A season without a night

From the ground, a right ascension is a date. The sidereal clock turns each direction on the sky into the time of year at which it crosses the meridian at midnight, and an object is observable for the months on either side of that date on which it is high enough while the Sun is far enough below the horizon. The two clocks — the sidereal one that sets where the sky is, and the solar one that sets whether it is dark — drift apart by one turn a year, and the drift is the observing season.

A telescope in space has neither a horizon nor a night. It can point anywhere the Sun, the Earth and the Moon do not forbid, and the forbidding is done by angles rather than by the rotation of a planet. It would be natural to expect that such a telescope sees the whole sky whenever it likes. It does not. Its season is set by a different geometry, and in one respect it is more restrictive than the ground’s: an object at opposition, the best time of year to see it from the Earth, is the one time a large space telescope at the Sun–Earth L2 point cannot look at it at all.

An angle from the Sun, not a height above the ground #

The largest infrared telescope in space sits near the Sun–Earth L2 point, a million and a half kilometres beyond the Earth, where the Sun, the Earth and the Moon all lie in roughly the same direction. It is kept cold by a sunshield the size of a tennis court, and the one rule of its pointing is that the shield must stay between the telescope and the Sun. That confines the line of sight to a band of solar elongation — the angle between the target and the Sun — from 85 to 135 degrees. Nearer the Sun than 85 degrees, sunlight would reach the cold optics round the shield’s edge; further than 135, the shield would be tilted so far that it stops shading and the telescope would see the Sun over its top.

The elongation of a target at ecliptic longitude $\lambda$ and latitude $\beta$, when the Sun is at longitude $L$, satisfies $\cos e = \cos\beta\cos(\lambda - L)$. The Sun’s longitude advances by a degree a day, so each target’s elongation traces the same curve every year: it is smallest at conjunction, when the Sun passes the target’s longitude and the elongation is just the latitude, and largest at opposition, half a year later, when it is 180 degrees minus the latitude. The band of allowed elongations is a ring round the Sun on the sky, sweeping along the ecliptic once a year, and a target is observable whenever the ring passes over it.

Everything about such a telescope’s season is therefore written in ecliptic coordinates. The Earth’s axis, which decides everything about the season from the ground, plays no part at all: the telescope does not rotate with the Earth and has no latitude. What matters is how far a target is from the Sun’s path.

Two windows, and neither contains opposition #

A target on the ecliptic has an elongation that runs from zero at conjunction to 180 degrees at opposition and back. It is inside the 85–135 degree band twice: on the way out, about three months after conjunction, and on the way back, about three months before the next one. Each window lasts about 51 days — the band is fifty degrees wide and the Sun moves a degree a day — and together they cover 28 per cent of the year.

Neither contains opposition. At opposition the target is 180 degrees from the Sun, and pointing there would put the Sun directly behind the telescope, outside the shield’s shadow. The ecliptic target is seen before and after it is best placed, never at the moment a ground-based observer would choose. That matters for anything whose brightness or geometry changes around opposition — asteroids and outer-solar-system bodies, which are closest and fully lit then, and variable phenomena in the ecliptic plane — and it is why observations of them from such a telescope are arranged as two campaigns half a year apart.

Away from the ecliptic the windows lengthen, because the elongation’s excursion narrows: a target at latitude $\beta$ never gets closer to the Sun than $\beta$ nor further than $180° - \beta$. The two windows of an ecliptic target therefore grow towards each other as the latitude increases, and at 45 degrees — where $180° - \beta$ falls to 135 — opposition itself enters the band and the two windows join into one.

The zone that is never out of season #

The single window lengthens until, at 85 degrees of ecliptic latitude, the elongation at conjunction no longer falls below the band’s inner edge either. From there to the pole a target is never outside the band: its elongation stays between 85 and 95 degrees all year. That is the continuous viewing zone, and it is five degrees in radius round each ecliptic pole — one centred in the constellation Draco, near the north ecliptic pole, and one in Dorado, near the Large Magellanic Cloud.

