Find the orbital period (in years) of an asteroid whose average distance from the sun is 5 au.

By equating the centripetal force and the gravitational pull, we have the equation


where
G=gravitational constant=6.67408*10^(-11)  (m^3 kg^-1 s^-2)
m=mass of object
M=mass of sun=1.9885*10^(30) (kg)
v=tangential velocity of object
r=distance from the sun (m)

On simplification, we get the relation
(m/s)
Subtituting constants,including
1 au = 1.49597870700*10^(11)  m
and given
r=5 au = 7.47989*10^11 m
 
 
 
   m/s

Therefore the orbital period is
s
years
years

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