How much does the Moon cost astronomers?

The moon, bright , entrancing, intensely irritating for astronomers. Scattered moonlight makes observing more inefficient meaning astronomers have to stick on a target for longer. Observatories are expensive, high-tech facilities so the question is, how much does the Moon cost astronomy?

Astronomers are in essence counters. Telescopes collect photons from a source and astronomers count the number in their detectors. The telescopes also collect photons from the night sky. This is never 100% dark so there are also some additional background photons which must be subtracted off. As with all counting there are uncertainties. The fainter the object the higher the uncertainty, the brighter the sky the higher the uncertainty. The Moon is basically a big mirror reflecting sunlight into telescopes. As the amount of sunlight the Moon reflects towards the Earth varies over a lunar cycle, the sky background is much higher at Full Moon than at the New Moon. This means there is a much higher uncertainty in astronomical measurements at the Full Moon so astronomers have to observe for longer and get more signal to have a measurement as certain as one from a shorter observation taken at New Moon.

So how much observing time does this cost and how much is that in terms of money? I’m going to use some very rough estimates based on publicly available numbers. If these are off by a bit, feel free to correct them in the comments.

The Moon, just how much does it cost astronomy every year? Credit:NASA/JPL

So firstly how much time does this cost? Astronomers typically describe nights as dark, grey or bright depending on the phase of the Moon. Let’s assume that for 50% of the time when the telescope is open it is integrating in the optical*. This takes into account overheads such as slewing and that some of the time the telescope will be observing in the infrared. The wavelength is important as the amount of reflected sunlight varies with the colour of the filter you are observing through. Bluer, shorter wavelengths are typically more seriously affected by the Moon. Hence let’s ignore the effect on infrared observing. Picking a typical optical observation band (the R band) which is not really badly affected by scattered moonlight I had a look at some Integration Time Calculators. These are tools which allow astronomers to work out how long they have to observe a source for. To reach a particular uncertainty of observation you need to integrate for 60% longer in bright time than dark time and 5% longer in grey time than dark time. So assuming 1 week of bright time per lunar cycle plus one week of dark time and two of grey time. That means that astronomers lose about 6% of telescope time due to having to observe for longer in bright and grey time taking into account our 50% overheads/IR observing factor.

So how much money is this? Well the Keck Observatories (two 10m telescopes) have annual budget of $11m. But that is only the running cost, what about the construction cost? The VLT in Chile (four 8m telecopes) cost €330m in 1999 to construct. Converting to 2011 dollars that’s $650m. Assuming a 40 year lifetime for the telescopes about $16m per year is spent on construction. So $4m per annum for one 8m telescope and $5.5m running cost for one 10m telescope. Let’s assume these numbers are typical for one 8m class telescope. There are 16 telescopes of 6.5m diameter of larger, assuming all these have a $9.5m annual cost and ignoring other telescopes, that comes to $150m spent annually on large telescopes. Six percent of that time is taken away by the Moon at a total annual cost of $9m.

So that’s a very rough number for the annual cost to astronomy of the Moon. This was just for fun so I don’t expect it to be correct to the last cent but hopefully to an order of magnitude. Any better estimates are welcome in the comments section.

* Yes I know infrared observations are more likely to be scheduled during bright time.

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