Calculating Orbital Parameters of Halley's Comet

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In summary, Don't know how to do a problem with Newton's version of Kepler's 3rd law. Everytime I try, I get totally lost. I think it might be best if I ask one of the questions that's bothering me.
  • #1
conquertheworld5
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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.
 
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  • #2
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.
 
  • #3
What do you mean by R?
 
  • #4
distance from the sun i think
 
  • #5
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  • #6
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.
 
  • #7
conquertheworld5 said:
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.
 
  • #8
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.
 
  • #9
conquertheworld5 said:
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.
 

What is Kepler's 3rd Law of Planetary Motion?

Kepler's 3rd Law of Planetary Motion, also known as the Harmonic Law, states that the square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit around the sun.

What did Newton contribute to our understanding of planetary motion?

Sir Isaac Newton's contribution to our understanding of planetary motion was his Law of Universal Gravitation. This law states that every object in the universe is attracted to every other object with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

How does Newton's Law of Universal Gravitation relate to Kepler's 3rd Law?

Newton's Law of Universal Gravitation provides the explanation for why Kepler's 3rd Law holds true. The gravitational force between a planet and the sun is what keeps the planet in its orbit, and the strength of this force is directly related to the planet's orbital period and distance from the sun.

What is the significance of Kepler's 3rd Law and Newton's Law of Universal Gravitation?

Together, Kepler's 3rd Law and Newton's Law of Universal Gravitation allowed for a better understanding of the motion of planets and other celestial bodies. These laws have played a crucial role in the development of modern astronomy and have helped us make many important discoveries about our solar system and the universe.

Are Kepler's 3rd Law and Newton's Law of Universal Gravitation still accepted today?

Yes, both of these laws are still accepted today and are considered fundamental principles in the field of astrophysics. However, they have been refined and expanded upon by other scientists and theories, such as Einstein's theory of general relativity.

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