View Full Version : Nagging Comet Question

Chief Engineer Scott

2005-May-20, 05:52 PM

Not entirely sure how to formulate this question, but here goes -

AFAIK comets "accelerate" toward the Sun, "slingshot" around it, then "decelerate" as they move outward through the solar system. At apogee the gravitational attraction of the Sun then overcomes any outward acceleration and the return journey begins.

Would I be correct in surmising that there is a limit to this orbital period?

i.e a comet could return theoretically every 250 years, but not every 300 years as orbit could not be achieved and having travelled once round the Sun it then headed of in the general direction of Alpha Centauri never to return.

ToSeek

2005-May-20, 05:56 PM

You're absolutely right, though you're off on the limit. Comet Kohoutek (that fizzle from the 70's) was estimated (IIRC) to have an orbital period on the order of 50,000 years. And I bet the real limit is much, much higher than that.

JohnOwens

2005-May-20, 06:23 PM

Not entirely sure how to formulate this question, but here goes -

AFAIK comets "accelerate" toward the Sun, "slingshot" around it, then "decelerate" as they move outward through the solar system. At apogee the gravitational attraction of the Sun then overcomes any outward acceleration and the return journey begins.

Would I be correct in surmising that there is a limit to this orbital period?

i.e a comet could return theoretically every 250 years, but not every 300 years as orbit could not be achieved and having travelled once round the Sun it then headed of in the general direction of Alpha Centauri never to return. (em. added)

Right conclusion, but wrong approach. There is never any outward acceleration to be overcome, only inward acceleration, and sometimes (pretty much exactly half the time) outward velocity. The always accelerate towards the Sun, unles they're interacting strongly with a planet or other body.

The theoretical limits are when a comet reaches escape velocity, either by gravitational interaction with a planet or other body, or because it entered from outside the solar system; at this speed, the Sun's gravity will never quite eliminate the comet's outward velocity.

For practical limits, I'd figure roughly the period of a comet with aphelion (not apogee) halfway from here to the nearest star, so around two light-years. If it gets any further than that, it's probably going to be captured by someone else's gravity, sooner or later.

Russ

2005-May-21, 12:26 AM

IIRC comet Hale-Bopp has a 2400 or2600 year orbit. So they can be quite long. (from a human point of view)

Regarding parabolic orbits: Any comet that originates from an orbit, a Kuiper Belt Object (KBO) or in the Oort Clout (OCO), will tend to have a closed orbit. It continually orbits the Sun in a highly eliptical path.

It is possible, but not probable, that a comet could come from interstellar space and have a parabolic or open orbit. This means that it approaches the Sun, swings around and exits the Solar System with no return trajectory. To the best of my knowledge, there have been no doccumented comets of this type.

Anybody have better information?

Maksutov

2005-May-21, 12:36 AM

IIRC comet Hale-Bopp has a 2400 or2600 year orbit. So they can be quite long. (from a human point of view)

Regarding parabolic orbits: Any comet that originates from an orbit, a Kuiper Belt Object (KBO) or in the Oort Clout (OCO), will tend to have a closed orbit. It continually orbits the Sun in a highly eliptical path.

It is possible, but not probable, that a comet could come from interstellar space and have a parabolic or open orbit. This means that it approaches the Sun, swings around and exits the Solar System with no return trajectory. To the best of my knowledge, there have been no doccumented comets of this type.

Anybody have better information?

Here's a site that discusses this subject in general terminology. (http://encke.jpl.nasa.gov/orbits.html) Everything (so far) is elliptical, except when the period gets really long (1000+years) and the ellipse gets really stretched, at which point using a parabolic approximation is possible. But it's still really an elliptical orbit, since it's closed.

Chief Engineer Scott

2005-May-23, 11:39 AM

JohnOwen

Thanks for the corrections, I KNEW I hadn't formulated the question correctly! :oops:

You further stated that a comet with an aphelion of around 2 light years could have a parabolic orbit.

Taking this information into account, would it be of any use for correcting some of the woo-woos out there? I mean would it be possible to suggest that - "your scenario that we are in danger from a comet (this year / next year / sometime) which wiped out the civilisation of mahatmakoat 250,000 years ago is invalid, as comets with a period of > 220,000 would have to be on a parabolic orbit, and even if it had passed 250,000 years ago, it is now on it's merry way to Alpha Centauri/ Arcturus / Orion."

