There is confusion in my mind over the direction of JWST’s halo orbit, depending in the source of graphics.

Observing from the Earth, does JWST orbit clockwise or counterclockwise around the antisolar point? Looking "down" from the celestial north in a rotating frame of reference, does it orbit prograde or retrograde around the Z axis?

The first graphic shows the transfer trajectory above the ecliptic and an oblique retrograde halo orbit:

The next one, from Astronomy Magazine, shows the opposite, prograde orbit: https://astronomy.com/magazine/news/2021/10/the-james-webb-space-telescope-lives

But the Planetary Society says retrograde: https://planetary.s3.amazonaws.com/web/assets/pictures/webbs-orbit.png

Which way is JWST going?

Does it matter from a science observational point of view?

Was the orbital direction picked for launch convenience? Fuel consumption?

• Your 1st link is from 2017 & says "The L2 orbit shape is not constrained, [...] A representative example of a valid JWST trajectory and orbit". And all the other diagrams show a simple circular / elliptical trajectory relative to L2, not a Lissajous. So I don't think we can trust any of them. ;) The last trajectory file on Horizons is for "NOBURN_2021363-2022012_01U.OEM.V0.1 2021-Dec-29 00:01 2022-Feb-09 00:01", and we can't get much of a plot from that. Jan 18 at 3:19
• @Woody because of the Coriolis force, I think the halo orbits are obliged to be clockwise viewed from the north pole. But I assume the vertical component can be either way round. So this inside edge of the orbit can be either above or below L2. Jan 18 at 4:35
• @RogerWood ---- Which way about the X axis? I have some astronomy buddies who were trying to figure JWST's path around the antisolar point (clockwise vs counterclockwise). Jan 18 at 6:19
• @Uhoh --- can you provide some thoughts? This is one of your areas of expertise. Jan 18 at 6:42
• @Woody that first graphic seems consistent with z pointing north and the near edge of the orbit towards the south. The orbit is clockwise viewed from +z, so it will be counter-clockwise viewed from +x. And roughly linear viewed from +y Jan 18 at 8:14

Horizons now has data for the JWST upto 2024-JAN-22 00:01:09.1845 TDB! The trajectory relative to L2 is a simple 3D Lissajous curve resembling the seam on a tennis ball or baseball. Here's a plot from 2021-Dec-26 to the above date (at 00:00 TDB), with a 7 day timestep. The green sphere is the observation center, L2.

The numbers on the frame are coordinates in kilometres, relative to L2.

Here's a link to the 3D interactive plotter with those parameters. I urge you to take a look at the interactive view. It makes it a lot easier to see the 3D structure of the trajectory. Also take a look at the trajectory relative to Earth (@399) or the Earth-Moon barycentre (@3).

The trajectory relative to the Moon (@301), with a 1 day timestep is also fun to look at.

Here's a 3D plotter that uses a rotating frame. It uses the frame corotating with the observation center, relative to the Sun. The default center is the Sun-EMB L2 point.

Here are a couple of screenshots. The grey plane is the ecliptic. Note that the JWST halo is between the Earth and L2 (that's obvious in the interactive view).

This version has a few other minor differences to the previous versions. It now uses ICRF as the underlying reference frame, rather than the J2000.0 frame, but it still uses the J2000.0 ecliptic as the XY plane. From the Horizons output:

REFERENCE FRAME AND COORDINATES Ecliptic at the standard reference epoch
Reference epoch: J2000.0
X-Y plane: adopted Earth orbital plane at the reference epoch
Note: IAU76 obliquity of 84381.448 arcseconds wrt ICRF X-Y plane
X-axis : ICRF
Z-axis : perpendicular to the X-Y plane in the directional (+ or -) sense of Earth's north pole at the reference epoch.

You can now control the thickness of the Bézier curves.

If you want to plot using the ICRF X-Y plane (essentially the J2000.0 equatorial plane), change the REF_PLANE setting in the script from 'ECLIPTIC' to 'FRAME'.

At this point in time, it's still not perfectly clear whether the James Webb Space Telescope will be in a simple halo orbit, or a more complex Lissajous orbit (relative to L2). But in either case, I hope this answer will be useful. ;)

Here's a Sage program that plots trajectories in 3D, using vector data from JPL Horizons. You can specify any bodies that Horizons knows about for the target and observation centre; Horizons also knows some Lagrange points. The Sun-Earth L2 point (technically, the L2 point of the Sun and the Earth-Moon barycentre) has body number 32.

