Calculating the Year Length of a Gak Planet

[Stevemotto]

Question: A Gak it a type of alien that lives on a planet in another galaxy. One day a Gak decides to find out a little more about his planet. He drops a ball (it starts at rest) with a mass of 6.18 kg and notes that it takes 0.928 s to fall a distance of 8.37 m.
The Gak’s planet orbits its sun in a roughly circular orbit. The average distance to the Gak’s sun is 6.85 × 10^8 km. The Gak measures the force of attraction between his planet and his Sun and finds that this is 2.89 × 10^20 N.

How long is a year on the Gak’s planet?My Attempt:

So I started with the formula T^2 = 4(pi^2)(R^3)/GM

R = 6.85*10^8 (from avg distance)

Since on a previous question I found the mass of Gak's planet to be M = 2.12*10^24 (and got it right). Subbing it in & all relevant variables;

So; T^2 = 4(pi^2)(6.85*10^11)^3/(6.67*10^-11)(2.12*10^24)

T = 2.9956*10^11
Then multiply this by 1/(60*60*24*365) for Earth Years, I get;

T = 9499 yrs

And this is apparently wrong...


Can someone tell me what I did wrong? I'm starting to suspect that R didn't include the radius of the planets and I might need to add it in... I've attached the quiz for reference.

 

[PeroK]

Are you sure you are using all the right variables in the formula for Kepler's law?

 

[Stevemotto]

I believe so from my understanding.

 

[PeroK]

I believe so from my understanding.

Why did you use $M =$ mass of the planet?

 

[Stevemotto]

Isn't the "M" variable the mass of the planet?

 

[PeroK]

Isn't the "M" variable the mass of the planet?

In Kepler's 3rd law, no. A planet's orbit is independent of its mass.

 

[Stevemotto]

Oh it's the mass of the sun...