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

In summary, the asteroid has a moon that is 1.6 km wide and orbits at a distance of 148 km from the center of the asteroid. The moon's orbit is circular with a period of 21 hours. To calculate the mass of the asteroid, the Law of Periods can be used, which is equivalent to using centripetal acceleration and gravity. The equation used should include the conversion of km to m.
  • #1
GingerBread27
108
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?
 
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  • #2
It's a circular orbit. Use what you know about centripetal acceleration and gravity.
 
  • #3
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.
 

1. What is the formula for calculating the mass of an asteroid given the moon's size, distance, and orbit?

The formula for calculating the mass of an asteroid is: mass = (moon's mass * distance from moon^2) / (distance from asteroid^2 * moon's orbit^2).

2. Can this formula be used for any asteroid and moon in the solar system?

Yes, this formula can be used for any asteroid and moon in the solar system as long as the necessary data (moon's size, distance, and orbit) is available.

3. How accurate is this calculation method?

This calculation method can provide a fairly accurate estimate of the mass of an asteroid given the moon's size, distance, and orbit. However, factors such as irregular shape and composition of the asteroid may affect the accuracy of the result.

4. How does the moon's size, distance, and orbit affect the mass of the asteroid?

The moon's size and distance play a significant role in determining the gravitational force exerted on the asteroid, which in turn affects its mass. The moon's orbit also influences the gravitational pull on the asteroid, which can impact its mass calculation.

5. What other factors should be considered when calculating the mass of an asteroid?

In addition to the moon's size, distance, and orbit, other factors that may affect the mass calculation of an asteroid include its own size, density, and composition. These factors can vary greatly among different asteroids and should be taken into account for a more accurate calculation.

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