<p>Yes, your diagram and numbers are basically correct.</p>
<p>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 &amp; latitude. So these coordinates are essentially ecliptic longitude &amp; latitude, but using L2 as the zero point, instead of the vernal equinox. Here are the results.</p>
<p>The curve was calculated using 1 day steps, but the red dots are 7 days apart.</p>
<p><a href="https://i.sstatic.net/n06Xx.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/n06Xx.png" alt="Equirectangular plot of the JWST halo" /></a></p>
<hr />
<p>Here are a few other relevant graphics.</p>
<p>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.</p>
<p>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.</p>
<p><a href="https://i.sstatic.net/5hhGh.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/5hhGh.png" alt="Distances from Earth to JWST &amp; L2" /></a></p>
<p>Here's the corresponding plot of their distance from the centre of the Sun.</p>
<p><a href="https://i.sstatic.net/YIAS0.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/YIAS0.png" alt="Distances from the Sun to JWST &amp; L2 " /></a></p>
<p>The script for those plots can be found <a href="https://astronomy.stackexchange.com/a/49823/16685">here</a>.</p>
<p>Here's a daily plot of the distance from L2 to JWST, using the script in <a href="https://astronomy.stackexchange.com/a/49267/16685">this answer</a>.</p>
<p><a href="https://i.sstatic.net/BZ0eH.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/BZ0eH.png" alt="L2 to JWST distance" /></a></p>
<hr />
<p>The Horizons data for the JWST was revised a couple of weeks ago. Trajectories are now &quot;based on data through ~15:00 UTC May 30, predicts thereafter&quot;. See the <a href="https://ssd.jpl.nasa.gov/api/horizons.api?format=text&amp;MAKE_EPHEM=NO&amp;COMMAND=JWST" rel="nofollow noreferrer">Horizons JWST body data page</a> for current details.</p>
<p>Here's an <a href="https://sagecell.sagemath.org/?z=eJzFWP1y2kgS_5-nmJWzK4nIMmAn2VClumAb7zrrDwpI9nKEogQMRomQlNEI23Hlge457sWuu2f0gezs3W5d1VEJRj3T393Tv5FhGGzIpQj4lrMtX8hYsKUvfbYS8Yb9GovgaxylbAVkn0lf3HDJ5vHyvsHgI3joywAYZcz8iMXzlIstUOKILXgkuXCAvGRyzaMFZ0kYS2LDrWIeSBZE7PCUZWkQ3bDjf_3za8AFW2Riy1O3QTvH6yAFq0SKIrOUpwwN8zegce1LJmLpSyDeBnKNWrRWMyXmTUyW-CLOlBFslEUuLZ1LtgAr_DCNySxa7ftCrs2UJXEaIGeK9uECqUEbSTUJII0cvsDiUjFbBXd86YB3pUBFU-78LgIpecTm92xwyTpDlNlpdTpuq-12XtGW3nLJl5ozN0Tv6bjto_qefZKuN7x0268bhmE0GsEmiQXEhzvw_0vGU5k2KKGrLIIUxyH4praEIpst_MWaq_UAvNhZT0S8zBay0chEyDxmrKVM0u7BQZou3U9J6EZ-6rs38fbAT4KDtS6X2SoIuQsUowFfszyBwN52W2De3E_5bLFZIgXMvez91p_1B7_2L70P_VFj3Du-6M_GHwZ9z3zfPxlfD0dm4_rdePbu6nw88szfLvdPzcawfzYbXPSuYFP_5OJ8MD4_UcTRh9EYJJnnJ8Mzs4ECZifXw6FnXl1f9Ykwu-gd9y9GSFHPp_2LcW82VoST0fvZ2fXwsgfPYA6oPn47O-2Ne2qZ4vumCJu18e_S4Cv3gkhaL227seQrtuJysZ5hG1mqZZyiH1IgSPwTJ_jN4Ru6bib9ecjtLqVXBWaFin549mx0fdZ4yAP2rXFyfXnZuzr1zAcl-RsY3L8a98G_B6UDKKNxbziejc8vITgPpJGI14OSFidE6g9mo_N_KBJHEoaDEgCkwjCggyV9sIS8V63_BYzMi8uFUpUWlIhDh4f3YMKBsfGl2WWm5HfS_OYwrIkUVoIoyXDBMsEh00F37W-26lgS6abcF4u1JYze4Jy97w9H59dX3Y9p0_o4atoGlbSLUhVTsAI-OCau4oirAOInEZgQ49IP0RJokUW82eBhhGbAsTSH4ob2M-waB1pTI-2qU87LTESkUUWjrPCNewPnTWK1C-PytR88VmmGuqUr43dfRGBRl6HXORP49aB_QwjnGZ5UQEsXIkgkruLB_FCR-w08ejKW1t9S--Ozj1BPfctt0s_-df_PRfPqmlGb9ofno0eR-y_CRIOlGqNJuzullb2nZGiiyX40WZMdthQ1DCI48r3CbjdNwkAS1VI7tLUfI8P9FAeRRWuTo2775dS2GxXL0J4GdSzIEf5CYs_yGRSzhUtUzFDe_iZJ89_YsDLY8FQ3q3YJ_zw2RC9OUrVkmY5pT7r77SmljeYLbtEhQJqIb3NqN49rfKtTuscGSFFnCPuJDhH2NgsDHznuUyCRkdUgnMGp3oUsN1HkpDWddDvTnSiN4y5jxQawTe3I7efgOcQDvZg68J_oaGng5MbyKNtwAVspaHZZNXusr8IKwzbk0dInaMGLdaDiM-Yyvp20p40nOPMZWBYVKAVjVmHsw4ljky0ZmoEyOt3ptCzLOIUZlIBiSwEbCqVd1XLpf-Zk0wHllDJdLEMrlPknIBOwH4syYJ7HWqWv-LnfwOxfbzBY2jWdd6zzw-nuXodtoKZgK3DpbcZ-panwI1HUkj2HlnzO7tG7nWUwkMzetUIzPofZCh0AjGBRrsCFREPXtXblkEt5qGRabxFdAruNkvfI_6UN8uK4g4q_L_GawyKcOiGM42VDVwDq1dn_bs0cTae2W7JaeRJqlkyrcaGA7LHjLAiX7JhXoCuFac6_WrAFzoobqUMEjzN4AoO-Bkm5qNZa8NCCpQjia-mdOg-q3hOdM6WD2rFoRTyS0EjNV5YD7vPnqZWwfVBhswN2WO0jF5RhykE4lIlsNTHRsFXSj2lZixqT6wqhTFTElMbsuIJWVSOmowNBOxX-LQB5gP7z-M5RWDpOKI2ApGMRwSiD9Z_YnGJ5Gwg-g50WHMhzOKian291SLeouqkhqtXEuOIe21bmDGAZ6_AQXNxOAlVuAUbKajlt59DpOC17qiVqjuffZTlyXjivnJfO0RMsabaxNJvUi8RJaUGzthOoMoB6MIVqM2ig-ioN44RbWwjetq290xusbRtysm3VSrTxJkC0B21A_BsfBp2ChJ759vfR2Mwxp2e-OeyYDoikueEZeFnYv_Tv99uGAqJEOqqQOJBeLQ3k4XjL8MYiA9BEv2d049AUyqn-DcBk8RmaPvXacLDFMtV0Qsct92eUVp6n3hlcvriepflDfrZ6R7iZbltaSAIlkUAbw2Wz3Cw-61U_k_EsS5BdrUIEczQTwe3OQnPwVkb22o9wzYiHIJvBjTLkfioZABYWr9gOl1HHNQ09ReNPaBeBP7NiponKK8-Mg13MBNi5jm-En0C0TJIAN8UNzkATHTLV1BGf9fYwuFlLMz_3foHLd3kg60sq1RklXonbuXCAXEVwU7jjJ5adL-TPxPPoUgJsRCu5cK36xIunHWj3F28-XgmXSdAjAKpDXkyrHJT8BdxWVAaVM-a3Utc74AXJzs5LjvKqX-xTzPrNCGTx8PVrM2emNyV1hseRqor4c_H6w5jV4oafWd7Efxg93WBt_Uupwnrs1rxWUkp8ryq0NpVVgT79GkUUcVNeF_cBUZSv-abdwoCO1fub7xSbyKMn_tflJnZDVeAeZQgP9SVCua_gQOksnApwCxbBQoPynEoDnFburIkFMxDgYAv6ytqHH3f6N8yCFsK1qZoluIswC5gwLbQLAiJK-5Beh5F6HdcyCeol2_ct01Bpw-CmlZC-DYIBPb4Ku6nv7OluD2FQni4NkPcfxBW77YpP-XJNTa1DtQpELF9yHPQlV0H4qi4cP1AfuXH7io14iq3TJx3RyWg91QulxHKXzsg7OMPLqc1SvvAjmCk-_EtgctwFG0qYH91A1apEKIg4UXigmajcJztuwRfeBbRTNQZYwwvcFBEdrDzfWdlXbPltMqbbJJimSgBdKJ52p1cl6ilrKsCTESCxKnAaIw0gE-56aGgRhRNwTvACkiWoFpCSjptGCD838bBexGEsPONGcB4ZhYBxOd4CNZZLewh_5SJLcS-q4gRfGuW5T-O8JmBOCB4k7AD3KqgpflWPDj1kasIwOPhmAtEgpsuBCEF60Szjbj-Fagh3Lno5hk8rWZ50u_ngmuoZZtdG13diUJStjsTLaiTmYcbzUMwBU0M6Bu4cX5DD8UAg285jrs5baC41yhDePsbIFgrB1wqtqS59OLiI1q7QpoX-JBNJyCvJoFlQ86QA_M05XRBqRZHv3WN__8CS0I94LRBhjHEAzc0J3QlIjE0vNgphe77vA9aNE38RyHvAp50X2qiBm67jW0uhTz0KS5TnlT8dBd08-rb_DZn1jIA=&amp;lang=sage&amp;interacts=eJyLjgUAARUAuQ==" rel="nofollow noreferrer">interactive 3D plot</a> of the JWST's orbit in the rotating frame (essentially an update to a script in <a href="https://space.stackexchange.com/a/57832/38535">my answer to a Space.SE question</a> 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!</p>
<p>Here's a cropped, frameless, perspective view from that plot.</p>
<p><a href="https://i.sstatic.net/KiMO3.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/KiMO3.png" alt="JWST Halo, in perspective" /></a></p>
<p>Sorry, it doesn't show the angular size of the Moon, but at least it illustrates the shape of the halo. ;)</p>
<h2>Update</h2>
<p>The 3D plot can now show the trajectory either in the corotating frame where L2 is fixed, or where Earth is fixed.</p>