Currently, the Horizons trajectory data for JWST (body -170) only goes up to 2022-Feb-09, so we can't get much of a plot for it yet. But in the mean time, we can look at older L2 satellites, eg WMAP, which has a classic Lissajous trajectory relative to L2.

The data is plotted in a coordinate system aligned with the J2000 ecliptic, with the Y axis aligned with the equinox axis. It may be helpful to plot the Earth relative to the Sun (or vice versa) to get your bearings.

Please see the Horizons documentation for full details on specifying body IDs, times, and time steps. Briefly, a number from 1 to 9 identifies a planet barycenter (including Pluto), eg, 1 is Mercury, 4 is Mars. Append 99 to specify the body center. Planet satellite numbers are derived from their planet's, eg the Moon is 301. You need to prefix the observation center with @, otherwise the number is treated as the ID of an observatory. If you type a string into the target or center fields, Horizons will respond with a list of IDs that match that string.

Horizons accepts numerous date and time formats. To input a Julian day number, prefix it with jd.

The datestep parameter of my program sets how often a plotted point is labelled with a date / time stamp. A datestep of 7 means that every 7th point gets a date.

To reduce the number of Horizons requests, the program caches the last 4 sets of data that it fetches. If you make "cosmetic" changes to the graph without altering the target, center, or time parameters, the old data is reused.

The notions of prograde and retrograde do apply to Lissajous figures, but since such paths zig-zag back & forth, except for the simplest Lissajous curves (circles & ellipses), such descriptions aren't very helpful. And things get even more complicated for the 3D Lissajous paths typically used for satellites like WMAP.

Here's a simple 2D Lissajous figure with the parametric equations $$x=\cos(3\theta)$$ $$y=\sin(4\theta)$$

The coloured dots indicate the direction of increasing $$\theta$$, with the hues going around the red, orange, yellow, green, cyan, blue, magenta, red cycle. So technically, it's going prograde (anticlockwise). You can draw other Lissajous figures with this Sage script.

Here's the current Horizons object data for the JWST.

Revised: Jan 25, 2022 James Webb Space Telescope / (E-S L2)
-170 https://www.jwst.nasa.gov/index.html

The James Webb Space Telescope ("JWST" or "Webb") is a space-based infrared observatory and NASA's successor to the Hubble Space Telescope.

Launched by Ariane 5 booster on 2021-Dec-25 @ 12:20 UTC from the ELA-3 launch complex near Korou, French Guiana.

After launch, the telescope will deploy during its 30-day, 1.5 million km journey to halo orbit at the second Earth-Sun Lagrange point (E-S L2). Mission duration is nominally 5-10 years.

GOALS

• Search for the first galaxies or luminous objects formed after the Big Bang
• Determine how galaxies evolved from their formation until now
• Observe the formation of stars from the first stages to the formation of planetary systems
• Measure the physical and chemical properties of planetary systems, including our own Solar System, investigating the potential for life in those systems.

TELESCOPE * total launch mass : ~6200 kg (observatory, fuel, launch adaptor) * primary mirror : 25 m^2 mass : 705 kg material : beryllium coated w/48.25 grams gold (golf-ball size) segment mass : 20.1 kg, 39.48 kg for entire segment assembly No. of segments : 18 * focal length : 131.4 meters * optical resolution: 0.1 arcseconds * wavelength : 0.6 - 28.5 microns * size of sun shield: 21.197 m x 14.162 m * Sun shield layers : 1: Max temp 283K, 231 deg. F. 5: Max temp 221K, -80 F Min temp 36K, -394 F * Operating temp : < 50K (-370 deg. F)

INSTRUMENTS

• Near Infrared Camera (NIRCam)
• Near Infrared Spectrograph (NIRSpec)
• Mid Infrared Instrument (MIRI)
• Fine Guidance Sensors/Near Infrared Imager & Slitless Spectrograph (FGS/NIRISS)

TRAJECTORY MCC1A (65-minute engine burn) began 2021-Dec-26 12:50 UTC, completed 01:55 UTC. MCC1B (09:27 engine burn) began 2021-Dec-28 00:20 UTC, completed 00:29:27 UTC. MCC2 (04:57 engine burn) began 2022-Jan-24 19:00 UTC, completed 19:04:57 UTC.

