Comet Elliptical Orbits Question

  • Thread starter Thread starter Chaso
  • Start date Start date
  • Tags Tags
    Comet Orbits
Click For Summary

Homework Help Overview

The discussion revolves around the motion of comets in elliptical orbits, specifically focusing on Comet Halley's speed as it crosses Neptune's orbit. The original poster presents a problem involving the application of conservation laws in celestial mechanics.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to use a momentum conservation equation but finds it leads to an incorrect result. Some participants question the choice of radius for the calculation and suggest alternative approaches, including conservation of energy.

Discussion Status

Participants are exploring different methods to approach the problem, with some suggesting the need to consider the conditions under which the initial formula applies. There is a shift towards discussing energy conservation as a potentially more suitable method for solving the problem.

Contextual Notes

There is a mention of the specific distances involved, such as the distance from Neptune to the sun and the distance at the closest approach of the comet. The discussion also highlights the importance of understanding the relationship between kinetic and potential energy in the context of orbital mechanics.

Chaso
Messages
23
Reaction score
0

Homework Statement


Comets move around the sun in very elliptical orbits. At its closet approach, in 1986, Comet Halley was 8.79 x 10^7 km from the sun and moving with a speed of 54.6 km/s.

What was the comet's speed when it crossed Neptune's orbit in 2006?

Homework Equations



Mv1r1=Mv2r2

The Attempt at a Solution



What I did was use the equation above, and solve for v2. But it says I'm wrong. Any Suggestions?
 
Last edited:
Physics news on Phys.org
What did you use for r2?
What did you get for v2?
 
For r2, I use the radius from Neptune to the sun.
 
Oh I see ... excuse me, didn;t read it properly.
That formula should be:

##\vec{r}_1\times m\vec{v}_1=\vec{r}_2\times m\vec{v}_2##

At Neptune's orbit, the velocity won't be tangential to the radius.
 
Chaso said:

Homework Statement


Comets move around the sun in very elliptical orbits. At its closet approach, in 1986, Comet Halley was 8.79 x 10^7 km from the sun and moving with a speed of 54.6 km/s.

What was the comet's speed when it crossed Neptune's orbit in 2006?

Homework Equations



Mv1r1=Mv2r2

The Attempt at a Solution



What I did was use the equation above, and solve for v2. But it says I'm wrong. Any Suggestions?

The formula you've chosen would apply when the velocities are both perpendicular to the radii, say at perihelion and at aphelion. Here this holds true for only one of the given points (the closest approach).

Instead, consider a conservation of energy approach.
 
gneill said:
The formula you've chosen would apply when the velocities are both perpendicular to the radii, say at perihelion and at aphelion. Here this holds true for only one of the given points (the closest approach).

Instead, consider a conservation of energy approach.
So use K2 + U2 = K1 + U1

expansion to:
(1/2)(Mc)(v2^2) + -(G)(Me)(Mc)/(R) = (1/2)(Mc)(v1^2) + -(G)(Me)(Mc)/(R2)

R = Distance of neptune from sun
R2 = 8.79 x 10^7

Is this what I do?
 
Last edited:
Mc is the mass of the comet and Me is the mass of the body the comet is orbiting?

Note: another way thinking about it is "potential energy gained equals kinetic energy lost".
 

Similar threads

A comet at its closest approach to the Sun
  • · Replies 1 ·
Replies
1
Views
2K
Did I Calculate the Speed of a Comet Correctly?
  • · Replies 6 ·
Replies
6
Views
4K
Velocity of Comet at a given distance
  • · Replies 2 ·
Replies
2
Views
2K
Example in chapter: Gravitation
  • · Replies 3 ·
Replies
3
Views
2K
Investigating Comet 67P's Elliptical Orbit
  • · Replies 3 ·
Replies
3
Views
2K
Calculating Comet Halley's Speed Across Neptune's Orbit
  • · Replies 1 ·
Replies
1
Views
6K
Comet on a parabolic orbit around the Sun
  • · Replies 5 ·
Replies
5
Views
3K
Use angular momentum to find the velocity (comet orbit)
  • · Replies 14 ·
Replies
14
Views
3K
High School 3I/ATLAS, Interstellar Comet
  • · Replies 21 ·
Replies
21
Views
7K
What Is the Speed of the Comet at a Different Distance?
  • · Replies 17 ·
Replies
17
Views
3K