CC BY-SA 4.0
2022-07-21T04:17:03.857Z
Nice interactive plot!
Charles Staats
CC BY-SA 4.0
2022-07-21T04:27:02.567Z
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 https://astronomy.stackexchange.com/a/49823/16685
PM 2Ring
CC BY-SA 4.0
2022-11-13T18:44:22.420Z
The Horizons data was updated a few days ago. So plots can now span upto  2024-Nov-07 00:01:09.1826 TDB
PM 2Ring
CC BY-SA 4.0
2022-06-19T05:55:55.340Z
2022-07-21T09:05:15.093Z
2022-07-21T09:05:15.093Z
PM 2Ring
<h3>Close!</h3>
<p>From the Space SE question <a href="https://space.stackexchange.com/q/57822/12102">Is JWST Halo orbit prograde or retrograde and why?</a> I found the graphic below , originally from Webb Space Telescope's <a href="https://jwst-docs.stsci.edu/jwst-observatory-characteristics/jwst-orbit" rel="noreferrer">JWST Orbit</a> and in PowerPoint added some lines.</p>
<p>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.</p>
<p>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 <a href="https://en.wikipedia.org/wiki/Lunar_precession" rel="noreferrer">precesses over time (~18.6 years)</a>.</p>
<p><a href="https://i.sstatic.net/kQAjg.png" rel="noreferrer"><img src="https://i.sstatic.net/kQAjg.png" alt="enter image description here" /></a></p>

