By Duncan Steel 23/11/2020

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A few days ago the US National Science Foundation (NSF) announced the decommissioning of the Arecibo Observatory in Puerto Rico. This story has been the subject of items in the mass media around the globe, and also in New Zealand. Cables supporting the massive horns and radio receivers above the dish have snapped, the actual dish surface has been badly damaged, and following more than half-a-century of intensive use it has been decided that it would be too costly and dangerous to try to fix the telescope. Many astronomers and space scientists have been stunned by this decision. (There are numerous other reports on space-related websites, such as here and here, and here, and here, and here; and you might also be interested to follow this Twitter feed: #whatarecibomeanstome .)

Most of the coverage has seemed to focus on the role of the 305-metre dish in radio astronomy (i.e. the detection of radio emissions from distance stars, galaxies, pulsars, quasars and the like), but the Arecibo Observatory could do far more than that: it could send out powerful radar pulses towards solar system objects, the faint returned echoes enabling researchers to do such things as identify likely sites of sub-surface ice on Mars and Mercury, map the surface profile of Venus underneath its perpetual cloud-covering of sulphuric acid droplets, investigate the structure of the rings of Saturn, and determine the separation of the Earth and the Sun with unprecedented precision.

If one turns to the NASA statement about the closing of the Arecibo Observatory, it comes under the heading Asteroids (see also the NASA Planetary Defense website). The Reuters report on the closing, which was carried by many media outlets, stated incorrectly that it has been used to “find potentially hazardous asteroids”. I would imagine that other wire services have made the same mistake. The Arecibo dish has been invaluable in tracking potentially-hazardous asteroids (i.e. asteroids which could impact Earth), but radars are not of any real use in searching for them. That seems a paradoxical statement, and so I will explain below.

Radars Not of Utility in Asteroid Searches

Asteroids are discovered mostly using relatively small optical telescopes (compared to the behemoths used in astrophysics research) with apertures between about 0.5 and 1.5 metres, but designs giving a wide field of view. The word ‘asteroid’ means ‘star-like’, and that is the way they appear: as pin-pricks of light, which can be distinguished from background stars by dint of the fact that they are moving relative to those stars, as they (the asteroids) orbit the Sun. The billions of asteroids in the main-belt between Mars and Jupiter appear to shift relatively slowly. Asteroids that are closer to Earth, including those which cross our orbit and so are potential impactors, might appear to move by one degree (twice the angular diameter of the Moon) or more per day.

Once they have been spotted using a wide-field telescope (or a satellite such as NEOWISE), such asteroids can be tracked from night to night by narrower-field telescopes. For example, Alan Gilmore and Pam Kilmartin use the one-metre telescope at Mount John Observatory near Lake Tekapo in such invaluable follow-up work.

People often imagine that a radar could be used to discover asteroids, but a radar is of no use in that regard for the following fundamental reasons:

(a) You need to range-gate echoes, and prior to discovery you do not know the asteroid distance.

(b) The distances involved are huge, and the returned echo power drops off as the inverse-fourth power of the distance: you might transmit a pulse with an instantaneous power of a megawatt, but the echo power you get back will be much less than a billionth of a watt, and that must be pulled out of the noise.

(c) The asteroid has a line-of-sight speed which may be 10 kilometres per second; the doppler effect therefore shifts the radio frequency in the returned echo by a substantial amount, and for unknown asteroids you don’t know how much to alter the tuning of the radio receivers so as to be sensitive to that returned frequency.

(d) Out in space the majority of the cross-section of solid lumps of material able to return echoes is dominated by smaller chunks or meteoroids which are around the same size as the radar wavelength (about 10 cm), rather than asteroids (perhaps 100 metres to 1 km in size). Trying to discover asteroids by radar therefore becomes similar to looking for a snowman in a snowstorm.

