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There are two approaches, one potentially of zero additional cost.
If you are going to be using a colour camera, a typical DSLR for instance, it already comes with a set of three filters — one each for red, green and blue. None of these are standard photometric filters but it is possible to make usefully accurate estimates of what the intensity would have been in standard bands such as Johnson-V. The process takes far too many words to explain here but comprehensive instructions are available on-line. I don’t have URLs immediately to hand but can dig out the references later if you want them (and if you haven’t found them independently).
If you have a mono camera and/or wish to purchase a filter to begin your research-quality observation program, I would recommend buying a Johnson-V filter. They are available from a number of suppliers but please be careful to buy a Johnson-V photometric filter. Supplier’s product listings can be confusing at times.
In the case of DSLR (and other colour) cameras, always download your images in RAW format. Conversion to JPG or whatever will destroy the accuracy of your data. If you are using a filter as well, post-process the images first to separate out the RGB components and then sum or average (not median) combine them to produce a grey-scale image for subsequent analysis.
If you have a colour camera then I would personally use it as-is to learn the basics of the trade before spending more money. But, then, I’m a cheapskate. You are going to have to educate yourself anyway …
It’s not the size that is important, it’s how you use it.
You can do accurate photometry with telescopes of almost any aperture. The only thing that increased aperture buys you is a fainter limiting magnitude for a given exposure time.
People do precision photometry with nothing more than a DSLR and a standard lens. It is rare for the aperture of such a system to exceed 50mm, or half that of your telescope.
sim is the LaTeX markup for the ~character. Likewise % for %, because % has a mark-up meaning in LaTeX.
It happens. Several times to me in my career as a sysadmin. Thankfully you know the golden rule: always have a backup available for when (not if) things go pear shaped, as they will do occasionally.
Thanks for all your hard work.
“this morning at about 14.25 BST.”
I hope you mean 04:25 BST, or dawn comes remarkably late where you live 😉
I am not too sure how you “polynomial fit to the radial distortion in the lens”. Is it a one-off calibration done back in the distant past by, say, imaging a sheet of graph paper?
Alternatively, do you apply a rough calibration then iterate (plate-solve, polynomial-fit) until convergence?
Further, is the calibration polynomial assumed to depend only on the radial coordinate? If so, have you considered a full (x,y) polynomial fit? The distortion *should* be angle-independent but if you haven’t located the coordinates of the centre pixel (centre of the lens, not the centre of the detector) accurately enough you are likely to have problems.
No chance of me observing it yet, put I’ve put out a call for help. Let’s see what happens, if anything.
I now have software which measures everything it can find in an image and records all those data which have a formal error better than 0.15 magnitudes (which corresponds to a SNR ~7) in a SQL database, along with other meta-data such as the sequence used and relevant excerpts from Gaia-DR2. I will be able to report cases as discussed above to the BAA photometry database if given permission to do so.
I can do rather more too. An article may be written for a forthcoming VSSC. The software will be made freely available on my web site in due course. Whether access to the database will also become forthcoming depends on a number of matters which include security, bandwidth and storage capacity.
APT has a variety of sky background models. You might find one that works well in this situation.
APT is the workhorse of my photometry though I’ve never used it where the “sky” varies that much on such a small scale. It appears to work fine where the background gradient is relatively small, such as variables in M31 and M33.
Otherwise I would suggest PSF-fitting photometry such as IRAF/DAOPHOT. Again I’ve never used it in such extreme circumstances but the documentation has reassuring words about what to do where a star is positioned within nebulosity. Be warned: this package has a steep learning curve and is generally labour intensive.
I could well have an old PC with installed // port in my collection of antiques. If so, and it meets other hardware requirements, you can have it for the price of shipping — free if you are willing and able to collect.
Contact me by email if you’re interested.
(Added in edit: A very quick rummage in the loft unearthed a Pentium-II system. Unfortunately it doesn’t have a PSU but I may be able to find one. Alternatively, perhaps just the motherboard may be sufficient and you could use the rest of your old kit to complete the system.
