Calculating Orbital Parameters of Halley's Comet

[conquertheworld5]

Okay, so I get the concept behind Newton's version of Kepler's 3rd law, but everytime I go to do a problem with it, I get totally lost. This may be because I have never seen one done in a way that did not totally confuse me... I think it might be best if I just ask one of the questions that's bothering me...

"The distance of closest approach of Halley's comet to the Sun is 8.9X10^10 m. Its period is 76 yr. Calculate the following: a) semimajor axis (b) eccentricity (c) aphelion distance (dist. farthest from sun)"

So, here's what I know, semimajor axis = a = (Rmin +Rmax)/2, eccentricity = e = (Rmax - Rmin)/2a
and of course Kepler's law T^2 is proportional to R^3, or Newton's
T^2/R^3 = 4(pi^2)R^3/GM

So... I don't expect (or want) to be given the answer... i want to finally understand this stuff so that I don't have to continue struggling with it. Maybe there's some basic aspect of this that I've missed every time I've seen it...or maybe it's the continual use of different letters for variables that confuses me. I don't know... Any help would be appreciated.

 

[conquertheworld5]

p.s. the "ACK!" in the subject was just an onomatopoeiatic exclamation of dismay... i realized after that it could be mistaken for some part of a formula or something.

 

[OlderDan]

What do you mean by R?

 

[conquertheworld5]

distance from the sun i think

 

[OlderDan]

distance from the sun i think

For a comet, the distance from the sun is constantly changing. What do you use for R then?

http://www.go.ednet.ns.ca/~larry/orbits/kepler.html

 

[conquertheworld5]

yeah...R is constantly changing, it's the distance from one of the focii in the ellipse to the body that's orbiting... sooo yeah, I don't know.

 

[OlderDan]

yeah...R is constantly changing, it's the distance from one of the focii in the ellipse to the body that's orbiting... sooo yeah, I don't know.

For elliptical orbits the period is related to the semi-major axis. Take a look at the link I posted near the bottom.

 

[conquertheworld5]

Hmm...but i can't use p^2 = a^3 because it shouldn't be an equality, I thought that's why Newton had to develope the equation that's below that one... but that one relies on masses which are not given to me in the problem. Arg... I think I'm giving up for the night, I have to head off to bed. Thanks for the help though - Feel free to respond to me again, I'll check it in the morning.
Thanks again.

 

[OlderDan]

Hmm...but i can't use p^2 = a^3 because it shouldn't be an equality, I thought that's why Newton had to develope the equation that's below that one... but that one relies on masses which are not given to me in the problem. Arg... I think I'm giving up for the night, I have to head off to bed. Thanks for the help though - Feel free to respond to me again, I'll check it in the morning.
Thanks again.

Don't worry about the Newton refinement. You only need that if the masses of the two objects are comparable. The mass of the sun is huge compared to a comet, so only the mass of the sun is needed.