JohnW

2005-May-23, 03:51 PM

I'm not an orbital mechanics expert by any means, but as I understand it, the higher the eccentricty of a closed orbit, the easier it is to perturb it into an open one. This means that comets with VERY long periods are not likely to remain in them for many turns around the sun - sooner or later they will come close to a planet and either be nudged into a shorter-period orbit, or thrown out of the solar system altogether. And the longer the period, the easier it becomes to do this.

ToSeek

2005-May-23, 04:40 PM

If I did my math right, according to Kepler's Third Law, a comet with a 2 light-year aphelion would have an orbital period of about 15,000,000 years.

A Thousand Pardons

2005-May-23, 04:47 PM

If I did my math right, according to Kepler's Third Law, a comet with a 2 light-year aphelion would have an orbital period of about 15,000,000 years.

And that wouldn't necessarily be a maximum--if the aphelion was away from the nearest star rather than close to it.

JohnOwens

2005-May-24, 01:07 AM

If I did my math right, according to Kepler's Third Law, a comet with a 2 light-year aphelion would have an orbital period of about 15,000,000 years.

And that wouldn't necessarily be a maximum--if the aphelion was away from the nearest star rather than close to it.

But remember the timescale you're talking about here - so, if the aphelion was away from which of the stars that pass nearest over the next 15 megayears? There might be a few passing by, and the comet's aphelion would have to be kind of away from all of them.

Edit: corrected eon misuse

A Thousand Pardons

2005-May-24, 02:40 PM

If I did my math right, according to Kepler's Third Law, a comet with a 2 light-year aphelion would have an orbital period of about 15,000,000 years.

And that wouldn't necessarily be a maximum--if the aphelion was away from the nearest star rather than close to it.

But remember the timescale you're talking about here - so, if the aphelion was away from which of the stars that pass nearest over the next 15 eons? There might be a few passing by, and the comet's aphelion would have to be kind of away from all of them.

Is an eon equal to one million years? I thought an eon was a few eras.

Still, I'm pretty sure that there are not a lot of NSOS (Near Sol Wandering Stars), so they wouldn't be hard to miss, especially if the comet spends a bit of the time near Sol

Kullat Nunu

2005-May-24, 03:17 PM

But remember the timescale you're talking about here - so, if the aphelion was away from which of the stars that pass nearest over the next 15 eons?

Is an eon equal to one million years? I thought an eon was a few eras.

If you mean geological eons, Archaean lasted for about 2 billion years, Proterozoic about the same. Phanerozoic eon is the ongoing eon and has lasted for 542 million years. Each eon is subdivided into eras, and one era spans from couple to several hundred million years. So these are much longer timespans.

Chief Engineer Scott

2005-May-24, 06:49 PM

ToSeek Wrote:

If I did my math right, according to Kepler's Third Law, a comet with a 2 light-year aphelion would have an orbital period of about 15,000,000 years.

I Wrote:

would it be possible to suggest that - "your scenario that we are in danger from a comet (this year / next year / sometime) which wiped out the civilisation of mahatmakoat 250,000 years ago is invalid, as comets with a period of > 220,000 would have to be on a parabolic orbit, and even if it had passed 250,000 years ago, it is now on it's merry way to Alpha Centauri/ Arcturus / Orion."

Guess I can't use that argument for a while then....... :lol:

JustAGuy

2005-May-24, 08:52 PM

If I did my math right, according to Kepler's Third Law, a comet with a 2 light-year aphelion would have an orbital period of about 15,000,000 years.

Out of curiousity, how fast would that bad boy be moving at perihelion, assuming it was earth-crossing? (1AU perihelion)

ETA: Me spel gud.

A Thousand Pardons

2005-May-24, 09:47 PM

If I did my math right, according to Kepler's Third Law, a comet with a 2 light-year aphelion would have an orbital period of about 15,000,000 years.

Out of curiousity, how fast would that bad boy be moving at perihelion, assuming it was earth-crossing? (1AU perihelion)

Orbit speed is 70% (sqrt(2)/2) of escape velocity, so it can't go any faster than just 41% faster than whatever planetary orbit it reaches down to, if it is to return. So, at 1AU, it'd be going a lot slower than Mercury (48km/s).

JustAGuy

2005-May-24, 09:58 PM

If I did my math right, according to Kepler's Third Law, a comet with a 2 light-year aphelion would have an orbital period of about 15,000,000 years.

