(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Calculate the Orbital Period for the following: Earth's orbit to the Sun. I get stuck towards the end. I must use Newton's second law and have the Universal Law of Gravitation equal the Centrifugal Force.

Newton's gravitational constant: G= 6.67*10^-11 Nm^2/kg^2

Mass of Sun = 1.98*10^30 kg

Mass of the Earth 5.97*10^24 kg

Distance of the Earth from the Sun: 149.6*10^6

T = time

2. Relevant equations

Centrifugal Force = (mv^2)/r

v=(2(pi)(r))t

Force of Gravity = (GMm)/d^2

Mm being mass, and G/d^2 being acceleration.

3. The attempt at a solution

I multiplied Newton's gravitational constant by the mass of the Earth by the mass of the Sun, and then divided it all by the distance of the Earth from the Sun. I got 5.270280882*10^35 km. This was for the gravitational pull.

For the Centrifugal Force, I multiplied the mass of the Earth by v=((2(pi)(r))^2)/t^2. And put it over 149.6*10^6 km. I got (3.52229083*10^34 kg*km)/t^2.

I then set my two results equal to each other. Next, I multiplied by t^2 as that is the variable I am trying to find. This gave me 5.270280882*10^35 km*t^2 = 3.5229083*10^34 kg*km. Then, I divided by km on both sides to cancel it. I now have 5.270280882*10^35 t^2 = 3.5229083*10^34 kg. If I divide by the number on the left side of the equation and then square root both sides, I get a number than can't possibly be the Orbital Period of the Earth.

Can you tell where I am going wrong? Any advice is appreciated.

Thanks.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Calculating the Orbital Period

**Physics Forums | Science Articles, Homework Help, Discussion**