# calculating a planet's orbit **URL:** \ **Category:** Factual Questions\ **Created:** [April 7, 2004, 4:16pm UTC](https://boards.straightdope.com/t/calculating-a-planets-orbit/238770 "2004-04-07T16:16:30Z")\ **Posts on this page:** 12\ **Page:** 1
**Author:** ![shijinn](https://avatars.discourse-cdn.com/v4/letter/s/cc9497/32.png) [@shijinn](https://boards.straightdope.com/u/shijinn)\ **Post date:** [April 7, 2004, 4:16pm UTC](https://boards.straightdope.com/t/calculating-a-planets-orbit/238770/1 "2004-04-07T16:16:30Z")
“sedna takes 10,500 years to revolve around the sun.” IANAA. given that we’d only recently (this year?) discovered this “shiny planetoid” right at the edge of our own solar system, how accurate is the above statement? is it possible to explain in layman’s terms how the data to calculate the line of orbit is retrieved without going into details? thanks. ---
**Author:** ![CurtC](https://avatars.discourse-cdn.com/v4/letter/c/ce73a5/32.png) [@CurtC](https://boards.straightdope.com/u/CurtC)\ **Post date:** [April 7, 2004, 5:30pm UTC](https://boards.straightdope.com/t/calculating-a-planets-orbit/238770/2 "2004-04-07T17:30:28Z")
They have to observe it moving. Measure its position at one time, then wait a while and measure its position again. This will tell you its speed, and from that you can work out the ellipse that it orbits around. The problem is that we can measure its angular position very well, but it’s hard to say exactly how far away it is. If you have a long time to observe it, you don’t need its distance, since you can use its motion through the sky to infer its distance. I’m not sure how they measured its distance, but it seems like it would be hard to do, so I’d say the 10,500 years is an approximation. ---
**Author:** ![David\_Simmons](https://avatars.discourse-cdn.com/v4/letter/d/9de053/32.png) [@David\_Simmons](https://boards.straightdope.com/u/David_Simmons)\ **Post date:** [April 7, 2004, 8:48pm UTC](https://boards.straightdope.com/t/calculating-a-planets-orbit/238770/3 "2004-04-07T20:48:20Z")
In the case of the newly discovered object, astronomers went back through old photographs, identified the thing on them so they had several observations through time to compute the orbit. But I’m sure it is subject to some revision. ---
**Author:** ![sturmhauke](https://avatars.discourse-cdn.com/v4/letter/s/e47c2d/32.png) [@sturmhauke](https://boards.straightdope.com/u/sturmhauke)\ **Post date:** [April 7, 2004, 10:17pm UTC](https://boards.straightdope.com/t/calculating-a-planets-orbit/238770/4 "2004-04-07T22:17:47Z")
[More info about Sedna](http://www.gps.caltech.edu/~mbrown/sedna/) ---
**Author:** ![Optihut](https://avatars.discourse-cdn.com/v4/letter/o/edb3f5/32.png) [@Optihut](https://boards.straightdope.com/u/Optihut)\ **Post date:** [April 8, 2004, 12:57am UTC](https://boards.straightdope.com/t/calculating-a-planets-orbit/238770/5 "2004-04-08T00:57:48Z")
Well, if it is somehow possible to determine the distance from the sun, then one wouldn’t need to observe it moving and determine its speed, as one could calculate the revolution time with kepler’s law ([http://home.cvc.org/science/kepler.htm](http://home.cvc.org/science/kepler.htm)). ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [April 8, 2004, 2:49am UTC](https://boards.straightdope.com/t/calculating-a-planets-orbit/238770/6 "2004-04-08T02:49:12Z")
Not quite, **Optihut**. For Kepler’s law you need the average distance from the Sun. From just one observation, there’s no telling how elliptical the orbit is, and whether it’ll get closer or further away over the course of its orbit. To determine the orbit of an object, you need at least six pieces of information. This can be, for instance, three photographs of the sky (each one gives you two coordinates of position information), or two photographs and two measurements of distance (however you measure that), or two photographs and two radial velocity measurements (using Doppler shift). In principle, any such six observations are necessary and sufficient to determine the orbit, to within some discrete degeneracies, but in general, you can be a lot more confident with more observations (especially for a slow, distant object like Sedna). You can also guesstimate an orbit using fewer observations, if you can guess some of the orbital parameters. For instance, if you assume that the object is orbiting in the ecliptic plane, then you can make do with only four pieces of information, and if you assume a parabolic orbit (a decent approximation for most comets, for instance), you can dispense with one datum that way. ---
