# Centripetal motion, find radius - which solution is correct?

1. Apr 24, 2015

### Tyrannosaurus_

1. The problem statement, all variables and given/known data
The planet Saturn will orbit the Sun every 19 Earth years (= 599 184 000 seconds). Assume Saturn travels on a circular orbit with a speed of 9 690m/s. What is the radius of the orbit of Saturn?

I can solve this in two different ways, and get two different values. Which is the correct approach, & why?

2. Relevant equations & attempt at solution.

T = (2πr)/V - that is, period is 2π*radius over speed.,
so, r = (T*V)/2π
so, radius = 9.24 x 1011m

However, if, the centripetal forces equals the universal law of gravitation, that is,
Fc = Fg
(m*v2)/r = (Gm1m2)/r2
r = (G*msun)/v2
r = [(6.67x10-11)(1.99x1030kg)]/(9690m/s2)
r = 1.41 x 1012m

So, why the difference? What applies, and what doesn't apply and why?

Thanks!

2. Apr 24, 2015

### ehild

Both of your methods are correct, but the problem maker gave wrong orbital period. It is 29 years, instead of 19.

3. Apr 29, 2015

### Tyrannosaurus_

Thanks so much! I was going crazy!