Image JWST: Amateur Astronomy Success?

[collinsmark]

I understand 2 and 3 and agree. But for 1 you are saying the sun-earth-L2 line is rotating nce a year but the Webb primary mirror axis is fixed on a star. Is the heat mirror axis rigidly fixed wrt the primary axis? I guess it must be?

Yes, the heat shield is rigidly fixed to the primary mirror. If JWST changes the orientation of the primary mirror, the orientation of the heat shield changes along with it. That means its heat shield will slowly rotate with respect to the sun, while JWST is pointing at a give star. Ignoring JWST's orbit around L2 considerations, this rate is:

$$\mathrm{rotation \ rate} = \frac{\left( 360 \mathrm{\frac{deg}{year}}\right) \left( 60 \mathrm{\frac{arcmin}{deg}} \right) \left(60 \mathrm{ \frac{arcsec}{arcmin}} \right) } {\left( 365.4 \mathrm{\frac{days}{year}} \right) \left( 24 \mathrm{\frac{hours}{day}}\right) \left( 60 \mathrm{\frac{minutes}{hour} }\right) } = 2.463054 \left[ \mathrm{\frac{arcsec}{minute}} \right]$$

It goes without saying, that JWST can only point in a limited area of sky for any particular time of the year, because it must keep its heat shield in the general direction of the Sun. Once pointed at a star, JWST can't stay pointed at that star forever, since the solar illumination angle keeps changing at the above rate, and eventually, if JWST doesn't change to a new star, the heat shield's direction won't be far enough away from the Sun's direction.

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Trying to do a little bit better eyballing/ballparking, JWST moved 3.5' dec N, and 10' RA W, in ecliptic coordinates. JWST's midpoint declination was right around -12 deg 55 arcmin declination at the time (this midpoint declination figure might be important for later).

So of JWST's 10' RA motion (ecliptic coordinates),
$$\frac{(5 \ \mathrm{hours} ) \left( 60 \mathrm{\frac{minutes}{hour}} \right) \left( 2.463054 \mathrm{\frac{arcsec}{minute}} \right)}{\left(60 \mathrm{\frac{arcsec}{arcmin}} \right) } = 12.31527 \ \mathrm{arcmin}$$
12.3' can be attributed to L2's movement (ballpark).

So yeah, 12.3' and 10' are roughly in the same ballpark. So the "sanity check" checks out. (But there's still more things to consider than that though.)

[Edit: the direction is surprising though. Hypothetically, if JWST was smack at L2, I would expect its apparent motion (with respect to the background stars) to be East in ecliptic coordinates. But here it was moving West. Could the discrepancy be due to its orbit around L2?]

[Another edit: I think it's starting to make sense. JWST must presently be in the southern part of its L2 orbit, yet past the most southern part. So it's heading north and west within it's orbit, as viewed from Earth, in ecliptic coordinates. And this westerly motion in its orbit dominates its eastward apparent motion caused by Earh's/L2's motion around the Sun. In other words, JWST's orbit around the L2 point is the dominant source of JWST's apparent motion. Yes, it has a component of eastward apparent motion caused by Earth's/L2's motion, but JWST's orbit around L2 dominates this. (The surface of the Earth's movement might figure into this a little too. I haven't figured that into things yet...)]

 

[collinsmark]

The apparent westerly motion of the JWST (with respect to the background stars) is also influenced by parallax caused by the surface of the Earth rotating. This is somewhat easy to calculate.

The radius of the Earth is roughly 4000 miles at the equator, and the Earth spins around roughly once per day (it's slightly less than once per day, because we're on solar time, not sidereal time, but close enough for ballparking). So the Earth's surface at the equator is roughly moving at
$$\frac{2 \pi \left( 4000 \mathrm{mi} \right)}{ \left( 1 \mathrm{day} \right) \left( 24 \mathrm{\frac{hours}{day}} \right) \left( 60 \mathrm{\frac{min}{hour}}\right) } \approx 17.5 \mathrm{\frac{mi}{min}}$$
My latitude, at about 33 deg, is moving a little slower, So we'll modify that speed to be, at my telescope,
$$\mathrm{speed \ at \ my \ telescope } \approx \left(17.5 \mathrm{\frac{mi}{min}} \right) \cos(33^\circ) \approx 14.7 \mathrm{\frac{mi}{min}}$$

The parallax angle $\theta$ subtended by a surface distance $s$ of a point $r$ distance away is $s = r \theta$, assuming $\theta$ is measured in radians. Taking the time derivative,
$$\frac{ds}{dt} = r \omega$$
where $\omega$ is the time derivative of $\theta$. And we know $r$, the distance to JWST is about a million miles.

Putting everything together, we have,
$$\omega = \frac{\left( 14. 7 \mathrm{\frac{mi}{min}} \right)}{1,000,000 \ \mathrm{miles}} \left( \frac{180 \ \mathrm{deg}}{2 \pi \ \mathrm{rad} } \right) \left(3600 \mathrm{\frac{arcsec}{deg}} \right) \approx 1.5 \ \left[ \mathrm{\frac{arcsec}{min}} \right]$$

This rate, of course, only applies when the parallax is maximum at my telescope's local midnight. But it is significant. Considering the parallax alone, this causes JWST's apparent motion to be westward (in equatorial coordinates) which lessens the apparent eastward motion discussed in the previous post which was due to L2's apparent motion (i.e., L2's apparent eastward motion with respect to the background stars, in ecliptic coordinates).

The remaining apparent westward motion must be due to JWST's orbital velocity around L2. That's the only thing I can think of anyway.

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So there's enough motion going on, not just with JWST's apparent motion with respect to the Earth's viewing angle, but also with JWST's illumination angle, that I am inclined to agree that the flaring is due to solar reflection variation of JWST's heat shield. I.e., it's reflecting sunlight back to Earth in weird patterns, like the weird patterns caused by the reflections of a ball of alluminum foil. Or a disco ball.

JWST is also functioning like a disco ball. A big, dance-floor sized, space-disco ball.

 

[anorlunda]

It sounds analogous to a satellite flare. https://en.wikipedia.org/wiki/Satellite_flare

I've seen Iridium flares many times with the naked eye, even though there would be no hope of seeing the Iridium satellite sans the flare. There was even a phone app, Heavens Above, that predicted the time and lat/lon of flare occurences.

 

[Tom.G]

Heavens Above interactive star chart (and much more) is at:
http://www.heavens-above.com

 

[collinsmark]

Heavens Above interactive star chart (and much more) is at:
http://www.heavens-above.com

Heavens-Above is and has been a wonderful resource for satellite tracking through the years. And we have a lot to be thankful for to Chris Peat for setting it up and maintaining it.

But unfortunately, at this time at least, even Heavens-Above doesn't seem to be tracking JWST. I'm guessing that's because Heavens-Above, like others I mentioned in a previous post, use two-line element (TLE) data to track satellite positions and trajectories. But TLEs aren't cut out for objects in L2 orbits. JWST is in Heavens-Above database, but the most recent TLE has an epoch of Dec 28, 2021. That's before its L2 insertion. Even Space-Track.org last entry for JWST was Dec 28, 2021. So those won't help with JWST predictions; at least not presently.

Which makes me wonder, what is(are) the source(s) of Unistellar Optics website and The Sky Live's JWST info calculator, which seem to be pretty spot on? Don't get me wrong, they seem to be working well. It's just that I'm curious about how I would go about reproducing them myself, and what raw resources I would need, if I was so inclined to do so.