How are comet orbits calcluated?

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Offline thedoc

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How are comet orbits calcluated?
« on: 09/04/2013 05:30:01 »
Neil Briscoe asked the Naked Scientists:
How is (a comet's) orbit, and hence return period, calculated?

What do you think?
« Last Edit: 09/04/2013 05:30:01 by _system »


Offline yor_on

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Re: How are comet orbits calcluated?
« Reply #1 on: 09/04/2013 14:58:20 »
Historically it started as guesswork based on mathematics. Halley's Comet

"In 1687, Sir Isaac Newton published his Principia, in which he outlined his laws of gravity and motion. His work on comets was decidedly incomplete. Although he had suspected that two comets that had appeared in succession in 1680 and 1681 were the same comet before and after passing behind the Sun (he was later found to be correct; see Newton's Comet), he was unable to completely reconcile comets into his model. Ultimately, it was Newton's friend, editor and publisher, Edmond Halley, who, in his 1705 Synopsis of the Astronomy of Comets, used Newton's new laws to calculate the gravitational effects of Jupiter and Saturn on cometary orbits.

 This calculation enabled him, after examining historical records, to determine that the orbital elements of a second comet which had appeared in 1682 were nearly the same as those of two comets which had appeared in 1531 (observed by Petrus Apianus) and 1607 (observed by Johannes Kepler). Halley thus concluded that all three comets were in fact the same object returning every 76 years, a period that has since been amended to every 7576 years. After a rough estimate of the perturbations the comet would sustain from the gravitational attraction of the planets, he predicted its return for 1758."

As for how we do it today, and how far we can see and compute other orbits I'm not sure, maybe you can find the answer here?
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Offline evan_au

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Re: How are comet orbits calcluated?
« Reply #2 on: 10/04/2013 10:07:57 »
After Newton, astronomers knew that the orbit of a comets must follow an orbit around the sun which is a conic section - usually an ellipse (but you can also have a parabola, hyperbola or circle).

There are 6 numbers needed to define an elliptical orbit, called the Keplerian elements. This site shows how to calculate it for satellites orbiting the Earth, but the same principles apply for comets orbiting the Sun. Once you know the orbit, you can work out the period of the orbit.

As soon as a comet was discovered, astronomers traditionally tracked the motion of the comet against the stars, until it eventually disappeared from view. Astronomers try to "fit" these observations to one of the conic sections.

The comet is somewhat fuzzy and asymmetrical, so the position measurements will have some errors, and may not fit any of the conic sections. By taking a large number of measurements, and using regression analysis, the "best" conic section can be selected.

Today, radar provides an additional source of information, in that it is able to measure the velocity and distance very accurately along the line of sight.

There is an orbital adjustment needed if a comet passes close to a planet, as the planet's gravity can divert it into a different orbit, changing some of the orbital elements. This is most easily predicted by a computer.

Comets which have parabolic or hyperbolic orbits return to interstellar space, so the orbital period is infinite.

Unfortunately, if the comet is only tracked over a small part of its orbit, the uncertainties may be so large that the comet is effectively "lost", until it returns on the next pass of an elliptical orbit.
« Last Edit: 10/04/2013 21:36:43 by evan_au »