CC BY-SA 4.0
2022-06-19T06:00:20.827Z
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.
BradV
CC BY-SA 4.0
2022-06-19T06:14:30.910Z
Also... that old NASA plot shows JWST approaching from north and meeting orbit at south, opposite what actually happened.
BradV
CC BY-SA 4.0
2022-06-19T07:42:42.523Z
Thanks uhoh!  this has been interesting to understand how large the halo really is!
BradV
CC BY-SA 4.0
2022-06-19T09:08:21.880Z
@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](https://astronomy.stackexchange.com/a/49616/7982) 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
CC BY-SA 4.0
2022-06-19T09:19:09.803Z
@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
CC BY-SA 4.0
2022-06-19T09:19:24.187Z
no worries!! You were absolutely correct in your understanding about my original 'ballpark' request! However, the more I discovered I had screwed up and as more information became available I started getting more demanding. oops. Thanks again.
BradV
CC BY-SA 4.0
2022-06-19T09:35:53.360Z
On a side note... in [Is JWST actually in a lissajous orbit]( https://space.stackexchange.com/questions/57452/is-jwst-actually-in-a-lissajous-orbit-what-will-it-look-like-implications-for)  I saw paper of [Solar Radiation Pressure Effects on the Orbital Motion at SEL2 for the James Webb Space Telescope](https://ntrs.nasa.gov/api/citations/20190029609/downloads/20190029609.pdf) which did a great job of showing how launch time greatly affected resulting orbit
BradV
CC BY-SA 4.0
2022-06-19T04:18:47.947Z
2022-06-19T04:18:47.947Z
uhoh
<p>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.</p>
<p>halo width  56.6 degrees ( 108.8 x Moon's .52 deg )</p>
<p>halo height 35.8 degrees (  68.8 x Moon's .52 deg )</p>
<p>NEW halo Z 32.0 deg ( 61.6 x moon )</p>
<p>Are these values and image reasonably correct?</p>
<p><a href="https://i.sstatic.net/Qj7K5.png" rel="noreferrer"><img src="https://i.sstatic.net/Qj7K5.png" alt="enter image description here" /></a></p>
<p>New view using 8E5 km height instead of 9E5 km
<a href="https://i.sstatic.net/kpvK2.png" rel="noreferrer"><img src="https://i.sstatic.net/kpvK2.png" alt="enter image description here" /></a></p>
<p>NEW side view from current Horizons data, using Earth at farthest position using tool provided by PM 2Ring.
<a href="https://i.sstatic.net/yzucc.png" rel="noreferrer"><img src="https://i.sstatic.net/yzucc.png" alt="enter image description here" /></a></p>

