Max Aphelion Distance of Kuiper Belt Comet w/216 yr Orbital Period

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Discussion Overview

The discussion revolves around determining the maximum possible aphelion distance for a Kuiper Belt comet with an orbital period of 216 years. Participants explore the implications of the semi-major axis, eccentricity, and the conditions that define a Kuiper Belt object versus a periodic comet.

Discussion Character

  • Homework-related
  • Exploratory
  • Debate/contested

Main Points Raised

  • One participant calculates the semi-major axis as 36 AU using the equation P^2 = a^3.
  • Another participant questions the meaning of "maximum possible aphelion" in relation to perihelion distance and whether there is a minimum perihelion for Kuiper Belt objects.
  • A participant suggests that the maximum aphelion could be 71.99 AU but later admits this was an arbitrary choice.
  • There is a discussion about whether a comet that grazes the Sun at perihelion can still be classified as a Kuiper Belt object.
  • One participant proposes that the inner edge of the Kuiper Belt is 30 AU, leading to a calculated maximum possible aphelion of 42 AU based on the minimum perihelion distance.
  • Another participant speculates that a lower eccentricity might be needed for a valid orbit of a short-period comet, but acknowledges uncertainty about the implications.
  • A later reply discusses the nature of comets and their origins, suggesting that the classification as a Kuiper Belt comet relates to its origin rather than its perihelion distance.

Areas of Agreement / Disagreement

Participants express differing views on the maximum possible aphelion distance, with calculations yielding different results (71.99 AU vs. 42 AU). There is no consensus on the implications of perihelion distance for classifying the comet as a Kuiper Belt object or a periodic comet.

Contextual Notes

Participants note the dependence on definitions of Kuiper Belt objects and the conditions under which a comet can be classified as periodic. The discussion highlights unresolved aspects regarding the minimum perihelion distance and its impact on classification.

bri7
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Homework Statement


Find maximum possible aphelion distance for a Kuiper Belt comet with an orbital period of 216 years?
What is the eccentricity of this orbit?
What prevents a periodic comet from following this precise orbit?

Homework Equations


perihelion = a(1-e)
aphelion = a(1+e)
2a = perihelion + aphelion
P^2=a^3

The Attempt at a Solution


P^2=a^3
(216)^2 = a^3
a = 36 AU (semi major axis)

From here, I'm not sure where to go because I don't know the eccentricity, perihelion or aphelion distance
 
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You've calculated the semi-major axis (I think correctly), and you are asked to find the maximum possible aphelion. What does maximum possible aphelion mean in terms of the perihelion? Is there a minimum possible perihelion that the object can have and still be a Kuiper belt object?
 
phyzguy said:
You've calculated the semi-major axis (I think correctly), and you are asked to find the maximum possible aphelion. What does maximum possible aphelion mean in terms of the perihelion? Is there a minimum possible perihelion that the object can have and still be a Kuiper belt object?
Okay so since the aphelion is the point where the comet is furthest form the Sun, the max aphelion is 71.99 AU, and then I can calculate the eccentricity of the orbit
 
bri7 said:
Okay so since the aphelion is the point where the comet is furthest form the Sun, the max aphelion is 71.99 AU, and then I can calculate the eccentricity of the orbit

How did you come up with the 71.99 AU number?
 
phyzguy said:
How did you come up with the 71.99 AU number?
The major axis is 72 au and the max distance that the comet can be from the Sun is some number very close to 72, such that the orbit goes very close to the Sun at perihelon and very far away at aphelion
71.99 was just something I picked
 
If it grazes the sun at perihelion, would it be considered a Kuiper belt object?
 
phyzguy said:
If it grazes the sun at perihelion, would it be considered a Kuiper belt object?
No, I suppose it wouldn't
 
Is the definition of a Kuiper Belt object that it lies between 40 and 50 AU from the Sun?
 
Please don't solve problems for others, that's against forum rules you agreed to when registering. Instead prod them in the right direction.
Here are my thoughts:
The inner edge of the Kuiper Belt is 30 AU, outer edge is 50 AU. Hence, the closest the comet's orbit can get to the Sun is 30 AU. This is our perihelion, because in order to maintain that the semi major axis is 36, and we want the maximum possible aphelion, we calculate with the minimum possible perihelion.

So, we use the equation; semi major axis = (aphelion + perihelion)/2, giving us
36= (A+30)/2
A=42
The max possible aphelion is 42 AU.
 
  • #10
Emi11 said:
Here are my thoughts:
The inner edge of the Kuiper Belt is 30 AU, outer edge is 50 AU. Hence, the closest the comet's orbit can get to the Sun is 30 AU. This is our perihelion, because in order to maintain that the semi major axis is 36, and we want the maximum possible aphelion, we calculate with the minimum possible perihelion.

So, we use the equation; semi major axis = (aphelion + perihelion)/2, giving us
36= (A+30)/2
A=42
The max possible aphelion is 42 AU.
Thanks, this makes sense :)
I am still wondering why this is not a valid orbit for a periodic comet
 
  • #11
Hmmm, well a short-period comet must have an orbit of 200 years, so perhaps the eccentricity should be lower in order for it to be a valid orbit for a short period comet? However, this doesn't tangibly prevent the comet from following this orbit so I am unsure.
 
  • #12
Sorry for the late reply, but I just noticed this thread. I don't often browse here.

bri7 said:
I am still wondering why this is not a valid orbit for a periodic comet

I think that's a clue that there's no restriction on the minimum perihelion distance for a comet. A comet is an object that passes through the inner solar system where it can be warmed by proximity to the Sun and rendered visible in our night sky. I believe that the designation of the comet as a "Kuiper Belt comet" refers to its place of origin, it being an object perturbed from the Kuiper belt. The aphelion of a periodic comet is a good indication of its origin distance.

So your initial line of though regarding the orbit intersecting the Sun looks valid to me. Look up "degenerate ellipse" or "radial trajectory".

Just because an orbit has a period it doesn't mean it will every have a chance to complete one :smile:
 

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