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

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To calculate the mass of an asteroid given the size and orbit of its moon, Kepler's Laws can be applied, specifically the Law of Periods. The moon's circular orbit has a period of 21 hours and is located 148 km from the asteroid's center. A common mistake is not converting units properly, such as kilometers to meters, which can lead to incorrect calculations. The formula used involves the gravitational constant (G) and the radius of the orbit. Ensuring unit consistency is crucial for accurate results.
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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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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.
 

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