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# Calculate the ideal period of rotation of Pluto about the Sun if you can ignore the gravitational effects of all bodies other than the Sun?

Calculate the ideal period of rotation of Pluto about the Sun if you can ignore the gravitational effects of all massive bodies other than the Sun. Pluto’s average distance from the Sun is 39.4 times the Earth’s distance from the Sun. Provide a numerical result with units of Earth years.

### 1 Answer

- billrussell42Lv 71 month ago
Satellite motion, circular

T = 2π√[R³/GM]

T is period of satellite in sec

G = 6.673e-11 Nm²/kg²

M is mass of central body in kg

R is radius of orbit in m

distance earth to sun 1.5e11 m

1 yr = 31556736 sec

sun mass 1.9891e30 kg

R = 39.4•1.5e11 m

T = 2π√[R³/GM] = 2π√[(39.4•1.5e11)³/(6.673e-11)(1.9891e30)]

this will give you period in seconds. divide by 31556736 to get earth years.