**Author:** ![scr4](https://avatars.discourse-cdn.com/v4/letter/s/59ef9b/32.png) [@scr4](https://boards.straightdope.com/u/scr4)\ **Post date:** [April 8, 2004, 7:38am UTC](https://boards.straightdope.com/t/calculating-a-planets-orbit/238770/7 "2004-04-08T07:38:40Z")
Just looking at the number “10,500”, it’s a safe bet that the meas urement accuracy is roughly 500. 😃 ---
**Author:** ![Optihut](https://avatars.discourse-cdn.com/v4/letter/o/edb3f5/32.png) [@Optihut](https://boards.straightdope.com/u/Optihut)\ **Post date:** [April 8, 2004, 9:56pm UTC](https://boards.straightdope.com/t/calculating-a-planets-orbit/238770/8 "2004-04-08T21:56:34Z")
> [@Chronos](#): > > Not quite, **Optihut**. For Kepler’s law you need the average distance from the Sun. From just one observation, there’s no telling how elliptical the orbit is, and whether it’ll get closer or further away over the course of its orbit. Oh, oops. Good point, I didn’t consider that. ---
**Author:** ![Jinx](https://avatars.discourse-cdn.com/v4/letter/j/c6cbf5/32.png) [@Jinx](https://boards.straightdope.com/u/Jinx)\ **Post date:** [April 9, 2004, 2:14am UTC](https://boards.straightdope.com/t/calculating-a-planets-orbit/238770/9 "2004-04-09T02:14:36Z")
> [@CurtC](#): > > …The problem is that we can measure its angular position very well, but it’s hard to say exactly how far away it is… I beg to differ. I thought the parallax method worked fine for such applications. It’s when the parallax angle becomes too small where we have had to find other ways of determining distances. - Jinx ---
**Author:** ![shijinn](https://avatars.discourse-cdn.com/v4/letter/s/cc9497/32.png) [@shijinn](https://boards.straightdope.com/u/shijinn)\ **Post date:** [April 9, 2004, 5:03am UTC](https://boards.straightdope.com/t/calculating-a-planets-orbit/238770/10 "2004-04-09T05:03:55Z")
> [@David Simmons](#): > > In the case of the newly discovered object, astronomers went back through old photographs, identified the thing on them so they had several observations through time to compute the orbit. But I’m sure it is subject to some revision. from **sturmhauke** ’s link: > [@](#): > > \*\*How well is the orbit known? \*\* > We know the orbit fairly well. After finding Sedna in November 2003, we were able to trace it back in archival data to 2001. With this nearly 3 year arc, we know that the perihelion (closest approach distance) is most likely to be within about 7 AU of our 76 AU perihelion estimate. With a perihelion of 76 AU, Sedna has a 60% farther closest approach than any other solar system object. We expect that the orbit will be improved in coming weeks as people search though archival data. guess that answers my question, thanks. i’d thought a few months would be too little to calculate anything… it’s been photographed but not identified all this time? ---
**Author:** ![David\_Simmons](https://avatars.discourse-cdn.com/v4/letter/d/9de053/32.png) [@David\_Simmons](https://boards.straightdope.com/u/David_Simmons)\ **Post date:** [April 9, 2004, 5:13am UTC](https://boards.straightdope.com/t/calculating-a-planets-orbit/238770/11 "2004-04-09T05:13:16Z")
> [@shijinn](#): > > from **sturmhauke** ’s link: > guess that answers my question, thanks. i’d thought a few months would be too little to calculate anything… > it’s been photographed but not identified all this time? Oh sure. Each photograph includes a patch of sky and astronomers don’t spend any time identifying each object in them without good reason. One way that moving objects like Sedna can be found if there is a reason to suspect one is to use a blink projector. I suppose this is all computerized now, but the technique is to project in rapid sequence photographs taken at different times with a reference star at the same location in each projection. All of the fixed stars stand still and the moving object switches postion to and fro as the pictures are sequentially projected. ---
**Author:** ![dtilque](https://avatars.discourse-cdn.com/v4/letter/d/d6d6ee/32.png) [@dtilque](https://boards.straightdope.com/u/dtilque)\ **Post date:** [April 9, 2004, 5:35am UTC](https://boards.straightdope.com/t/calculating-a-planets-orbit/238770/12 "2004-04-09T05:35:13Z")
> [@shijinn](#): > > it’s been photographed but not identified all this time? Yep. Do you know how many little dots there are on an astronomical image taken to show 27th magnitude stars? Sagans of them. And they all look pretty much the same. When they discover a new solar system object, they watch it for a couple weeks and compute a rough orbit. Based on that, they can then look through their library of previous images to find ones that the object should appear on. They do this because the longer the time period that they can find images of the object, the better the orbit they can calculate. Example: after they discovered Pluto in 1930, they found that it was on a plate taken in 1919 at the Lowell Observatory.