# Why do these two Hubble Space Telescope star cameras point in nearly the same direction, and what's the other window for?

The article in Forbes Former Astronauts Share Ways To Cope With Social Distancing & Isolation includes the following image of the Hubble Space Telescope.

Question: I believe that those three holes are cameras, but are they very fancy star cameras or for science, and if star cameras why do the two lower ones point nearly in the same direction? And what is the big black rectangular "bay window"?

Astronaut John Grunsfeld performs work while participating in the first of five scheduled spacewalks while servicing the Hubble Space Telescope. GETTY IMAGES & NASA

• They're the three fixed head star trackers – user20636 Mar 22 '20 at 3:32
• @JCRM "...why do the two lower ones point nearly in the same direction?" – uhoh Mar 22 '20 at 3:35
• Ask yourself "what's the FOV of a star tracker?" Ask yourself "How far apart would they need to point for there not to be significant overlap?" Ask yourself "Am I making assumptions based on a 2D picture of a 3D object?" – user20636 Mar 22 '20 at 4:12

The three "fixed head star trackers" don't point in the "nearly the same direction", they're nearly* orthogonal.

They provide attitude detection to around 60 arcseconds to point the observatory in pretty much the right direction.

As to why this arrangement is used, it provides sufficient accuracy while working well for the spacecraft design. (I suspect the cutouts in the aft shroud are a strong driver for the design)

* Yes, nearly is hyperbole, however because trigonometry is used to determine attitude, 44.4 degrees is 70% of the way to orthogonal compared to the 18% for a (generous) 10 degrees for something "pointing in nearly the same direction"

• 44.4 degrees is kinda small, I'll call it closer to "nearly the same direction" than to "nearly orthogonal since numerically it's less than 45 degrees. My question asks why? – uhoh Mar 22 '20 at 16:17
• you're wrong, obviously @uhoh. as to why: the usual reason. It works with the practicalities of the design, and it's good enough – user20636 Mar 22 '20 at 17:25
• Edit (and rationalization) looks great; I love it! Of course an argument based on solid angles subtended by a cone of half-angle 44.4 degrees would only give 28% of π sr (14% of 2π) but that's stretching it. – uhoh Mar 23 '20 at 1:55
• Interesting, many Earth observation satellites carry two mounted in a similar way but this is for redundancy at unit-level rather than because orthogonality is really need, i.e. they can cover their geolocation requirements for a 50cm resolution payload with just one startracker. Looking at it the other way, what does Hubble do for redundancy? – Puffin Nov 30 '20 at 18:28

And what is the big black rectangular "bay window"?

That is one of Hubble's radial instrument bays. It currently holds the Wide Field Camera 3. This DOUG rendering shows the camera "popped" out of the bay.

why do the two lower ones point nearly in the same direction?

As this answer says, the three orifices below the "bay window" are the openings for Hubble's Fixed Head Star Trackers. This DOUG rendering shows the FHSTs, and a photograph of them is in the linked answer.

The look angles on the two lower FHSTs are separated by 60 degrees in the Hubble's "1-2" plane. The look angle between the lower and upper FHSTs is separated by 45 degrees in the "1-3" plane. The axes are as shown here.

The unit vectors for the FHSTs are given here.

The unit vectors and coordinate system image come from this paper which contains a useful discussion of how the FHSTs are used in the Hubble's overall pointing scheme. Here is an excerpt:

The FHSTs are NASA Standard 1970’s vintage star trackers manufactured by Ball Brothers.7 They employ an electronic search and track technique using an analog image dissector tube and a photomultiplier detector along with supporting electronics. The FHSTs have an 8° x 8° FOV and are capable of acquiring and tracking stars between 2.0-6.5 magnitude visual (mv). The trackers provide digital horizontal and vertical star position output to the HST flight computer at a 10 Hz sample rate. The FHST noise equivalent angle is 16 asec RSS. Unlike modern star trackers, the FHSTs have no internal processing to output attitude quaternions, and attitude errors from the FHSTs are computed on-board the HST flight computer.

• Thanks! I've used those numbers to calculate the angles between cameras. The pair in question seem to be only 44.4 degrees apart, and each is 49.1 degrees from #1 ($\mathbf{\bar{e}_3}$) direction). It's not "nearly the same direction" but its not perpendicular either. At first I thought that the ideal configuration would be one along $\mathbf{\bar{e}_3}$ and the other along $\mathbf{\bar{e}_2}$ but then I realized the gyros are at "crazy" angles, so maybe the control algorithm works best with these cameras at these angles for that reason. – uhoh Mar 22 '20 at 16:26
• @uhoh Thanks to you also. I made a dumb mistake calculating the angles in the "1-3" plane. Since FHST 2 & 3 have essentially the same "1" and "3" coordinate, the angle has to be 45! Note to me, check all work graphically. – Organic Marble Mar 22 '20 at 17:06
• If not I'm gonna change the title to "Is Hubble a Tennis Racket?" – uhoh Mar 23 '20 at 12:06

updated to be supplementary answer only. There was a question about the two cameras on either side of the symmetry line and if they pointed in "nearly the same" direction or pointed closer to orthogonal directions.

...why do the two lower ones point nearly in the same direction?

If I understand the linked document correctly, it turns out that the angle between the two is less than 45 degrees and while not "nearly the same" closer to parallel than to orthoginal.

Table 3. in the linked paper Hubble Space Telescope Reduced-Gyro Control Law Design, Implementation and On-Orbit Performance; AAS 08-278 in @OrganicMarble's answer appears to give just that, unit vectors for the directions of the three cameras. Arccosines of the dot products give us the angle between pairs, which is

pair        angle (deg)
1 - 2       49.1,
2 - 3       44.4
3 - 1       49.1


Number 1 [0, 0, -1] is the top camera in the question since it is the only one pointing perpendicular to the telescope's axis. I'm getting the angle between the other two cameras as 44.4 degrees.

import numpy as np

degs = 180/np.pi
vecs = np.array([[0, 0, -1],
[-0.6547, -0.3779, -0.6546],
[-0.6547, +0.3779, -0.6546]])
print([degs*np.arccos(np.dot(vecs[i], vecs[(i+1)%3])) for i in range(3)]) # they're fairly well normalized