies 2 ·
Replies
2
Views
2K
Can Conservation of Angular Momentum Help Estimate the Mass of Binary Asteroids?
  • · Replies 19 ·
Replies
19
Views
4K
Advanced Engineering Problem: Asteroid on a collision course
  • · Replies 16 ·
Replies
16
Views
2K
Maximum safe mass of an asteroid in geostationary orbit
  • · Replies 17 ·
Replies
17
Views
3K
What is the Mass and Density of the Asteroid Ida and its Satellite?
  • · Replies 2 ·
Replies
2
Views
2K
Orbital Velocity Calculation for an Asteroid at Perihelion
  • · Replies 1 ·
Replies
1
Views
2K
Calculating Angle & Speed to Reach Planet's Moon from Station Orbit
  • · Replies 1 ·
Replies
1
Views
2K
Calculating Orbital Period of Asteroid Between Mars & Jupiter
  • · Replies 11 ·
Replies
11
Views
3K