Troubleshooting Kepler's Third Law with Halley's Comet

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Homework Help Overview

The discussion revolves around the application of Kepler's third law to Halley's Comet, specifically regarding the calculation of its semimajor axis. The original poster expresses confusion over a calculated value significantly different from expected results.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants inquire about the specific parameters being used in the calculations and the equations applied. There is a focus on the relationship between the period of Halley's Comet and its semimajor axis, with some participants questioning the constants and values used in the calculations.

Discussion Status

Some participants have provided insights into the calculations, noting potential errors in the original poster's approach. There is an acknowledgment of the proportionality constant in Kepler's law when using astronomical units and years, and a recognition of common errors in numerical transcription.

Contextual Notes

Participants mention the mass of Halley's Comet as negligible compared to the mass of the Sun, and there are references to the specific values for gravitational constant and solar mass used in the calculations. The discussion reflects a mix of personal experiences and academic backgrounds in astrophysics and cosmology.

ehrenfest
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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

 
Last edited:
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What parameters are you trying to plug into what equation?
 
mass of halley's comet = negligable
mass of the sun
G
T = 76 years
 
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.
 
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?
 
ehrenfest said:
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.)
 
Last edited:
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.
 
Dick said:
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...
 
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.
 
  • #10
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.
 
  • #11
Dick said:
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...
 
  • #12
ehrenfest said:
30 minutes of frustration...

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

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