CC BY-SA 4.0
2022-06-19T04:21:36.037Z
different but related: [Will the James Webb Space Telescope be visible from earth?](https://astronomy.stackexchange.com/q/46744/7982)
uhoh
<orbit><james-webb-space-telescope><visualization>
Is this scaling of JWST halo reasonably correct
BradV
# Is this scaling of JWST halo reasonably correct

(Asked by: username_0 on 2022-06-19)

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?

[![enter image description here](https://i.sstatic.net/Qj7K5.png)](https://i.sstatic.net/Qj7K5.png)

New view using 8E5 km height instead of 9E5 km
[![enter image description here](https://i.sstatic.net/kpvK2.png)](https://i.sstatic.net/kpvK2.png)

NEW side view from current Horizons data, using Earth at farthest position using tool provided by username_2.
[![enter image description here](https://i.sstatic.net/yzucc.png)](https://i.sstatic.net/yzucc.png)

**Tags:** orbit, james-webb-space-telescope, visualization

> **Comments:**
> **username_1**: different but related: [Will the James Webb Space Telescope be visible from earth?](https://astronomy.stackexchange.com/q/46744/7982)  

---

## 2 answers

### Answer by username_2 on 2022-06-19. Score: 8

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.

[![Equirectangular plot of the JWST halo](https://i.sstatic.net/n06Xx.png)](https://i.sstatic.net/n06Xx.png)

---

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.

[![Distances from Earth to JWST & L2](https://i.sstatic.net/5hhGh.png)](https://i.sstatic.net/5hhGh.png)

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

[![Distances from the Sun to JWST & L2 ](https://i.sstatic.net/YIAS0.png)](https://i.sstatic.net/YIAS0.png)

The script for those plots can be found [here](https://astronomy.stackexchange.com/a/49823/16685).

Here's a daily plot of the distance from L2 to JWST, using the script in [this answer](https://astronomy.stackexchange.com/a/49267/16685).

[![L2 to JWST distance](https://i.sstatic.net/BZ0eH.png)](https://i.sstatic.net/BZ0eH.png)

---

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](https://ssd.jpl.nasa.gov/api/horizons.api?format=text&MAKE_EPHEM=NO&COMMAND=JWST) for current details.

