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Juliette [100K]
3 years ago
9

E asteroid belt circles the sun between the orbits of mars and jupiter. one asteroid has a period of 6.0 earth years. part a wha

t is the asteroid's orbital radius?
Physics
1 answer:
anzhelika [568]3 years ago
6 0

To solve the problem, use Kepler's 3rd law : 

T² = 4π²r³ / GM 

Solved for r : 

r = [GMT² / 4π²]⅓ 

but first covert 6.00 years to seconds : 

6.00years = 6.00years(365days/year)(24.0hours/day)(6... 
= 1.89 x 10^8s 

The radius of the orbit then is : 

r = [(6.67 x 10^-11N∙m²/kg²)(1.99 x 10^30kg)(1.89 x 10^8s)² / 4π²]⅓ 
= 6.23 x 10^11m

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Answer:

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(a)

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Now, we find the mass:

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<u>m = 1.6 x 10²¹ kg</u>

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(b)

The kinetic energy will be:

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