Radars are no use, then, for looking for asteroids… but they are really good for tracking them, in terms of determining precise orbital parameters. Once an asteroid has been discovered by the optical searchers, and a rough orbit measured over the first few nights, we know how far away it is (problem a above), we can integrate the returned power over many pulses because we know approximately when the echo should return (problem b above), we know the approximate line-of-sight speed (problem c above) and so we can tune the radio receivers appropriately, and we can reject the echo signals at other return times and doppler shifts (thus circumventing problem d above).

Radar Tracking of Asteroids

Why are radars better than optical telescopes for determining precise orbits? Here is a summary… To determine an orbit one needs six independent measurements, and these lead to the six parameters that define an orbit: the semi-major axis (orbit size), the eccentricity (orbit shape), inclination (tilt of the orbit compared to the ecliptic, the plane of Earth’s orbit around the Sun), the longitude of the ascending node (the place where the asteroid orbit crosses the ecliptic), the argument of perihelion (the orientation of the orbit in the plane defined by the preceding parameters), and the time of perihelion passage (where the asteroid is located in the elliptical path defined by the other parameters).

One can think of the orbit in a different way: you need the x, y and z coordinates at some time, along with the three-dimensional velocity (that is, the speeds in each of those three coordinate axes). That makes six.

Now, if you observe an asteroid with an optical telescope you can measure at any one time only two parameters: the position in the sky plane, which we normally term the right ascension and the declination (the equivalent of longitude and latitude mapped onto the sky). That makes two parameters per measurement, and so to get six overall you need three sets of measurements.

The optical measurements are inherently inaccurate, however. The asteroid is a long way away from Earth, usually. An astronomical unit (AU) is the average Earth-Sun distance, a little less than 150 million km. Imagine the asteroid is two-thirds of an AU away, or 100 million km. Imagine also that one can measure its location in the sky plane to an accuracy of one arc-second (which might be typical). That is equivalent to about 500 km. That is, each of the measurements you make of the asteroid positions (perhaps over three nights spaced by a week) is uncertain by 500 km, and so the orbit you calculate is going to have limited precision, likely good enough to find that it is going to come close by our planet, but not good enough to say for sure whether it will hit or miss, whether next month or perhaps in 17 years’ time.

That’s where the radar comes in. A planetary radar like Arecibo can be used to determine a different pair of parameters. Optical telescopes make measurements in the sky plane, but the radar makes measurements in the direction perpendicular to that: the line-of-sight from the radar to the asteroid. The radar data can tell us the distance to the asteroid with far better accuracy than 500 km: in principle, perhaps as good as a few tens of metres.

Not only that, but the doppler shift in the returned echo can deliver a good measurement of the line-of-sight speed, precise to a matter of centimetres per second.

If we think of the optical telescopes giving us measures of the asteroid position in the sky plane as X and Y, the radar gives us measures of Z and Z-dot: the distance, and the line-of-sight speed, and with considerable precision. A rule-of-thumb is that one radar detection is worth several years of optical astrometry, in terms of improving our knowledge of the asteroid’s heliocentric orbit.

I wrote previously about why radar detections are of pivotal importance in determining accurate future paths for Earth-approaching asteroids in a blog post here back in July.

Using Spherical Mirrors

Much of the expense incurred in designing and building large ground-based optical and radio telescopes is associated with having a steerable mount that moves smoothly and steadily. That is, you need to be able to point the telescope at your object of interest, and for long-exposures (integrating the photons in an electronic detector array, perhaps, for very faint targets) the mount needs to be able to revolve (about one axis for an equatorial mount, around two axes for an altazimuth mount) so as to compensate for Earth’s rotation. The Arecibo dish, however, is obviously fixed, as is the recently-opened huge Chinese device, the Five-hundred-metre Aperture Spherical radio Telescope (FAST).

The clue to how Arecibo and FAST function is in that letter S: Spherical. Most telescopes have primary mirrors shaped as paraboloids, because a parabolic shape produces an on-axis image without any geometrical aberrations. If you use a spherical mirror, then you get spherical aberration at the prime focus.

