Finding the mass of neptune

[shvnchizms]

[SOLVED] Finding the mass of neptune

Homework Statement

The planet Neptune has 8 moons, the largest of which is Triton. The Voyager II spacecraft has photographed large frozen swampts on the surface of Triton, indication it once had a much warmer climate. Triton may have been a planet itself, migration away from the sun where it was later captured by the gravitational field of Neptune. Neptune requires 164.83 Earth years to complete one orbit around the sun. The diameter of the planet Neptune is 49,528km. Triton orbits Neptune at a mean distance of 354,800km and has an orbital period of 5.88 Eath Days.
Find the mass of Neptune

Homework Equations

I used the equation:4(pi)(radius of satellite ^3 = (Period of Satellite )^2(Mass Focus)(Gravitational constant) , Using Triton as the Satellite and Neptune as the Focus.
My Professor adds some irrelevant information to make the problem more difficult, but I found that the most important figures were the Diameter of Neptune and Distance of Neptune's surface to Triton ( for the Radius of the Satellite) and the orbit time of Triton.

The Attempt at a Solution

When using the above equation I Divide the diameter of neptune in half to find the radius and add it to the distance of triton to neptune to find the Radius of the orbit path (in km). then i multiply it by 4*pi then divide by period^2(in days) and the gravitational constant (6.67*10^-11) to isolate the variable(mass of neptune), after reworking the problem several times and getting the same answer I always get 2.98*10^26kg which from what I can find is about twice the actual mass, if anyone could help me find out what I'm missing in the problem that would be great

 

[Doc Al]

(1) Use standard units for time, distance, and mass: seconds, meters, and kilograms.
(2) Double check your formula; Looks to be off by a factor of pi.

 

[shvnchizms]

I changed the factor of pi in the formula to pi^2 and the answer looks correct, thankyou for you help

 

[StarAngel]

I don't seem to get the pi^2...
when i tried to put that in my calculator the answer would be 2.34*10^26...

 

[rwisz]

Thank you for sharing your approach to finding the mass of Neptune. It seems like you have a good understanding of the relevant equations and have taken into account the important figures given in the problem. However, as you mentioned, the calculated mass of Neptune is about twice the actual mass. This could be due to a few factors:

1. Incorrect conversion of units: Make sure that all the units used in the equation are consistent. For example, the diameter of Neptune is given in kilometers, but the period of Triton is given in Earth days. You will need to convert the period to seconds to match the units of the gravitational constant.

2. Neglecting the mass of Triton: In the equation you used, the mass of the satellite (Triton) is not included. Since Triton has a significant mass compared to Neptune, neglecting it could lead to a large error in the calculated mass of Neptune.

3. Using the incorrect radius for Triton's orbit: You mentioned that you calculated the radius of Triton's orbit by adding the radius of Neptune to the distance between Neptune and Triton. However, this may not be an accurate representation of Triton's orbit. Instead, you can use the semi-major axis of Triton's orbit, which is given as 354,800km, as the radius in the equation.

I hope this helps you identify any potential errors in your calculation. Remember to always double-check your units and make sure you are using the correct values in your equations. Good luck!