Kepler's 3rd Law Question finding how long a year is for Pluto

[Jon Bori]

Homework Statement

Kepler's Constant for any object or planet orbiting the sun is 3.36x10¹⁸m³/s². Calculate how long a year is for Pluto given the "radius of object" is 3.0x10⁶m and the "mean radius of orbit" is 5.9x10¹²

Answer: 7.82x10⁹s

Homework Equations

K = T²/R³

The Attempt at a Solution

I tried plugging the values into the equation

T² = sqrt (5.9x10¹²m)+(3x10⁶)/3.36x10¹⁸m)

= 6.1x10¹⁹[/B]

 

[gneill]

Homework Statement

Kepler's Constant for any object or planet orbiting the sun is 3.36x10¹⁸m³/s². Calculate how long a year is for Pluto given the "radius of object" is 3.0x10⁶m and the "mean radius of orbit" is 5.9x10¹²

Answer: 7.82x10⁹s

Homework Equations

K = T²/R³

The Attempt at a Solution

I tried plugging the values into the equation

T² = sqrt (5.9x10¹²m)+(3x10⁶)/3.36x10¹⁸m)

= 6.1x10¹⁹[/B]

What equation is that? The one you listed in the Relevant Equations only involved one distance value, but you seem to have used two ("radius of object" and "mean radius of orbit"). The listed equation also cubed the distance, but you've used a square root to resolve it?

How does the given value of Kepler's constant relate to your Relevant equation? Do the units match?

 

[Jon Bori]

I got it. You only use the mean radius of orbit and I forgot to cube the distance.. lol