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Exploring ‘Oumuamua’s Perihelion Date

Adam Hibberd

October 2022

This blog may be a bit cheeky but do take heed of the last line before jumping to any conclusions!

I’ve been mucking around with ‘Oumuamua’s orbit on my computer lately. Mucking around in the sense of playing with its orbital parameters and seeing what crops up. Those of you who have been following my blog will have noticed this. Refer for example here.

Recall in my previous blog that there were three parameters which to all intents and purposes can be supposed to be randomly and uniformly distributed:

  1. The time of perihelion
  2. The impact parameter, b
  3. The Beta angle, β

The values of these which 'Oumuamua adopted were therefore arbitrary. Just as a reminder the following diagram provides a useful explanation as to the definition of the latter two of these three parameters:

Figure 1, Definitions of Impact Parameter, b and Beta angle β

Let’s have some fun here and in particular look at the date of perihelion, which was (for the real ‘Oumuamua) on 9th September 2017.

Specifically, what happens if we keep all of ‘Oumuamua’s parameters fixed and just change the perihelion date and time? So I did this for a range of perihelion times spread throughout the year 2017, and plotted out the consequent effect it has on the PERIGEE distance (the closest approach of ‘Oumuamua to Earth). We get the following:

Chart, line chart Description automatically generated
Figure 2 Perigee Distance as a dependency on Time of Perihelion Assuming 'Oumuamua's Orbital Parameters are Otherwise Identical

We find that the true perihelion of ‘Oumuamua was such that its subsequent perigee – 0.16 au - was nearly as low as it could possibly have been to Earth. Had the perihelion fallen on 19th September – 10 days later – then the perigee would have been even lower at 0.095 au.

Let’s now suppose hypothetically that ‘Oumuamua chose its perihelion date deliberately to be 9th September for some reason. What would be that reason?

The following plot (Figure 3) provides the same data as above, but also provides an additional (dotted) curve (with a second vertical axis on the right hand side) indicating the Sun-Earth-1I angle, in other words the angle subtended at the Earth between the Sun and ‘Oumuamua. If this S-E-1I angle is less than 90° then ‘Oumuamua will reach perigee on the sunward facing side of Earth. If however it is greater than 90°, then it will be on the night side of Earth and will potentially be observable by telescopes. Furthermore the larger this S-E-1I angle the more conducive ‘Oumuamua will be to observation by Earth-based telescopes. Look at Figure 3.

Figure 3: Dotted Line Represents the Angle Subtended at Earth Between the Sun and 'Oumuamua vs Possible Perihelion Times for 'Oumuamua

What we find is that ‘Oumuamua’s perihelion date was such that when perigee was achieved it reached almost the largest possible S-E-1I angle (the optimal angle for this is actually on a perihelion date of 9th/10th September), maximising its chance of observation.

There are some flaws to the above argument which I shall elucidate in my next blog.