What is the Orbital Period of Jupiter in Earth Years?

[petern]

Jupiter is 5.2 times farther than Earth from the sun. Find Jupiter's orbital period in Earth years.

Equation to use is: T^2 = Kr^3

Radius of Earth is 6378100 m and radius of Jupiter is 71492000 m.

I rearrange the equation to K = T^2/r^3 and set k of Earth equal to k of Jupiter. I enter all of it including 5.2 times radius of Earth into the equation. I solve for t of Jupiter but I always end up with 16.457 years when it should be 11.86 years. What am I doing wrong?

 

[petern]

Can anyone help me?

 

[tyco05]

Radius of Earth is 6378100 m and radius of Jupiter is 71492000 m.

I rearrange the equation to K = T^2/r^3 and set k of Earth equal to k of Jupiter. I enter all of it including 5.2 times radius of Earth into the equation. I solve for t of Jupiter but I always end up with 16.457 years when it should be 11.86 years. What am I doing wrong?

I don't know where you got those radii from, but you don't need them.

Use 1 Earth year as T (earth) and 1 Earth orbit as R (earth). Use 5.2 Earth orbits as R (jupiter).

Plug these into T(earth)^2 / R(earth)^3 = T(jupiter)^2 / R(jupiter)^3

and solve for T(jupiter).

 

[petern]

Thanks. Looks like it works but the only problem is that I know that I have to use the radii of the planets which is from the center to the edge of the planet. r stands for radius, not orbit so I don't understand why that's working.

 

[Shooting Star]

The r stands for radius of an orbit, considered circular, not the radius of a planet! All planets are considered to be point masses in this treatment.