# Astronomy help! How long Would it take for an object at 100 AU to orbit the sun once ? ?

Full question:

The wandering of remote planet like bodies, large spherical objects in the outer solar system, might be challenging to detect due to their long periods. How long would it take for an object at 100 AU to orbit the sun once?

A.) 100 years

B.) 500 years

C.) 50 years

D.) 1000 years

### 2 Answers

- skeptikLv 73 weeks agoFavourite answer
This one applies Kepler's 3rd law of planetary motion.

The square of the period of a planet's orbit is proportional to the cube of its semi-major axis.

Assuming a circular orbit (which is assumed if not specified) the planet's distance is 100 times Earth's.

Plugging in those values, and those for Earth, we get:

(T/1yr)^2 = (D/1AU)^3

(T/1yr)^2 = (100AU/1AU)^3

(T/1yr)^2 = 100^3

(T/1yr)^2 = 1000000

T/1yr = 1000

T=1000 yr

The correct answer is D.) 1000 years

- billrussell42Lv 73 weeks ago
100 AU = 1.50e13 m

T = 2π√[R³/GM]

T = 2π√[1.50e13³/6.673e-11•1.9891e30] = 3.17e10 s

3.17e10 s x 1hr/3600s x 1day/24hr x 1yr/365day = 1005 yrs (D)

Satellite motion, circular

V = √(GM/R)

V = √(gR)

T = 2π√[R³/GM]

T is period of satellite in sec

V = velocity in m/s

G = 6.673e-11 Nm²/kg²

M is mass of central body in kg

R is radius of orbit in m

earth GM = 3.98e14

sun mass 1.9891e30 kg