Calculating Mass-Kepler's 3rd Law

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In summary, Kepler's 3rd Law, also known as the Harmonic Law, states that the square of a planet's orbital period is directly proportional to the cube of its semi-major axis. This means that the further a planet is from its parent star, the longer its orbital period will be. To calculate the mass of a planet or star using Kepler's 3rd Law, you need to know the orbital period and the semi-major axis of the planet's orbit. The units used for mass in Kepler's 3rd Law depend on the units used for the other variables in the formula. Kepler's 3rd Law can be used for any object in orbit, as long as its orbit is elliptical and it is orbiting
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winterrose
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Okay, so I understand that a3/p2=M

I must be missing something though.

I know that (6x10^9)3 / (7.8x10^8)2 = 3.6x10^11 MSun

but I don't understand what step I'm missing. When I divide, I end up with 0.3550^12

what am I doing wrong?

Is my answer in kilograms, and do I have to convert it to MSun?
 
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welcome to pf!

hi winterrose! welcome to pf! :smile:

(try using the X2 icon just above the Reply box :wink:)
winterrose said:
… = 3.6x10^11 MSun

but I don't understand what step I'm missing. When I divide, I end up with 0.3550^12

they're (aproximately) the same, aren't they? :wink:
 

What is Kepler's 3rd Law?

Kepler's 3rd Law, also known as the Harmonic Law, states that the square of a planet's orbital period is directly proportional to the cube of its semi-major axis. This means that the further a planet is from its parent star, the longer its orbital period will be.

How do you calculate mass using Kepler's 3rd Law?

To calculate the mass of a planet or star using Kepler's 3rd Law, you need to know the orbital period and the semi-major axis of the planet's orbit. You can then use the formula M = 4π²a³/GT², where M is the mass of the planet or star, a is the semi-major axis, G is the gravitational constant, and T is the orbital period.

What units should be used when calculating mass using Kepler's 3rd Law?

The units used for mass in Kepler's 3rd Law depend on the units used for the other variables in the formula. The semi-major axis is typically measured in astronomical units (AU), the orbital period is measured in years, and the gravitational constant is measured in units of AU³/year². This will result in the mass being measured in units of solar masses.

Can Kepler's 3rd Law be used for any object in orbit?

Kepler's 3rd Law can be used for any object in orbit, as long as its orbit is elliptical and it is orbiting a single object. This law is commonly used to calculate the mass of planets orbiting around stars, but it can also be used for other celestial objects such as moons orbiting around planets.

Are there any limitations to using Kepler's 3rd Law to calculate mass?

Yes, there are certain limitations to using Kepler's 3rd Law to calculate mass. This law assumes that the orbit is circular or elliptical and that there are no other objects influencing the orbit. It also does not take into account the mass of the object being orbited, so it is not accurate for calculating the mass of a planet orbiting a binary star system.

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