Question

An asteroid is in an orbit around the sun whose closest point to the sun has a radius R and whose most distant point has a radius 9R, where R is equal to the radius of the earth's orbit = 1 AU = 1.5 x 10^11 m.

1. What is the asteroid's speed when it is closest to the sun?
2. How does this compare with the earth's orbital speed?
3. What is the period of this orbit, in years?

Answer 1

1) Orbital speed, v_pluto = sqrt(G*Msun/r)

= sqrt(6.67*10^-11*1.99*10^30/(9*1.5*10^11))

= 9915.7 m/s

2) v_pluto = v_earth/3

3) Time periode, T = 2*pi*r/v

= 2*pi*(9*1.5*10^11)/9915.7

= 855441387 s

= 855441387/(365*24*60*60)

= 27.1 years