Here's an [interactive 3D plot](https://sagecell.sagemath.org/?z=eJzFWP1y2kgS_5-nmJWzK4nIMmAn2VClumAb7zrrDwpI9nKEogQMRomQlNEI23Hlge457sWuu2f0gezs3W5d1VEJRj3T393Tv5FhGGzIpQj4lrMtX8hYsKUvfbYS8Yb9GovgaxylbAVkn0lf3HDJ5vHyvsHgI3joywAYZcz8iMXzlIstUOKILXgkuXCAvGRyzaMFZ0kYS2LDrWIeSBZE7PCUZWkQ3bDjf_3za8AFW2Riy1O3QTvH6yAFq0SKIrOUpwwN8zegce1LJmLpSyDeBnKNWrRWMyXmTUyW-CLOlBFslEUuLZ1LtgAr_DCNySxa7ftCrs2UJXEaIGeK9uECqUEbSTUJII0cvsDiUjFbBXd86YB3pUBFU-78LgIpecTm92xwyTpDlNlpdTpuq-12XtGW3nLJl5ozN0Tv6bjto_qefZKuN7x0268bhmE0GsEmiQXEhzvw_0vGU5k2KKGrLIIUxyH4praEIpst_MWaq_UAvNhZT0S8zBay0chEyDxmrKVM0u7BQZou3U9J6EZ-6rs38fbAT4KDtS6X2SoIuQsUowFfszyBwN52W2De3E_5bLFZIgXMvez91p_1B7_2L70P_VFj3Du-6M_GHwZ9z3zfPxlfD0dm4_rdePbu6nw88szfLvdPzcawfzYbXPSuYFP_5OJ8MD4_UcTRh9EYJJnnJ8Mzs4ECZifXw6FnXl1f9Ykwu-gd9y9GSFHPp_2LcW82VoST0fvZ2fXwsgfPYA6oPn47O-2Ne2qZ4vumCJu18e_S4Cv3gkhaL227seQrtuJysZ5hG1mqZZyiH1IgSPwTJ_jN4Ru6bib9ecjtLqVXBWaFin549mx0fdZ4yAP2rXFyfXnZuzr1zAcl-RsY3L8a98G_B6UDKKNxbziejc8vITgPpJGI14OSFidE6g9mo_N_KBJHEoaDEgCkwjCggyV9sIS8V63_BYzMi8uFUpUWlIhDh4f3YMKBsfGl2WWm5HfS_OYwrIkUVoIoyXDBMsEh00F37W-26lgS6abcF4u1JYze4Jy97w9H59dX3Y9p0_o4atoGlbSLUhVTsAI-OCau4oirAOInEZgQ49IP0RJokUW82eBhhGbAsTSH4ob2M-waB1pTI-2qU87LTESkUUWjrPCNewPnTWK1C-PytR88VmmGuqUr43dfRGBRl6HXORP49aB_QwjnGZ5UQEsXIkgkruLB_FCR-w08ejKW1t9S--Ozj1BPfctt0s_-df_PRfPqmlGb9ofno0eR-y_CRIOlGqNJuzullb2nZGiiyX40WZMdthQ1DCI48r3CbjdNwkAS1VI7tLUfI8P9FAeRRWuTo2775dS2GxXL0J4GdSzIEf5CYs_yGRSzhUtUzFDe_iZJ89_YsDLY8FQ3q3YJ_zw2RC9OUrVkmY5pT7r77SmljeYLbtEhQJqIb3NqN49rfKtTuscGSFFnCPuJDhH2NgsDHznuUyCRkdUgnMGp3oUsN1HkpDWddDvTnSiN4y5jxQawTe3I7efgOcQDvZg68J_oaGng5MbyKNtwAVspaHZZNXusr8IKwzbk0dInaMGLdaDiM-Yyvp20p40nOPMZWBYVKAVjVmHsw4ljky0ZmoEyOt3ptCzLOIUZlIBiSwEbCqVd1XLpf-Zk0wHllDJdLEMrlPknIBOwH4syYJ7HWqWv-LnfwOxfbzBY2jWdd6zzw-nuXodtoKZgK3DpbcZ-panwI1HUkj2HlnzO7tG7nWUwkMzetUIzPofZCh0AjGBRrsCFREPXtXblkEt5qGRabxFdAruNkvfI_6UN8uK4g4q_L_GawyKcOiGM42VDVwDq1dn_bs0cTae2W7JaeRJqlkyrcaGA7LHjLAiX7JhXoCuFac6_WrAFzoobqUMEjzN4AoO-Bkm5qNZa8NCCpQjia-mdOg-q3hOdM6WD2rFoRTyS0EjNV5YD7vPnqZWwfVBhswN2WO0jF5RhykE4lIlsNTHRsFXSj2lZixqT6wqhTFTElMbsuIJWVSOmowNBOxX-LQB5gP7z-M5RWDpOKI2ApGMRwSiD9Z_YnGJ5Gwg-g50WHMhzOKian291SLeouqkhqtXEuOIe21bmDGAZ6_AQXNxOAlVuAUbKajlt59DpOC17qiVqjuffZTlyXjivnJfO0RMsabaxNJvUi8RJaUGzthOoMoB6MIVqM2ig-ioN44RbWwjetq290xusbRtysm3VSrTxJkC0B21A_BsfBp2ChJ759vfR2Mwxp2e-OeyYDoikueEZeFnYv_Tv99uGAqJEOqqQOJBeLQ3k4XjL8MYiA9BEv2d049AUyqn-DcBk8RmaPvXacLDFMtV0Qsct92eUVp6n3hlcvriepflDfrZ6R7iZbltaSAIlkUAbw2Wz3Cw-61U_k_EsS5BdrUIEczQTwe3OQnPwVkb22o9wzYiHIJvBjTLkfioZABYWr9gOl1HHNQ09ReNPaBeBP7NiponKK8-Mg13MBNi5jm-En0C0TJIAN8UNzkATHTLV1BGf9fYwuFlLMz_3foHLd3kg60sq1RklXonbuXCAXEVwU7jjJ5adL-TPxPPoUgJsRCu5cK36xIunHWj3F28-XgmXSdAjAKpDXkyrHJT8BdxWVAaVM-a3Utc74AXJzs5LjvKqX-xTzPrNCGTx8PVrM2emNyV1hseRqor4c_H6w5jV4oafWd7Efxg93WBt_Uupwnrs1rxWUkp8ryq0NpVVgT79GkUUcVNeF_cBUZSv-abdwoCO1fub7xSbyKMn_tflJnZDVeAeZQgP9SVCua_gQOksnApwCxbBQoPynEoDnFburIkFMxDgYAv6ytqHH3f6N8yCFsK1qZoluIswC5gwLbQLAiJK-5Beh5F6HdcyCeol2_ct01Bpw-CmlZC-DYIBPb4Ku6nv7OluD2FQni4NkPcfxBW77YpP-XJNTa1DtQpELF9yHPQlV0H4qi4cP1AfuXH7io14iq3TJx3RyWg91QulxHKXzsg7OMPLqc1SvvAjmCk-_EtgctwFG0qYH91A1apEKIg4UXigmajcJztuwRfeBbRTNQZYwwvcFBEdrDzfWdlXbPltMqbbJJimSgBdKJ52p1cl6ilrKsCTESCxKnAaIw0gE-56aGgRhRNwTvACkiWoFpCSjptGCD838bBexGEsPONGcB4ZhYBxOd4CNZZLewh_5SJLcS-q4gRfGuW5T-O8JmBOCB4k7AD3KqgpflWPDj1kasIwOPhmAtEgpsuBCEF60Szjbj-Fagh3Lno5hk8rWZ50u_ngmuoZZtdG13diUJStjsTLaiTmYcbzUMwBU0M6Bu4cX5DD8UAg285jrs5baC41yhDePsbIFgrB1wqtqS59OLiI1q7QpoX-JBNJyCvJoFlQ86QA_M05XRBqRZHv3WN__8CS0I94LRBhjHEAzc0J3QlIjE0vNgphe77vA9aNE38RyHvAp50X2qiBm67jW0uhTz0KS5TnlT8dBd08-rb_DZn1jIA=&lang=sage&interacts=eJyLjgUAARUAuQ==) of the JWST's orbit in the rotating frame (essentially an update to a script in [my answer to a Space.SE question](https://space.stackexchange.com/a/57832/38535) 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.

