T² = 4π²r³ / GM
Solved for r :
r = [GMT² / 4π²]⅓
Where G is the universal gravitational constant, M is the mass of the sun, T is the asteroid's period in seconds, and r is the radius of the orbit.
Covert 5.00 years to seconds :
5.00years = 5.00years(365days/year)(24.0hours/day)(6...
= 1.58 x 10^8s
The radius of the orbit then is :
r = [(6.67 x 10^-11Nâ™m²/kg²)(1.99 x 10^30kg)(1.58 x 10^8s)² / 4π²]â…“
= 4.38 x 10^11m
The orbital speed can be found from the circular velocity formula :
v = âš[GM / r]
= âš[(6.67 x 10^-11Nâ™m²/kg²)(1.99 x 10^30kg) / 4.38 x 10^11m
= 1.74 x 10^4m/s
