The asteroid belt circles the sun between the orbits of mars and jupiter. one asteroid has a period of 6.2 earth years. what are

Question

Otrada [13]

3 years ago

10

The asteroid belt circles the sun between the orbits of mars and jupiter. one asteroid has a period of 6.2 earth years. what are

the asteroid's orbital radius and speed?

Physics

1 answer:

mash [69] · Answer 1 · 2021-12-10T13:10:44+03:00

<span>TÂ˛ = 4Ď€Â˛rÂł / GM Solved for r : r = [GMTÂ˛ / 4Ď€Â˛]â…“ 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™mÂ˛/kgÂ˛)(1.99 x 10^30kg)(1.58 x 10^8s)Â˛ / 4Ď€Â˛]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™mÂ˛/kgÂ˛)(1.99 x 10^30kg) / 4.38 x 10^11m = 1.74 x 10^4m/s</span>