[![JWST Halo, in perspective](https://i.sstatic.net/KiMO3.png)](https://i.sstatic.net/KiMO3.png)

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.

> **Comments:**
> **username_3**: Nice interactive plot!  
> **username_2**: 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 https://astronomy.stackexchange.com/a/49823/16685  
> **username_2**: The Horizons data was updated a few days ago. So plots can now span upto  2024-Nov-07 00:01:09.1826 TDB  

---

### Answer by username_1 on 2022-06-19. Score: 5

### Close!

From the Space SE question [Is JWST Halo orbit prograde or retrograde and why?](https://space.stackexchange.com/q/57822/12102) I found the graphic below , originally from Webb Space Telescope's [JWST Orbit](https://jwst-docs.stsci.edu/jwst-observatory-characteristics/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)](https://en.wikipedia.org/wiki/Lunar_precession).

[![enter image description here](https://i.sstatic.net/kQAjg.png)](https://i.sstatic.net/kQAjg.png)

> **Comments:**
> **username_0**: 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.  
> **username_0**: Also... that old NASA plot shows JWST approaching from north and meeting orbit at south, opposite what actually happened.  
> **username_0**: Thanks username_1!  this has been interesting to understand how large the halo really is!  
> **username_1**: @username_0 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](https://astronomy.stackexchange.com/a/49616/7982) 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.  
> **username_1**: @username_0 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.  
> **username_0**: no worries!! You were absolutely correct in your understanding about my original 'ballpark' request! However, the more I discovered I had screwed up and as more information became available I started getting more demanding. oops. Thanks again.  
> **username_0**: On a side note... in [Is JWST actually in a lissajous orbit]( https://space.stackexchange.com/questions/57452/is-jwst-actually-in-a-lissajous-orbit-what-will-it-look-like-implications-for)  I saw paper of [Solar Radiation Pressure Effects on the Orbital Motion at SEL2 for the James Webb Space Telescope](https://ntrs.nasa.gov/api/citations/20190029609/downloads/20190029609.pdf) which did a great job of showing how launch time greatly affected resulting orbit  

---