Post-launch trajectory from Goddard Flight Dynamics Facility (FDF), based on data through ~19:00 UTC Jan 22, predicts thereafter.

Trajectory files Start (TDB) End (TDB) -------------------------------------- ----------------- ----------------- BURN_TTF_01_2021359124800_02U.OEM.V0.3 2021-Dec-25 12:50 2021-Dec-25 20:01 BURN_MCC_1A_2021359200000_04U.OEM.V0.1 2021-Dec-25 20:01 2021-Dec-26 15:01 BURN_MCC_1B_2021360150000_01U.OEM.V0.1
2021-Dec-26 15:01 2021-Dec-27 14:01 BURN_MCC_1B_2021361140000_02U.OEM.V0.1 2021-Dec-27 14:01 2021-Dec-29 00:01 NOBURN_2021363-2022017_01U.OEM.V0.1
2021-Dec-29 00:01 2022-Jan-18 00:01 BURN_MCC_02_2022018000000_01U.OEM.V0.1 2022-Jan-18 00:01 2022-Jan-22 00:01 2Y_SCHEDULE_2022022000000_02U.OEM.V0.1
2022-Jan-22 00:01 2024-Jan-22 00:00

You can fetch the latest version of that info using this script: Horizons object data. It can be used for any body that Horizons knows, either by name or ID number. If the body name is ambiguous, Horizons will print a list of matching bodies, with their ID numbers. Use the name news to get the recent Horizons news info. Use ?! to get the Horizons manual in ASCII format.

Here's a bookmarklet version of the body data fetcher:

javascript:(function(){let%20s=prompt('Body');if(s)location.href='https://ssd.jpl.nasa.gov/api/horizons.api?format=text&OBJ_DATA=YES&MAKE_EPHEM=NO&COMMAND='+encodeURIComponent(s)})()


With the bookmarklet, if the body name string contains spaces or commas, you must enclose it in single quotes.

If the Sage window is too narrow on your device, you can expand it with this bookmarklet:

javascript:(function(){let%20w=prompt('Width?','130%');if(w)jQuery('.sagecell').css('width',w);})()


Or use this bookmarklet to add a Fullscreen button below the Sage output window.

javascript:(function(){let%20b=document.createElement('button');b.innerHTML='Fullscreen';b.onclick=()=>window.open($$('iframe').get(0).src);$$('#cell').get(0).appendChild(b)})()

• Fascinating, love the plotter. Much clearer! Jan 26 at 4:02
• @PM2Ring That's super! I gather it's plotted point by point in non-rotating coordinates centered on L2. I presume the fact that it's non-rotating is why you get the tennis-ball Lissajous. It's the mixture of 6-month halo period and 12-month annual period. If I was smarter, I'd figure out how to put it in rotating co-ordinates :-). I guess it's something like theta = 2pi*elapsed-time/1 year and then x' = x.cos(theta) - y.sin(theta) and y' = x.sin(theta) + y.cos(theta) and z remains unchanged. Jan 26 at 5:37
• @Roger Yes, it's using J2000 coordinates, centred on the observation point (L2, in the above image). See the section Ecliptic of Standard Epoch in ssd.jpl.nasa.gov/horizons/manual.html#frames for details. The plot using Earth as the centre is a little simpler. It wouldn't be hard to make a plot in a rotating frame. Of course, a constant angular speed for the frame would be easiest, but I think it'd be better to use a variable speed, eg a frame that rotates with the Earth-Moon barycentre. Jan 26 at 6:07
• @PM2Ring got it! I fiddled with your Sage code and printed and pasted it into Excel then de-rotated it. I assume it's looking down from the North pole. I was going to paste it into your answer, but I thought you wouldn't like me messing with it. So I added it into my answer Jan 26 at 7:22
• @PM 2Ring : I suggest it would be clearer to indicate in each diagram an arrowed line of the sun->earth direction extended outwards, and an orthogonal arrowed line pointing in the direction of earth motion along its orbit. Complete accuracy not needed. I assume that (ecliptic) north is 'up', but if that's not so, then an indication where it really is would help. Jan 28 at 2:51

From a northern-hemispheric perspective we usually have the z-axis pointing up and we look down on the North pole and see everything rotating counter-clockwise (prograde) - and even JWST's overall motion is counterclock-wise around the Sun.

