# Is this scaling of JWST halo reasonably correct

After thinking about accurately visualizing the size of the Andromeda galaxy I began to wonder about the halo orbit of the James Webb Space Telescope. Using an estimate of 1.5E6 km for halo width and 9.0E5 km for halo height and using 1.39E6 km from earth surface to L2' (JWST is actually inward from L2) I've put together this image of halo scaled to the Moon.

halo width 56.6 degrees ( 108.8 x Moon's .52 deg )

halo height 35.8 degrees ( 68.8 x Moon's .52 deg )

NEW halo Z 32.0 deg ( 61.6 x moon )

Are these values and image reasonably correct?

New view using 8E5 km height instead of 9E5 km

NEW side view from current Horizons data, using Earth at farthest position using tool provided by PM 2Ring.

Yes, your diagram and numbers are basically correct.

Here's a plot from Horizons. I got the 3D coordinates of the JWST (in the frame where Earth is fixed and L2 isn't rotating, with the ecliptic as the XY plane), projected them onto a sphere (centred on the centre of the Earth), and converted them to longitude & latitude. So these coordinates are essentially ecliptic longitude & latitude, but using L2 as the zero point, instead of the vernal equinox. Here are the results.

The curve was calculated using 1 day steps, but the red dots are 7 days apart.

Here are a few other relevant graphics.

The distance from Earth to L2 isn't constant, but its variation is fairly small relative to the overall distance, and relative to the variation in the distance from Earth to the JWST.

Here's a daily plot (courtesy of Horizons) of the distance from the centre of the Earth to the JWST and the SEMB-L2, covering 2 years.

Here's the corresponding plot of their distance from the centre of the Sun.

The script for those plots can be found here.

Here's a daily plot of the distance from L2 to JWST, using the script in this answer.

The Horizons data for the JWST was revised a couple of weeks ago. Trajectories are now "based on data through ~15:00 UTC May 30, predicts thereafter". See the Horizons JWST body data page for current details.

Here's an interactive 3D plot of the JWST's orbit in the rotating frame (essentially an update to a script in my answer to a Space.SE question on the JWST orbit). This version shows the Earth (in blue). The green dot is L2, and the purple line is the Sun-Earth axis. The body dots are not to scale!

Here's a cropped, frameless, perspective view from that plot.

Sorry, it doesn't show the angular size of the Moon, but at least it illustrates the shape of the halo. ;)

## Update

The 3D plot can now show the trajectory either in the corotating frame where L2 is fixed, or where Earth is fixed.

• Nice interactive plot! Jul 21, 2022 at 4:17
• Glad you like it, @Charles! There are older versions of the script in the Space.SE link I just added; the 1st version shows the JWST trajectory around L2 in the non-rotating frame. If you want to see general orbits in non-rotating frames, see astronomy.stackexchange.com/a/49823/16685 Jul 21, 2022 at 4:27
• The Horizons data was updated a few days ago. So plots can now span upto 2024-Nov-07 00:01:09.1826 TDB Nov 13, 2022 at 18:44

### Close!

From the Space SE question Is JWST Halo orbit prograde or retrograde and why? I found the graphic below , originally from Webb Space Telescope's JWST Orbit and in PowerPoint added some lines.

It looks like your 56° wide fits quite nicely, but because these halo orbits are substantially tilted to the Earth's orbit, they are substantially foreshortened as seen from Earth, so your original 36° now becomes 26° as seen from Earth.

The thin ~5° line that extends out ~400,000 km from Earth indicates the approximate plane of the Moon's orbit, though we have to be careful because that plane precesses over time (~18.6 years).

• I recall that plot... I argued it was flawed because for a while I did not realize the view C +Z axis label location is wrong. This plot is old data! Current data from Horizons data shows greater Z amplitude. On revisiting new data plot I see I did make a copying error for my Z amplitude. I used 9E5 km instead of 8E5 km for this view angle calculation. The old NASA plot shows less than 8E5 km. Jun 19, 2022 at 6:00
• Also... that old NASA plot shows JWST approaching from north and meeting orbit at south, opposite what actually happened. Jun 19, 2022 at 6:14
• Thanks uhoh! this has been interesting to understand how large the halo really is! Jun 19, 2022 at 7:42
• @BradV my feeling was that you needed a ballpark-ish sanity check of your ballpark estimate, so that's all I was willing to generate. PM2Ring's answer is on its way to a precise one because it's based on an actual trajectory, once they find a way to query Horizons the way I've suggested there.
– uhoh
Jun 19, 2022 at 9:08
• @BradV Re. north/south stuff; the two manifolds that define the two sets of halo orbits are sort-of mirror images of each other, so that part doesn't matter. As I recall (and I could be wrong) the original ("old") period for JWST and the new one are very close to the same ~six months, so the sizes are going to be about the same despite the changes of the details. So I'm betting that the answer with the latest trajectory will not be much different in terms of average opening angles (averaged over several years). I will be surprised but pleased to find out if it's more than a degree or two off.
– uhoh
Jun 19, 2022 at 9:19