# Orbital velocity help

1. Mar 27, 2003

### tinksy

If a small planet were discovered with a distance from the sun eight times that of the Earth, what would you predict for its period in (Earth) years. (i.e. how many times longer would it take to go round the sun than the Earth does.)

Last edited: Mar 28, 2003
2. Mar 27, 2003

### teddy

i will not give you the answer straight away, but here's the hint---
get orbital velocity v as a function of radius r

dynamics of the system(*) :

from newton's second law and law of gravitation,
(m*v^2)/R = (G*M*m)/R^2

get v(r) and substitute in the kinemetical relation which you got correct,that is, T=2(pi)r/v

this will give you T(r) which is usually called "kepler's third law".

*assumption: all orbits are circular

justification : though the orbits that actually elliptical ,the eccentricity is very small.(dont worry if you don't understand this,take this as a side remark).

cheers

Last edited: Mar 27, 2003
3. Mar 28, 2003

### tinksy

thanks teddy...

could u tell me if i'm right?

i've used kepler's law T^2 (directly proportional to) R^3
so if R = 8R (as for Earth, R = 1AU so for the planet, R = 8AU)
kepler's law: R^3/T^2 = 1
therefore, T^2 = 8^3/1
so T = (root)512 = 16(root)2 .....???? is that correct???

4. Mar 28, 2003

### teddy

yup,its right.
bye

5. Mar 28, 2003

### tinksy

yaaaaaay!!! thanks