Apocentre and Eccentricity of a Comet's Orbit

In summary, the problem asks for the apocentre distance and eccentricity of a comet with a velocity of 38km/s that passes close to Earth. Using the vis-viva equation, the semi-major axis is determined to be approximately 4.02x10^11 meters, which suggests a highly eccentric orbit. However, without more information, it is difficult to determine a more precise value for the eccentricity. The aphelion could be as far as 5.4 AU, but could also be closer to 1 AU if the eccentricity is closer to zero.
  • #1
PChar
11
0

Homework Statement


If a comet passes close to the Earth with a velocity of 38km/s, how far is the apocentre of its orbit from the Sun? What is the eccentricity of its orbit?


Homework Equations


Vis-Viva Equation:

(V)[itex]_{ecc}[/itex][itex]^{2}[/itex] = GM [ [itex]\frac{2}{R}[/itex] - [itex]\frac{1}{a}[/itex] ]

Apocentre distance:

a(1 + e)


The Attempt at a Solution



I found the semi-major axis using the vis-viva equation, but I'm really not sure what to do next,I think I should be trying to find where the radial velocity is zero, but I don't seem to have enough information.
 
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  • #2
I think I just realized what I need to do. Do I just need to plug the apocentre distance into the vis-viva equation and solve for e?

EDIT: nevermind, still stuck, just tried this and I got a negative eccentricity.
 
Last edited:
  • #3
PChar said:

Homework Statement


If a comet passes close to the Earth with a velocity of 38km/s, how far is the apocentre of its orbit from the Sun? What is the eccentricity of its orbit?

Is the above the entire problem statement, word for word?

As it is, the problem statement doesn't provide enough information to determine the precise shape of the comet's orbit. The semimajor axis is accessible via the vis-viva equation as you've already determined. What value did you get? What does that say about the general overall shape of the orbit? Can you at least put bounds on the possible values of the eccentricity?
 
  • #4
Yeah, that's all the problem statement says, word for word.

Anyway, I got 4.02*10[itex]^{11}[/itex] metres as the semimajor axis. Given that it's a comet, I'm at least assuming that the orbit is highly eccentric, less than 1, since it asks for the apocentre, but greater than, probably 0.9, but without more information it's difficult to get more precise.
 
  • #5
PChar said:
Yeah, that's all the problem statement says, word for word.

Anyway, I got 4.02*10[itex]^{11}[/itex] metres as the semimajor axis. Given that it's a comet, I'm at least assuming that the orbit is highly eccentric, less than 1, since it asks for the apocentre, but greater than, probably 0.9, but without more information it's difficult to get more precise.

Yup. 4.02x1011m is about 2.7 AU. 2a about 5.4 AU. Mars' orbit is about 1.5 AU, Jupiter's about 9.5 AU. Looks more like a wayward asteroid than a comet. The aphelion could be as far out as nearly 5.4 AU (assuming the comet is to survive its passage around the Sun), and could be a lot closer to the Earth's 1 AU if the eccentricity is closer to zero.
 

1. What is the apocentre of a comet's orbit?

The apocentre is the point in a comet's orbit that is farthest away from the sun.

2. How is the apocentre of a comet's orbit determined?

The apocentre of a comet's orbit can be determined by measuring the distance between the comet and the sun when the comet is at its farthest point in its orbit.

3. What is the significance of the apocentre in a comet's orbit?

The apocentre is significant because it helps determine the shape and size of a comet's orbit, as well as its distance from the sun at its farthest point.

4. What is eccentricity in relation to a comet's orbit?

Eccentricity is a measure of how elongated or circular a comet's orbit is. A low eccentricity indicates a more circular orbit, while a high eccentricity indicates a more elongated orbit.

5. How does the eccentricity of a comet's orbit affect its behavior?

The eccentricity of a comet's orbit plays a role in its behavior, as it can affect the comet's speed and distance from the sun at different points in its orbit. A higher eccentricity can also result in more dramatic changes in a comet's appearance and behavior as it approaches the sun.

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