Troubleshooting Kepler's Third Law with Halley's Comet

[ehrenfest]

Homework Statement

When I plug in all of the parameters for Halley's comet (from Wikipedia) into Kepler's third law a get a semimajor axis of 38.56 AU when it should be about 17? Can someone else try it and see if I am crazy?

Homework Equations

The Attempt at a Solution

 

[Dick]

What parameters are you trying to plug into what equation?

 

[ehrenfest]

mass of halley's comet = negligable
mass of the sun
G
T = 76 years

 

[Dick]

I get that 76^2 is pretty close to 17.8^3. Perhaps you are crazy. :) Remember that the Earth semimajor axis is 1 AU and it's period is 1 year.

 

[ehrenfest]

OK here are the details:

38.5654 = (T^2/(4 pi^2) * G * (Ms))^(1/3)/(1.4*10^11)

where T is the period in seconds, Ms = 1.991*10^31 and G = 6.674 * 10^(-11)
what am I doing wrong?

 

[dynamicsolo]

OK here are the details:

38.5654 = (T^2/(4 pi^2) * G * (Ms))^(1/3)/(1.4*10^11)

where T is the period in seconds, Ms = 1.991*10^31 and G = 6.674 * 10^(-11)
what am I doing wrong?

The mass of the Sun is 1.99*10^30 kg... (Your result for a is off by very nearly the cube root of 10.)

 

[Dick]

You beat me! I just figured that out. But, ehrenfest, for solar orbits if you work in AU and years, the constant proportionality k in R^3=k*T^2, is one.

 

[dynamicsolo]

You beat me! I just figured that out. But, ehrenfest, for solar orbits if you work in AU and years, the constant proportionality k in R^3=k*T^2, is one.

My training's largely in astrophysics, so I have the solar mass by heart. I would usually take the proportionality approach myself as well, though...

 

[Dick]

Funny, my training is in cosmology, so I know it's like to ten the fifty some proton masses. And fifty plus what I forget. Good job.

 

[ehrenfest]

Ahh! 30 minutes of frustration because my short-term memory is not good enough to look at a computer screen and then write down a two-digit number without botching a digit!

Thanks guys.

 

[dynamicsolo]

Funny, my training is in cosmology, so I know it's like to ten the fifty some proton masses. And fifty plus what I forget. Good job.

Close enough... ;-) When I was an undergraduate, cosmology was called "the science where you're happy when your order of magnitude is right to an order of magnitude". Nowadays we speak of "precision" cosmology -- what an age we live in...

 

[dynamicsolo]

30 minutes of frustration...

Everybody makes copying errors (when they're not making *sign* errors), so I know just how you feel...