BTW, how did your old system die? It may well be reparable with components from my parts collection.)
I can’t help but think of the following …
Arthur: I am your king!
Dennis’ Mother: Well I didn’t vote for you.
Arthur: You don’t vote for kings!
Dennis’ Mother: How’d you become king, then?
Arthur: The Lady of the Lake, [Angel chorus begins singing in background] her arm clad in the purest shimmering samite, held aloft Excalibur from the bosom of the water signifying by Divine Providence that I, Arthur, was to carry Excalibur. [Angel chorus ends] That is why I am your king!
Dennis: Listen. Strange women lying in ponds distributing swords is no basis for a system of government. Supreme executive power derives from a mandate from the masses, not from some farcical aquatic ceremony.
Arthur: Be quiet!
Dennis: You can’t expect to wield supreme power just ’cause some watery tart threw a sword at you!
Arthur: Shut up!
Dennis: I mean, if I went ’round saying I was an emperor just because some moistened bint had lobbed a scimitar at me, they’d put me away!
Arthur: Shut up! Will you shut up?! [Grabs Dennis and shakes him]
Dennis: Ah, now we see the violence inherent in the system!
Arthur: Shut up!
Dennis: Oh! Come and see the violence inherent in the system! Help! Help! I’m being repressed!According to http://convertalot.com/asteroid_impact_calculator.html the energy yield of that impact, with an assumed relative density of 3 (about that of a stony asteroid) is 75 megatons TNT which will dig a crater a kilometre in diameter and a quarter of that in depth. The calculator assumes a terrestrial impact. The lower gravity on the moon ensures that somewhat more (but not a lot more, because mass is proportional to the cube of the size of the excavated material) excavation can be performed at the same energy cost.
I do not know the depth to which it would penetrate before exploding, partly because it depends on the structural strength of both the impacting body and the lunar regolith, but note that until the asteroid hits something it travels its own diameter in 5 milliseconds, so perhaps 500m might be a reasonable guess, a distance which requires a travel time of well under a tenth of a second.
See https://en.wikipedia.org/wiki/Aperture_Photometry_Tool for an introduction and a download link.
You are quite correct in that a larger circular aperture can be used. Unfortunately that will include a larger amount of sky and increases the likelihood that the sky annulus will itself contain stars as you indicate.
Elliptical apertures really come into their own when measuring galaxies but there is nothing to stop one exploiting that feature in other circumstances.
The best way of doing photometry, in my view, is to use PSF fitting as implemented in DAOPHOT because then one is fairly sure that you are measuring only the absolute minimum of sky and that stars within the sky annulus are properly accounted for. Unfortunately the only code I have yet found is labour-intensive and very hard to script for reliable use.
Here is another version. Nowhere near as good as yours, not least because the limb was drifting out of the FOV, but I find it really quite remarkable because it was taken with an iPhone pointed at a 25mm eyepiece of a 25cm aperture 1200cm FL undriven reflector. Took two people acting in concert, a friend holding his phone to the eyepiece and taking the exposure and me driving the focus on the phone when the camera was pointing in the right direction. It’s sufficiently encouraging that perhaps I’ll get a proper phone holding gizmo.
That is excellent data, thank you! Just what I was looking for.
I recognize the difficulty of extrapolation but for present purposes any number which is good to within a factor of two is easily precise enough. For instance, 10s for mag 11 tells me that 30s should give about mag 12 because a factor of 3 in flux collection is close enough to the 2.5 times lower flux from a target one magnitude fainter. The precision value you quote is also encouraging. I chose 0.1mag as an upper limit because that corresponds to the best which can be reasonably expected without a camera.
Last night an interesting observation of the moon with an iPhone and eyepiece projection suggests that using the 25cm Dob with the DSLR at prime focus might be feasible. It might not be, but it is certainly worth trying.
BTW, have you come across Russ Laher’s Aperture Photometry Tool (APT)? It runs on any OS with Java installed and can told to use elliptical apertures — just the thing for poorly tracked images.
