Is the JWST halo orbit period sync'd with earth's elliptical orbit about sun?

Question

I was looking at the JWST halo and wondering if getting the halo orbit phased with earths elliptical orbit would be a way of keeping gravitational variations regular and periodic so that station keeping burns could be more predicable, preserving fuel and thereby extending useable life of JWST. Right now JWST is near max +Y travel... when earth is just past Periapsis. Is this a coincidence? The halo could be tailored with precision burns to get max Y at Periapsis and min Y at midpoint between Periapsis and Apoapsis. At Apoapsis JWST would be at max Y again, 1 halo orbit in 1/2 year.

and so the question: Is (or will) the JWST halo orbit period sync'd with earth's elliptical orbit about sun?

EDIT: More directly about my "Sync'd orbit" question... Is there a need or benefit to have JWST at a specific place in its halo when earth is at a specific place in its orbit.

Answer 1

Is the JWST halo orbit period sync'd with earth's elliptical orbit about sun?

Wow, It's surprisingly close!

At first I figured it would be closer to 6.5 or 7 months due to past information and questions and answers based on an earlier JWST trajectory, but wow, trying to define the period of a complicated 3 or 4 body orbit (including the Moon's effect) in a simple way, I've come up with 180 days!

I took the new predicted orbit for JWST in Horizons

Revised: Jan 28, 2022
2Y_SCHEDULE_2022027000000_01U.OEM.V0.1   2022-Jan-27 00:01  2024-Jan-27 00:01

downloaded the heliocentric positions of JWST and Earth, subtracted Earth/Moon barycenter from JWST then rotated by Earth's angle to be in a pseudo-synodic frame (it rotates with EM/Bary angle, not steadily), and got the following (data starts 2022-Feb-08, ends 2024-Jan-27):

The offset in X is the average distance from Earth, close to the 1.5 million km of the classical L2 distance.

If I pick off the maxima and calculate a period for X, Y and Z motion I get 179.3, 180.0, and 180.7 days!

As this is an ad hoc method, I'll say that these periods are *currently indistinguishable from a half year so my answer is a qualified but quite surprised "yes!"

import numpy as np
import matplotlib.pyplot as plt
fnames = ('Earth orbit heliocentric horizons_results.txt',
          'JWST orbit heliocentric horizons_results.txt')
JDs, datas = [], []
for fname in fnames:
    n_offset = 10
    with open(fname, 'r') as infile:
        lines = infile.readlines()
    a = [i for (i, line) in enumerate(lines) if 'SOE' in line][0]
    b = [i for (i, line) in enumerate(lines) if 'EOE' in line][0]
    lines = lines[a+1+n_offset: b]
    info = [line.split(',') for line in lines]
    JD = np.array([float(line[0]) for line in info])
    data = np.array([ [float(thing) for thing in line[2:8]] for line in info])
    JDs.append(JD)
    datas.append(data)
JD = JDs[0]
Earth, JWST = [thing.T.copy() for thing in datas]
dJWST = JWST - Earth
z = dJWST[2]
th = np.arctan2(Earth[1], Earth[0])
s, c = [f(-th) for f in (np.sin, np.cos)]
x = dJWST[0] * c - dJWST[1] * s
y = dJWST[1] * c + dJWST[0] * s
fig, axes = plt.subplots(3, 1)
for thing, name, ax in zip([x, y, z], 'XYZ', axes):
    ax.plot((JD - JD[0]) / 365.2564, thing)
    ax.set_ylabel(name + ' (km)')
plt.show()
maxima = [np.where((p[2:] < p[1:-1]) * (p[1:-1] >= p[:-2])) for p in (x, y, z)]
maxima = [thing[0] for thing in maxima]
periods = [(m[-1] - m[0]) / (len(m) - 1) for m in maxima]
print(periods)