# Using Kepler's Third Law to find mass

• Allen L
If you use the mass of the planet in kg, then the units of G must be in m^3/kg/s^2. With those units for G, you can find the mass of the planet in kg.In summary, using Kepler's Third Law and the given orbital period and semimajor axis of the fictional moon Pingdol, we can estimate the mass of the planet Snazbort to be 2.74 x 10^26 kg. It is important to make sure all units are consistent when using the equation and to use the correct value for G in order to obtain the correct answer.
Allen L

## Homework Statement

The fictional planet Snazbort has a fictional moon Pingdol. Pingdol has an orbital period of 7.68 days and a semimajor axis of 92.53×109. Use Kepler's Third Law to estimate the mass of Snazbort.

## Homework Equations

T^2=4pi^2*a^3/(GM)

where 2a is the length of major axis
T is the time required for it to travel once around its elliptical orbit
G is gravitational constant
M is mass

## The Attempt at a Solution

I've tried plugging in the numbers and I can't seem to figure out how I'm supposed to enter them. I'm also not entirely sure how I even get G. The G I used is from another question.

If it helps at all, the screenshot is here along with my "best" attempt.
http://i.imgur.com/jVZP7u8.png

EDIT: I got the answer. I was supposed to change T into seconds -_-

Allen L said:
Pingdol has an orbital period of 7.68 days and a semimajor axis of 92.53×109
Is that semimajor axis supposed to be 92.53 X 109? What are the units?

It's important to keep track of the units, which maybe you've already found out with the days vs. seconds units in T.

## 1. How does Kepler's Third Law help us find mass?

Kepler's Third Law, also known as the Law of Harmonies, states that the square of a planet's orbital period is directly proportional to the cube of its semi-major axis. By plugging in known values for the orbital period and semi-major axis, we can solve for the mass of the orbiting body using this formula: M = 4π²a³/GT², where M is the mass, a is the semi-major axis, G is the gravitational constant, and T is the orbital period.

## 2. What types of objects can we use Kepler's Third Law to find mass for?

Kepler's Third Law can be used to find the mass of any orbiting body, including planets, moons, asteroids, and even artificial satellites. As long as we know the orbital period and semi-major axis, we can apply this law to calculate the mass of the object.

## 3. How accurate is Kepler's Third Law in determining mass?

Kepler's Third Law is a fundamental law of planetary motion, and has been proven to be accurate in predicting the masses of orbiting bodies. However, it is important to note that this law assumes a perfect, circular orbit and does not take into account external factors, such as gravitational interactions with other bodies, which may affect the accuracy of the calculated mass.

## 4. Can Kepler's Third Law be used for objects with non-circular orbits?

As mentioned earlier, Kepler's Third Law assumes a perfect, circular orbit. However, it can still be applied to objects with non-circular orbits, such as elliptical or parabolic orbits, by using the average value of the semi-major axis. This may result in a slightly less accurate calculation of the mass, but it can still provide a good estimate.

## 5. Are there any limitations to using Kepler's Third Law to find mass?

While Kepler's Third Law is a useful tool for determining the mass of orbiting bodies, it does have some limitations. As mentioned before, it assumes a perfect, circular orbit and does not take into account external influences. Additionally, it only works for objects orbiting a single body, such as a planet orbiting a star. For objects with multiple orbiting bodies, a more complex formula is needed to calculate the mass.

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