There is a way around this, however: employ a secondary mirror that corrects for the spherical aberration. Such a secondary might be a convex hyperboloid, for example. With judicious (and highly-complicated) design one can produce extended (i.e. not only on-axis) images with acceptably-low aberrations (which one can think of as being a bit of blurring).

Aerial view of the Arecibo Observatory; note the igloo-shaped structure suspended above the main reflector dish, which was built in a natural concavity. Photograph courtesy the National Astronomy and Ionosphere Center, as is the picture at the head of this blog post.

Looking at the preceding photograph of the Arecibo Observatory, note the huge structure suspended high above the main reflector dish, held up by cables from three towers. That instrument platform has a mass of about 900 tonnes; it is about 135 metres above the centre of the dish (remember that the dish itself is 305 metres in diameter). It is the breaking of some of the cables holding the platform in place that has led to the closing of the facility.

The igloo-shaped enclosure forming an obvious white feature far above the main dish is the business-part of the overall system. Note that in the preceding photo it is not above the centre of the dish, and it is tilted away from the vertical. Essentially, the telescope is looking at a point in the sky that is above but slightly to the left in that photograph. The main dish being spherical, it has no single axis of symmetry, as is the case for a paraboloid, and so in effect the telescope can look in any direction that can be accommodated by the range of positions to which that transmitter/receiver structure can be moved and tilted.

Arecibo instrument platform.  The igloo-shaped enclosure contains the effective-secondary mirror corrector and the radar transmitters and receivers. This can be moved along the crescent-shaped support structure, which itself can be rotated about the circular support above, and in that way the telescope can be pointed towards different directions in the sky. Photo courtesy the National Astronomy and Ionosphere Center.
A view of the Arecibo instrument platform from below the primary mirror, which consists of a metallic mesh. Radio telescopes do not necessarily need a surface that is optically-reflective or impermeable: they just need the gaps to be smaller than the radio wavelength. Similarly, the holes in the door of a microwave oven are small enough to stop the microwaves from escaping, but large enough for you to be able to see your food cooking inside. Photo courtesy the National Astronomy and Ionosphere Center.

The beauty of using a spherical form for the huge primary mirror is that it can be fixed in place, with no need to steer it across the sky. The spherical shape means one can think of it as being able to look in all directions above it. All you need to do is to put your detector system in the right place and point it in the right direction at the dish below.

What one could do using the Arecibo design, for example, would be to have the detector looking straight down at the main dish, and over 24 hours scan the skies at a certain radio wavelength. The next day one could shift the detector to look at a slightly different declination, and repeat the process. Of course one can devise more-complicated observing regimes, but the fundamental point is that during observations you do not necessarily need any moving parts.

Now consider using Arecibo as a radar to probe Mars. You position the instrument platform above the dish in the correct position to look towards Mars, and you transmit a series of pulses with many such pulses every second for a whole minute, perhaps. Now, it might take five minutes for those pulses to get to Mars, and then another five minutes for the echoes to return to Earth, because Mars might be 90 million km away. After finishing the minute of transmitting pulses, you have nine minutes to shift the instrument platform to the correct place, because in that time interval the Earth has rotated a bit (and also Mars has shifted along its orbit). Similar considerations apply to tracking asteroids.

An Optical Arecibo?

Spherical mirror telescopes have a lot to recommend them, then, in terms of simplicity of engineering. It’s a basic design that can be used in a variety of ways, for specific tasks.

Some years ago (actually, beginning in 1995) I started wondering about whether a really big optical telescope might be constructed using a spherical primary. I am thinking here of a mirror (multi-segmented) that could be 30-metres or more in diameter.

This is not a novel idea in itself, and both the 10-metre Hobby-Eberly Telescope in Texas and the similar-sized Southern African Large Telescope (SALT) have spherical primaries. SALT is the largest telescope in the southern hemisphere, and New Zealand was a partner in its construction.

