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Help with question, with the use of Newton's version of Kepler's third law


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Hi

I don't know if this the right forum for this, but here it goes.

With use of Newton's version of Kepler's third law i have to calculate the question below.

Pluto's moon Charon orbits Pluto every 6.4 days with a semimajor axis of 19 700 kilometers. Calculate the combined mass of Pluto and Charon.

Some kind soul that have the ability to help me?

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I have all the data I need to calculate this. The problem is after countless times of trying, I just can't get the equation to work. After googling the question, I found several ways to find the answer, but for the lack of explanation I don't know how they got the answer. Or if its any difference with trying to find the mass when you only know the semimajor axis. 

Simply, I just need somone to guide me, maybe give me a headstart on how the right equation is.

 

 

 

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Hi there

so I am doing something similar ATM.  Newton showed us that you can calculate the mass of the primary from the observation of its satellite, and Kepler third law is the bit after the '=' sign (next three lines are the base equation, but I can't write it properly here!)

GM = r^3

----    -----

4pi^2  T^2

that enables you to call mass of pluto

Then..

m=(A^3/P^2)-M  to give you the mass of Charon 

where

G is Universal Gravitational constant

M is mass of primary body in kg

r is radius in AU

A is the distance between them in AU

T is period in years

m is mass of secondary in kg

 

I didn't do the calculation for you, but pretty sure that's the format of how to get there.  

PS: obviously disclaimers apply, , or 'don't blame me if it's wrong'?

Good Luck and post back with confirmation or correction please ?

Mike

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For the Pluto Charon problem you need to express semi-major in metres  axis and orbital period period in seconds. The combined mass then comes out on kilograms.

HyperPhysics is a good repository for formulas. Just google "hyperphysics + keyword" and you'll get your quick hints for just about any physics problem. For Kepler's laws you'll end up here: http://hyperphysics.phy-astr.gsu.edu/hbase/kepler.html.

                                   4 ⋅ pi^2 ⋅ a^3
Law of periods:  T^2 = ------------------
                                    G ⋅ (M+ M2)

                                     4 ⋅ pi^2 ⋅ a^3
Rewrite it:      M+ M2 = ------------------
                                         G ⋅ T^2

Use SI units and fill in the values for T, a, and G
G is the gravitational constant. You should find that M+ M2 is in the order of 10^22 kg.

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