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The Lunar Crater Radio Telescope LRTC is a proposed fixed dish radio antenna to be built in a far-side lunar crater.

enter image description here

https://en.wikipedia.org/wiki/Lunar_Crater_Radio_Telescope#/media/File:Niac2020_bandyopadhyay.jpg

The Wikipedia article describes it as

… the telescope would have a structural diameter of 1.3 km, and the reflector would be 350m in diameter.46 Robotic lift wires and an anchoring system would enable origami deployment of the parabolic reflector

Parabolic dishes are used with steerable radio telescopes. Because the focus is located on the axis of the parabola, the dish is aimed so its axis falls on the object of regard.

Fixed-dish radio antennae (like Arecibo in Puerto Rico or the FAST telescope in Guizhou, China) are spherical, not parabolic. A spherical dish has no axis, so it does not need to be pointed at the object of regard. Instead, the antenna moves while the dish remains stationary.

enter image description here

https://telescope.live/blog/arecibo-worlds-largest-radio-telescope-will-close-forever

enter image description here

https://www.ft.com/content/3f2ea81e-d53c-11e5-829b-8564e7528e54

Compared with spherical dishes, Parabolic reflectors have sharper focus of objects on their axis, but focus degrades for objects off-axis, as illustrated in this ray tracing:

enter image description here https://www.semanticscholar.org/paper/Focusing-a-TM(01)-beam-with-a-slightly-tilted-April-Bilodeau/64dce910249c01a2c8a72caaf382962be25243d9

Spherical reflectors have inferior resolution compared to parabolic reflectors, but because of symmetry, the image does not degrade further “off axis” … because there is no axis.

enter image description here

Spherical dishes are aimed by moving the antenna, not the dish. The two antennas in the photo of Arecibo (spike and dome) are receiving from different directions.

enter image description here

https://www.wired.com/story/the-iconic-arecibo-telescope-goes-quiet-after-major-damage

So, if LRTC is a fixed parabolic dish, it will only achieve its best resolution of whatever happens to be at the zenith at the moment. It will not be able to achieve high resolution of objects in the rest of the sky.

A spherical shape is as easy to attain as a catenary https://www.dropbox.com/scl/fi/d4pivfipd9rpb19fm87lq/LCRT_NIAC_Phase_1_Final_Report.pdf?rlkey=65c715o7k5f2qepoly3ftfess&e=3&dl=0

If we hold the two ends of a uniform string, it takes on a catenary shape. On the other hand, if we use a variable mass string, where the linear density is proportional to1/cos2θ, then the string would take a circular shape

Why is LRTC parabolic, rather than spherical like other large fixed radiotelescopes?

Further discussion of fixed spherical vs mobile parabolic dishes: Have spherical dish antennae been used with Molniya satellites to avoid switch-over signal loss?

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  • $\begingroup$ Unsourced speculation - they are making the system as cheaply as possible by hanging wires in a crater - they will naturally form a parabola. Getting a spherical shape would seem to require a more complex design with supports/tethers? $\endgroup$
    – GremlinWranger
    Commented Aug 17 at 8:25
  • $\begingroup$ Simplicity (aka cost) so they don't have to move the receiver most likely. "Parabolic shape Reason:Best shape for stationary feed and enables keeps the feed design simple,as signals from different directions get focused at a stationary receiver" Lunar Crater Radio Telescope (LCRT) on theFar-Side of the Moon NASA Innovative Advanced Concepts (NIAC) Phase 1 Report dropbox.com/scl/fi/d4pivfipd9rpb19fm87lq/… $\endgroup$
    – Organic Marble
    Commented Aug 17 at 12:39
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    $\begingroup$ @GremlinWranger natural shape is catenary, that's not exactly parabolic according to wiki $\endgroup$
    – user721108
    Commented Aug 17 at 12:47
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    $\begingroup$ There's a difference in cost if you have provide a system to move the receiver vs a fixed receiver. $\endgroup$
    – Organic Marble
    Commented Aug 17 at 13:27
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    $\begingroup$ @OrganicMarble ... "Parabolic shape... signals from different directions get focused at a stationary receiver" Not really. As the diagram in the OP illustrates, off-axis rays form a caustic curve, not a focus point. This is a big disadvantage for detecting weak signals. $\endgroup$
    – Woody
    Commented Aug 19 at 16:12

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According to Lunar Crater Radio Telescope (LCRT) on the Far-Side of the Moon NASA Innovative Advanced Concepts (NIAC) Phase 1 Report,

We propose to deploy a 1km-diameter wire-mesh ... to form a sphericalcap reflector.

A spherical cap is a section of a sphere, not a parabola. Apparently the quote from Wikipedia in the OP is in error.

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  • $\begingroup$ Can you link to the document? The one I linked to doesn't say that. It says "We will deploy a wire-mesh in a 3–5 km diameter lunar crater on the far side, with suitable depth-to-diameter ratio, to form a parabolic reflector with a 1 km diameter (See Fig.1.1)" Perhaps they are different versions. The one I linked is March 2021 dropbox.com/scl/fi/d4pivfipd9rpb19fm87lq/… $\endgroup$
    – Organic Marble
    Commented Aug 17 at 14:58
  • $\begingroup$ It's on page 2, so not too far in :) Cntrl-F is your searching friend. That web page has a 2020 date on it so they must have "revised their views". $\endgroup$
    – Organic Marble
    Commented Aug 17 at 15:09
  • $\begingroup$ @OrganicMarble ... nasa.gov/general/… $\endgroup$
    – Woody
    Commented Aug 17 at 15:10
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    $\begingroup$ @OrganicMarble ... in the Phase 1 document you linked, it says "In Phase II, we will focus on designing a reflector..." so maybe the profile had not been fleshed out in Phase 1 $\endgroup$
    – Woody
    Commented Aug 17 at 15:16

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