Out of curiousity, how fast would that bad boy be moving at perihelion, assuming it was earth-crossing? (1AU perihelion)

Orbit speed is 70% (sqrt(2)/2) of escape velocity, so it can't go any faster than just 41% faster than whatever planetary orbit it reaches down to, if it is to return. So, at 1AU, it'd be going a lot slower than Mercury (48km/s).

Which, of course, begs the question: Can an object even have a 2ly, 1AU orbit? And, if not, was is the max aphelion for a 1AU perihelion? (Yielding the longest period destruct-o-matic solar body possible)

JohnOwens

2005-May-24, 11:44 PM

But remember the timescale you're talking about here - so, if the aphelion was away from which of the stars that pass nearest over the next 15 eons?

Is an eon equal to one million years? I thought an eon was a few eras.If you mean geological eons, Archaean lasted for about 2 billion years, Proterozoic about the same. Phanerozoic eon is the ongoing eon and has lasted for 542 million years. Each eon is subdivided into eras, and one era spans from couple to several hundred million years. So these are much longer timespans.

Hmm, I'm not finding anything right off the bat to back me up, but I thought that while that was the geological usage, "eon" could also mean a million years? Or am I thinking of some other term, the next step beyond millenium?

But I don't like writing the same "15,000,000 years" over and over again, so I like to throw in some variety that way. It might have messed me up this time, though.

If I did my math right, according to Kepler's Third Law, a comet with a 2 light-year aphelion would have an orbital period of about 15,000,000 years. Out of curiosity, how fast would that bad boy be moving at perihelion, assuming it was earth-crossing? (1 AU perihelion)

Well, I'll start off by saying that my math pretty well agrees with yours, though I get something closer to 16,000,000 years. But considering how ballpark the 2 ly figure is, that's plenty close enough.

So anyway, for how fast at Earth's orbit, it's simple enough to figure by just assuming that its specific kinetic energy at 2 ly is 0 (it isn't, of course, but the amount will be trivial compared to what we add next), and then figure the specific potential energies at 2 ly (also almost 0) and 1 AU, find the difference between those two specific potentials, and add that to the specific kinetic energy. Then, apply E = m*v^2/2; v = sqrt(2*E/m). So, it's not going to be much different from the escape velocity of our Sun at 1 AU. Which, if I recall correctly off the top of my head, is about 47.1 km/s, the number you see crop up on some of those asteroid/comet impact simulators as a "speed limit" for something to hit Earth with. Wait, actually, the "speed limit" would be something like the Sun's 1 AU escape velocity, plus the Earth's orbital velocity, plus a little bit more for acceleration from Earth's own gravity well. And that might be more appropriate for the speed your asking about anyway. But for now, I'll take a slightly more rigorous approach than "off-the-top-of-my-head", and crunch the numbers....

Lessee, SPE of 7,000 m^2/s^2 at 2 ly, SPE of about 9x10^8 m^2/s^2 at 1 AU, so yeah, like I said, the 2 ly SPE isn't going to matter much. But let's subtract it anyway, and plug it into v = sqrt(2*SE) (SE = specific energy). We get 42122 m/s, or 42.1 km/s, pretty close to my top-of-the-head figure. I'll poke at a couple of those impact simulators and see what they say, exactly.

Added: Ah, here it is (http://www.lpl.arizona.edu/impacteffects/): "The minimum impact velocity on Earth is 11 km/s. Typical impact velocities are 17 km/s for asteroids and 51 km/s for comets. The maximum Earth impact velocity for objects orbiting the sun is 72 km/s." So I was probably thinking of a slightly different figure for the typical comet, rather than the max. Adding Earth's 29.8 km/s orbital velocity to the 42.1 km/s I figured above comes out just about right for the figure they list as max, though.

jnik

2005-May-25, 02:39 PM

Hmm, I'm not finding anything right off the bat to back me up, but I thought that while that was the geological usage, "eon" could also mean a million years? Or am I thinking of some other term, the next step beyond millenium?

Eon is 10^9 years, a billion (US) or thousand million (UK). Millennium is a thousand years.

ToSeek

2005-May-25, 02:39 PM

Can an object even have a 2ly, 1AU orbit?

There are no factors involving basic physics preventing such an orbit. However, as has been suggested, such an orbit isn't going to be stable for long: at aphelion, there's a good chance of a star passing by and disrupting the orbit; near perihelion, sooner or later the comet will pass close enough to a planet to have its orbit disrupted.

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