<p>The Minor Planet Center (MPC) routinely gives <a href="https://www.minorplanetcenter.net/mpec/RecentMPECs.html" rel="nofollow noreferrer">preliminary orbits for newly discovered asteroids</a>  with observations spanning only 48 hours.
Ordinary elliptical orbits are computed automatically.
After further observations are reported, MPC may issue a more precise orbit estimate.
The uncertainty never reaches zero, even if we track an asteroid for 100 years or longer.</p>

<p><a href="https://ssd.jpl.nasa.gov/sbdb.cgi?spk=3788040" rel="nofollow noreferrer">'Oumuamua's trajectory</a> took longer to determine because it didn't fit the usual elliptical model.
<a href="https://www.eso.org/public/archives/releases/sciencepapers/eso1737/eso1737a.pdf" rel="nofollow noreferrer">Meech et al. 2017</a> tell in their Methods section how they tried and rejected two different elliptical orbits before settling on a hyperbolic trajectory.
Even with observations spanning 6 days, MPC issued their <a href="https://minorplanetcenter.net/mpec/K17/K17UI1.html" rel="nofollow noreferrer">preliminary trajectory</a> with conditions:</p>

<blockquote>
  <p>Further observations of this object are very much desired.
  <em>Unless there are serious problems with much of the astrometry listed below</em>, strongly hyperbolic orbits are the only viable solutions.
  Although it is probably not too sensible to compute meaningful original and future barycentric orbits, given the very short arc of observations, the orbit below has e ~ 1.2 for both values.
  <em>If further observations confirm the unusual nature of this orbit</em>, this object may be the first clear case of an interstellar comet.</p>
</blockquote>

CC BY-SA 4.0
2018-06-06T22:36:17.840Z
2018-06-06T23:50:21.653Z
2018-06-06T23:50:21.653Z
Mike G
<p><a href="https://www.stardust2013.eu/Portals/63/Images/Training/OTS%20Repository/gronchi_OTS2013.pdf" rel="noreferrer">Three accurate observations are sufficient to fix a Keplerian orbit</a> (ie an elliptical or hyperbolic orbit with the sun at the focus)</p>

<p>In practice, observations are not perfectly accurate due to limitations of the equipment and observations over a short time are particularly prone to observational error being magnified. Moreover the orbit will be perturbed by the gravity of the planets, so won't be perfectly Keplerian. For this reason pre-discovery images will help fix the exact orbit more accurately.<br>
As the time difference between first and last observation is critical in the quality of the orbital determination, we talk about the length (in days) of the observation arc as a measure of how well defined the orbit is.</p>

<p>Multiple observations can reduce error by an averaging effect (the Gaussian curve is so named from Gauss's use of it in orbital determination) </p>

<p>However once you have three or more observations of a body you can determine its orbit almost immediately, using a computer to do the calculations for you. It would have been immediately obvious that the object was on a very unusual trajectory.</p>

<p>There is no need to use space probes for the observations. The relative motion of the Earth and the Object provide sufficient parallax to determine distance, position and velocity.</p>

CC BY-SA 4.0
2018-06-05T19:54:28.387Z
You need radar to do that.
James K
CC BY-SA 4.0
2018-06-05T23:57:33.843Z
Is there any path that an interstellar asteroid could take through the easily observable solar system that we couldn't extrapolate? Is there a lower limit on the orbital eccentricity we could use to determine an object's trajectory? I take it that an object would have to be significantly more massive than the sun to pass through the solar system without its course being perturbed?
jkade
CC BY-SA 4.0
2018-06-06T05:47:04.707Z
If we can observe it, we can fit an orbit to the observations. No upper or lower limits. There might be exceptional situations in which more than one sensible orbit can fit a small number of observations. Everything gets perturbed, but most orbits are very close to ellipses, or hyperbolae
James K
CC BY-SA 4.0
2018-06-07T01:21:46.253Z
James is right. The three-point method (augmented with extra points when possible) is canonical, and can be done using traditional instruments. Even amateurs can use it. It's sometimes called Gauss' method, and was used for the first time to determine the orbit of Ceres.
Florin Andrei
CC BY-SA 4.0
2018-08-16T21:34:20.093Z
I'm a little confused. Gronchi et al.'s very helpful paper on classical and modern orbit determination, in its section on modern solutions for problematic orbits where Gauss's hypotheses don't apply, specifically excludes interstellar objects: http://copernico.dm.unipi.it/~gronchi/PDF/gronchi_discuss.pdf

Was 'Oumuamua different because it passed close enough to the sun that it was similar enough to a solar system object?
jkade
CC BY-SA 4.0
2018-08-16T21:56:20.860Z
When you determine an orbit there might be more than one orbital solution. (It does involve solving a degree 8 polynomial) We can try to constrain the possible solutions by assuming the object is not an earth satellite, and not interstellar. Finding the orbit for 'Oumuamua was a problem because it the software for finding orbits makes this assumption. But you can still find an orbit that is interstellar, you just need to change your assumptions.
James K
CC BY-SA 4.0
2018-06-04T18:21:28.353Z
2018-06-04T18:21:28.353Z
James K
<p>The interstellar asteroid 'Oumuamua was discovered on October 19, 2017. Once discovered, less than a month's worth of precovery observations were found on various sky surveys. By mid-November, scientists had worked out its orbital eccentricity, and soon after its probable origin and destination.</p>

<p>With such a quick visit and so little data, how did scientists figure out so quickly where it came from and where it was going? Did using space probes for observations impart enough parallax to easily determine that, or did Earth-based observation have enough parallax themselves?</p>

<asteroids><interstellar><oumuamua>
How did astronomers determine the path of 'Oumuamua so quickly?
jkade
# How did astronomers determine the path of 'Oumuamua so quickly?