The two boundaries come from the band’s two edges separately, which is worth noticing because it means the scheduling rules follow from two numbers set by engineering. The outer edge, 135 degrees, decides where the windows merge; the inner edge, 85 degrees, decides where visibility becomes continuous. Widen the band inward and the continuous zone grows; widen it outward and the merger moves towards the ecliptic. A band that includes 90 degrees always has a continuous zone, because the ecliptic poles are always 90 degrees from the Sun.

The fraction of the year a target is observable follows directly. On the ecliptic it is twice the band’s width divided by 360 degrees, exactly, because the Sun’s longitude advances uniformly and the band is crossed twice. It grows slowly with latitude, jumps where the windows merge and opposition is added, and climbs to the whole year at the continuous zone. A narrower band, like the 82 to 120 degrees of an earlier infrared telescope in an Earth-trailing orbit, gives less time everywhere, merges its windows later, at 60 degrees, and has a continuous zone of eight degrees — but it has one. A telescope that could look anywhere more than 45 degrees from the Sun, as a ground telescope effectively can at night once the Earth is removed, would see an ecliptic target for three-quarters of the year.

The continuous viewing zones are where anything that must be watched without interruption goes. Deep fields that accumulate exposure over many months, calibration fields that are reobserved every few weeks, transiting-planet surveys that need unbroken light curves, and the monitoring of variable stars all gravitate there, and the two small patches of sky round the ecliptic poles are among the most intensively observed in astronomy for no reason except their angle from the Sun’s path.

One target, worked through #

The centre of the Galaxy makes the rules concrete. It lies at ecliptic longitude 267 degrees and latitude −5.6 degrees, almost on the ecliptic, and the Sun passes its longitude around the eighteenth of December — which is why it is a summer object from the ground, opposite the Sun in June. For a telescope confined to 85–135 degrees from the Sun, its elongation first reaches 85 degrees about eighty-five days after that conjunction, in mid-March, and passes 135 degrees about fifty days later, at the start of May. The second window opens in late July and closes in mid-September. The June opposition, when the Galactic centre is highest at midnight for every ground observatory in the southern hemisphere, falls in the gap between them.

Two windows of seven weeks each, half a year apart, set the rhythm of every programme that monitors the Galactic centre from such a telescope — the flares of the black hole at its middle, the orbits of the stars around it, the variability of the crowded bulge fields. A study that needs a continuous year of observations cannot be done there at all; one that needs a few days every six months fits exactly. The same object, from the ground, is observable at some altitude for more than half the year from a southern site. The Galaxy is measured from inside it, and a telescope at L2 sees its centre on a timetable set by the Earth’s orbit.

A telescope that stared at one field for four years shows the other side of the rules. The survey that found most of the known transiting planets by the light they remove watched a single field in Cygnus and Lyra continuously from an Earth-trailing orbit, and it could do so because the field sits at ecliptic latitude 65 degrees, far enough from the Sun’s path to stay out of it all year; the spacecraft rolled a quarter-turn every three months to keep its solar panels towards the Sun. When two of its reaction wheels failed, it could no longer hold that field steady, and its extended mission pointed instead along the ecliptic, where the pressure of sunlight on the spacecraft could be balanced symmetrically — and each field there could be watched for only about eighty days before the Sun’s advance forced a move to the next. The length of every campaign in that second mission was the Sun’s motion along the ecliptic, a degree a day, against the angle the spacecraft could tolerate.

A night every ninety minutes #

A telescope in low Earth orbit has the opposite problem. The Sun still matters — it cannot be looked at — but the main obstacle is the Earth itself, which from a few hundred kilometres up fills a large part of the sky and is swept round once every orbit.

From 540 kilometres, the height of the longest-lived optical telescope in low orbit, the Earth subtends a circle 67 degrees in radius, and with a margin of eight degrees kept from its bright limb it blocks a circle of 75. As the telescope goes round, the Earth’s direction sweeps round the orbital plane, and a target in that plane is hidden for 42 per cent of every 95-minute orbit. The hidden fraction falls as the target’s angle from the plane increases, and a target more than 75 degrees from it — within fifteen degrees of the orbit’s pole — is never hidden at all. That is the continuous viewing zone of a low orbit: two circles, fifteen degrees in radius, round the poles of the orbit rather than round the poles of the ecliptic.