In that first JWST diagram, we appear to have a right-hand set of axes. "x" increases away from the Sun & Earth. "y" increases in the counter-clockwise direction (prograde), "z" increases as one goes North.

So in the diagram: view a) is looking down from the North and shows JWST in a clockwise (retrograde) orbit around L2. View b) is looking backwards along the orbit and shows a roughly linear behavior. View c) is looking towards the Earth and Sun and shows JWST in a counterclockwise orbit.

The Halo orbit is necessarily retrograde with respect to L2. When JWST is closer to Earth, it is at a more negative gravitational potential and must therefore be traveling faster than L2. As it moves forward past L2, the Coriolis effect will swing it outward. When JWST is further from Earth, it is at a less negative gravitational potential and must be traveling slower than L2. As it slides backward past L2, the Coriolis effect will swing it inward. In other words, the Halo orbit is clockwise (retrograde) around L2.

For consistency with the right-hand set of axes in the diagram, the orbit looking towards the Earth-Sun is counter-clockwise. But either option is possible. The near edge of the orbit can be either North or South of the ecliptic. But it looks like the actual JWST orbit in that diagram has the near edge oriented South.

[Edit: adding a note on Coriolis force] The Coriolis force is an imaginary force which has to be included when considering motions in a rotating reference frame. The Coriolis force acts only on the components of motion in the plane of rotation. It acts at right angles to the motion. It tends to make an object move in a circular motion which, when seen in the rotating frame, appears as a rotation in the opposite direction to that of the rotating frame. For example, viewed from above the North pole, the Earth rotates counter-clockwise and the Coriolis force tends to make moving objects veer clockwise. This is equally true in the Southern hemisphere (looking from the North pole through the Earth). The end result in the atmosphere is that cyclones are always prograde and anticyclones are always retrograde.

 Here is exactly the same data from PM2Ring's answer but where I have it changed to the rotating reference frame. This removes the Lissajous appearance caused by combining the 6 month halo period with the 12 month annual period. I'm showing the three 2D projections where I've tried to label them very clearly. They do show a distinctly different halo orbit to that shown in the original question.

The data on which this is based is JWST trajectory from Jet Propulsion Laboratory_Development Ephemeris via the Horizons interface courtesy of @PM2Ring.

(add by BradV) I projected halo (middle orbits, discarded 1st & last) to auxiliary plane nominally flat to orbit. It is surprising how uniform this projection is!!!

• "The Halo orbit is necessarily retrograde with respect to L2." Do you mean this halo orbit or all halo orbits? They come in pairs (called "northern" and "southern") this one has a counterpart that is inclined in the opposite direction, but I don't know if it goes around the other way or not. It sounds like you'd conclude that it didn't? You can see the pairing here (this is the near-rectilinear limiting case of a halo orbit) youtu.be/X5O77OV9_ek?t=46
– uhoh
Jan 18 at 12:24
• @blobbymcblobby unless one of my answers is refuted conclusively and convincingly I don't delete them. Stack Exchange pages are all works in progress; the more that's shared, the more there is to think about.
– uhoh
Jan 18 at 13:10
• @Woody What little insight I've gained comes from your earlier simple harmonic motion (SHM) question. It's obviously a nonlinear space, but it seems like the z-axis oscillation is not very strongly coupled to the x-y oscillation. The Wikipedia article talks about how the period of the x-y orbit drops as it's amplitude increases until it matches the z-axis period. At that point you get a relatively closed orbit rather than Lissajous spaghetti. Jan 18 at 21:21
• @Woody I'm wondering if any relative phase relationship is acceptible? If so, that would mean that the Halo orbit could be inclined North or South or sideways or in any direction. However such orbits might be poorly closed. But it seems clear that the tilted-North and tilted-South orbits are equally valid and otherwise identical. Jan 18 at 21:21
• @RogerWood --- Unfortunately, I've never found an illustration of both North- and South- halo orbits with direction of rotation indicated. I suspect you are right that Coriolis force produces the "tilt" and direction of rotation determines direction of tilt. I will seek inspiration from the Jedi. May the (Coriolis) Force be with you. Jan 18 at 21:36