(Asked by: username_0 on 2018-06-04)

The interstellar asteroid 'Oumuamua was discovered on October 19, 2017. Once discovered, less than a month's worth of precovery observations were found on various sky surveys. By mid-November, scientists had worked out its orbital eccentricity, and soon after its probable origin and destination.

With such a quick visit and so little data, how did scientists figure out so quickly where it came from and where it was going? Did using space probes for observations impart enough parallax to easily determine that, or did Earth-based observation have enough parallax themselves?

**Tags:** asteroids, interstellar, oumuamua


---

## 2 answers

### Answer by username_2 on 2018-06-04. Score: 8 | Accepted answer

[Three accurate observations are sufficient to fix a Keplerian orbit](https://www.stardust2013.eu/Portals/63/Images/Training/OTS%20Repository/gronchi_OTS2013.pdf) (ie an elliptical or hyperbolic orbit with the sun at the focus)

In practice, observations are not perfectly accurate due to limitations of the equipment and observations over a short time are particularly prone to observational error being magnified. Moreover the orbit will be perturbed by the gravity of the planets, so won't be perfectly Keplerian. For this reason pre-discovery images will help fix the exact orbit more accurately.  
As the time difference between first and last observation is critical in the quality of the orbital determination, we talk about the length (in days) of the observation arc as a measure of how well defined the orbit is.

Multiple observations can reduce error by an averaging effect (the Gaussian curve is so named from Gauss's use of it in orbital determination)

However once you have three or more observations of a body you can determine its orbit almost immediately, using a computer to do the calculations for you. It would have been immediately obvious that the object was on a very unusual trajectory.

There is no need to use space probes for the observations. The relative motion of the Earth and the Object provide sufficient parallax to determine distance, position and velocity.

> **Comments:**
> **username_2**: You need radar to do that.  
> **username_0**: Is there any path that an interstellar asteroid could take through the easily observable solar system that we couldn't extrapolate? Is there a lower limit on the orbital eccentricity we could use to determine an object's trajectory? I take it that an object would have to be significantly more massive than the sun to pass through the solar system without its course being perturbed?  
> **username_2**: If we can observe it, we can fit an orbit to the observations. No upper or lower limits. There might be exceptional situations in which more than one sensible orbit can fit a small number of observations. Everything gets perturbed, but most orbits are very close to ellipses, or hyperbolae  
> **username_3**: username_2 is right. The three-point method (augmented with extra points when possible) is canonical, and can be done using traditional instruments. Even amateurs can use it. It's sometimes called Gauss' method, and was used for the first time to determine the orbit of Ceres.  
> **username_0**: I'm a little confused. Gronchi et al.'s very helpful paper on classical and modern orbit determination, in its section on modern solutions for problematic orbits where Gauss's hypotheses don't apply, specifically excludes interstellar objects: http://copernico.dm.unipi.it/~gronchi/PDF/gronchi_discuss.pdf  Was 'Oumuamua different because it passed close enough to the sun that it was similar enough to a solar system object?  
> **username_2**: When you determine an orbit there might be more than one orbital solution. (It does involve solving a degree 8 polynomial) We can try to constrain the possible solutions by assuming the object is not an earth satellite, and not interstellar. Finding the orbit for 'Oumuamua was a problem because it the software for finding orbits makes this assumption. But you can still find an orbit that is interstellar, you just need to change your assumptions.  

---

### Answer by username_1 on 2018-06-06. Score: 5

The Minor Planet Center (MPC) routinely gives [preliminary orbits for newly discovered asteroids](https://www.minorplanetcenter.net/mpec/RecentMPECs.html) with observations spanning only 48 hours.
Ordinary elliptical orbits are computed automatically.
After further observations are reported, MPC may issue a more precise orbit estimate.
The uncertainty never reaches zero, even if we track an asteroid for 100 years or longer.

['Oumuamua's trajectory](https://ssd.jpl.nasa.gov/sbdb.cgi?spk=3788040) took longer to determine because it didn't fit the usual elliptical model.
[Meech et al. 2017](https://www.eso.org/public/archives/releases/sciencepapers/eso1737/eso1737a.pdf) tell in their Methods section how they tried and rejected two different elliptical orbits before settling on a hyperbolic trajectory.
Even with observations spanning 6 days, MPC issued their [preliminary trajectory](https://minorplanetcenter.net/mpec/K17/K17UI1.html) with conditions:

> Further observations of this object are very much desired.
> *Unless there are serious problems with much of the astrometry listed below*, strongly hyperbolic orbits are the only viable solutions.
> Although it is probably not too sensible to compute meaningful original and future barycentric orbits, given the very short arc of observations, the orbit below has e ~ 1.2 for both values.
> *If further observations confirm the unusual nature of this orbit*, this object may be the first clear case of an interstellar comet.


---