The night of such a telescope is the orbit’s, and it comes sixteen times a day. Most targets are observable for about fifty minutes out of every ninety-five, and long exposures are built out of many orbits’ worth of fifty-minute pieces. From higher up the Earth is smaller: at 2,000 kilometres it blocks less than a third of each orbit in the plane, and the continuous zone grows to thirty-two degrees in radius.

A zone carried round by the Earth’s bulge #

The poles of a low orbit are not fixed on the sky, and the reason is the shape of the Earth. The Earth’s equatorial bulge pulls on an inclined orbit and makes its node — the point where it crosses the equator northward — regress westward at a rate set by the second zonal harmonic of the gravity field, the orbit’s height and its inclination. The orbit’s pole, which sits at the inclination’s complement from the celestial pole, circles the celestial pole at the same rate.

For an orbit at 540 kilometres inclined at 28.5 degrees — the latitude of the launch site, which is where such orbits usually end up — the node regresses once in about 55 days. The northern continuous zone is a circle fifteen degrees in radius centred at declination 61.5 degrees, and it travels round the sky at that declination with the 55-day period, visiting each right ascension in turn. A target at 61.5 degrees north is inside the zone for about seventeen per cent of each cycle, a few days at a time; one north of 76 degrees or south of 47 is never inside it. The southern zone does the same at declination −61.5.

That is why the deepest images made from low orbit were planned around specific dates. A deep field chosen at a declination the zone passes over could be observed without Earth occultation for a few days of each 55-day cycle, and those days, calculated from the Earth’s second zonal harmonic, fixed the schedule weeks in advance. The field’s position was chosen for its emptiness and the observing dates were set by the shape of the planet.

What the geometry leaves out #

The figures draw the constraint that dominates for each kind of telescope and ignore the others. A telescope at L2 must also avoid pointing near the Earth and the Moon, which from there are small and close to the Sun’s direction, so they rarely bind; but its pointing is further limited by how far it can roll about its line of sight, which constrains the orientation of the field on the sky through each window, and that matters for instruments with slits or for fields that must be imaged at a fixed angle. A telescope in low orbit also avoids the Sun and the Moon, loses time in the South Atlantic Anomaly where the radiation belts dip into its orbit, and has a bright-limb margin that is larger than the dark-limb margin used here, so real continuous zones are smaller on the sunlit side.

And the sky is not uniform in its background. Near the ecliptic, the zodiacal light — sunlight scattered by interplanetary dust — is brightest, and it sets the faintest level a detector can reach in the infrared. The continuous viewing zones near the ecliptic poles are also where that background is lowest, so the same patches are favoured twice, once by geometry and once by the dust.

What changes and what does not #

The comparison with the ground is instructive because the underlying question is the same. On the ground a direction on the sky becomes a date because the Sun’s position among the stars advances by a degree a day, and the season is the set of dates when the object is up at night. In space the same advance of the Sun turns a direction into a date, and the season is the set of dates when the object is at an allowed angle from it. The sidereal clock is still running; the difference is only in what is tested against it. For the ground it is the altitude at night, which depends on declination and so on the tilt of the Earth’s axis; for a telescope at L2 it is the elongation, which depends on ecliptic latitude and ignores the axis entirely. Coordinates are chosen by the question being asked, and here the question picks the ecliptic.

Still open: how to share a sky that is only half available #

A space telescope’s observing programme is a scheduling problem of a peculiar kind: every target has windows fixed by geometry, most targets have two a year, and the time within each window is contested by everything else at nearby longitudes. The most oversubscribed regions of the sky — the Galactic centre, the Magellanic Clouds, the best-studied deep fields — have their windows at fixed times of year, and the demand for them piles up there, while the telescope must be kept busy in between on whatever the band happens to be passing. How to plan a decade of observations so that the demand fits the geometry, with targets whose windows are known years in advance and proposals that arrive once a year, is solved each cycle by software rather than in closed form. The part of it that is closed form is the part drawn here: an angle from the Sun, a degree a day, and two edges of a band.