What I had in mind, though, was something a bit different. The expense of large telescopes is largely occasioned by the need for mirror surfaces of excellent quality, such that sharp images are formed (or, in many astrophysical applications, the light is all brought to the spectroscope’s entry slit). If you are interested in discovering asteroids, however, the situation is blurred (rather literally) by the fact that the asteroid is moving. You can’t get a good image of an asteroid unless you can track on it. And you can’t track on it until you have discovered it.

I reasoned, therefore, that a telescope system dedicated to asteroid discovery might be designed with the need to produce sharp images being relaxed. One gains little by having images that have better resolutions (in terms of angular blurring) than the angular distance moved during an effective exposure by a typical asteroid for which you are searching.

It took me 15 or 16 years to get around to it, but in the end I came up with a strawman design, and published a paper about it in 2012. I still think it’s a neat idea. Maybe someone will build it, one year soon.

A view looking upwards from the surface of the primary of an Optical Arecibo model. The primary mirror in this concept is 30 metres in diameter, and comprised of a large number of one-metre hexagonal spherical mirrors which are economically produced by slumping glass blanks into a mold in an oven. The black gaps are holes, beneath which are holographic correctors manufactured to correct to some extent the aberrations produced by the individual primary hexagonal mirrors. Above the primary, and closer than the prime focus, is a hemispherical frame holding an array of convex hyperboloidal mirrors which reflect light from selected directions down through the holes to the holographic correctors and thence the image detector arrays. Such a device would scan the sky as the Earth turns, producing detections of asteroids several hours apart, enabling them to be tracked with greater precision using conventional telescopes. This graphic was produced by my elder son Harrison Steel, who was my co-author on this paper; at that time (2011) he was an undergraduate at the University of Sydney, and he has now gone on to work in a quite different area of science and engineering.

Big Eye Wide, But Shut

Eyes Wide Shut (1999) was the final movie made by Stanley Kubrick, who also made 2001: A Space Odyssey. The following year David Jewitt (now at UCLA) wrote a review for Nature under the same title, though with fewer capitals (Eyes wide shut). Therein Jewitt decried the lack of adequate patrolling of the solar system for asteroids and comets which could cause humankind more than just a bad day. In 2002 I also tried to draw attention to the lack of sky surveillance with the Berlin Declaration on the cosmic impact hazard.

The significance of the closing of the Arecibo Observatory from the perspective of Planetary Defence is that although we have a certain level of sky reconnaissance using optical telescopes, our capability quickly to determine their path with the required precision has now been greatly reduced.

This does not mean that there is no longer any radar capability to track asteroids. The 70-metre dish at NASA’s Goldstone Deep Space Communications Complex is still used for solar system radar research, including asteroid tracking (and imaging). In the past the similar 70-metre radio telescope at Yevpatoria in the Crimea has been used for radar tracking of asteroids, sometimes with the 100-metre Effelsberg radio telescope near Bonn being used for reception of the echoes, but that work has all but ceased over the past twenty years and is unlikely to recommence at any time soon, especially given the political uncertainties in the region.

What this means is that at the start of the millennium humankind had three planetary radars which could be used to track near-Earth asteroids. As of the past month, we are down to one. That is not progress, and it might cause us problems.

Over the next few years you can expect to see an increasing number of situations in which asteroids are discovered and their orbits measured with sufficient accuracy to be able to say that they are going to pass close by Earth, but without the level of precision that would enable us to say for sure whether they are going to hit or miss. Keep your own eyes wide open, and on the lists of risky asteroids that are available for all to peruse: the NASA Sentry page here, and the University of Pisa/European Space Agency Risk page here.

Addendum, 2020 December 01: A new article on about what the loss of Arecibo means for tracking dangerous asteroids has just been published.

Addendum, 2020 December 02: The instrument platform at the Arecibo Observatory has now collapsed. Reports are here and here. We await aerial and satellite imagery…

Later addition, December 02: Aerial photographs of the collapsed structure are now available here and here and here and here and here.

Addendum, 2020 December 08: Movie footage of the collapse of the instrument platform is available here.