Geminid Meteor Shower 13th December 2022

Two weeks ago we had the Geminid meteor shower which peaked over the night of the 13th/14th December. The moon on this date was waning gibbous and about 3 days from last quarter. It rose about 20:44 UT and so would interfere with observations after this time. Nevertheless, this is now the best meteor shower of the year and so I decided to see if I could capture any events on my camera.

I am glad to say that I was quite successful in spite of the moon. In all I caught 6 meteors on camera in the period 22:00 UT (approximately) to 23:17 UT. I had a few problems to begin with and it took me a while to settle on a successful method. After 22:18 I had the correct date and time (UT to the nearest second) recorded in my camera (prior to this I still had the year as 2021! and the time was out by a few minutes). At 22:27 I settled on taking successive 15 second exposures at ISO1600. I was using a D90 camera with a 18-105mm lens set at 18mm. This gave me a field of view of about 66x46 degrees. I made a note of the frame numbers where I had seen a meteor which was in or near the part of the sky where the camera was pointing.

I noted that I had seen 10 meteors in all. Initially I was pointing the camera south and then later I pointed it east. The first meteor I detected was this one at 22:18 UT.

This was a 30s rather than a 15s exposure. If you click on the image you will see an enlarged version. The meteor crosses the boundary between Orion and Taurus near pi 1 Orionis. The Hyades, Mars and the Pleiades can be seen clearly above the short trail of the meteor.

The second meteor that was recorded was at 22:42.

This one is more difficult to see but it is found just above the cloud to the right of Orion. This meteor lies entirely in the constellation of Eridanus near 47 Eridani.

The third Geminid was the best of the night and recorded at 22:45 UT.

This was a bright meteor and as bright as Mars which was nearby and magnitude -1.8. It also had a similar yellowish orange colour. The trail starts in Taurus (passing 5 Tauri) and ends in Cetus crossing a little bit of Aries. A couple of things to note: 1) there is a bit of ghostly train left behind the trail where the meteor has passed and 2) the trail is wiggly in structure near the start. This latter point may have been caused by camera shake as the meteor appeared very shortly after I pressed the camera shutter. However, Mars is just as bright and there is no camera shake noticeable in its image.

The third meteor I detected was at 22:54 UT.

This was a noticeable meteor and can be seen just above the figure of Orion the hunter. The trail of this meteor starts in Orion but then crosses into part of Taurus (it ends between 131 and 133 Tauri).

The next meteor to be captured was at 23:08 UT. By this time I had moved the camera to look eastwards.

This one is very faint and difficult to see. The short trail appears in the constellation of Cepheus not far from the triangle of stars made by delta, epsilon and zeta.

The final capture was at 23:12 UT.

This meteor is in virtually the same part of the sky as the previous one but, perhaps, a bit brighter. It passes between 18 and 19 Cephei.

All text and images © Duncan Hale-Sutton 2022

RW Cephei 12th and 24th December 2022

I decided to have a go at observing a different variable star this month and that is RW Cephei. The star is located near the triangle of stars made by zeta, delta and epsilon Cephei (the "foot" at the base of the constellation's main rhombus of stars). RW is a red hypergiant whose apparent brightness ranges between 6.0 and 7.6 over a period of about 346 days. It is classified as a semi-regular SRd type. Earlier this month this star has become the focus of attention because it may be going through a period of exceptional dimming as did Betelgeuse in Orion in January 2020.

I had a look at this star on Monday the 12th December 2022 in the early evening. At this time the moon was 4 days past full and not due to rise until 19:32 UT. At 18:30 the sky was clear and dark and astronomical twilight had just ended.

At 18:32 UT RW was fainter than star E (=7.3 mag.) on chart 312.02. At 18:50 UT I thought it was marginally brighter than star H (=7.8 mag.) and my estimate was E(2)V(1)H or magnitude 7.6 (to 1 d.p.).

I had another go at this star a few days ago on Christmas Eve (24th December). Then it was just one day past new moon and again the sky was clear and dark but there may have been a slight mist.

At 18:45 UT RW was again fainter than star E (=7.3 mag.) but this time it was closer brightness to this star than star H (=7.8 mag.). My estimate at 18:55 UT was that it was E(1)V(2)H or magnitude 7.5. So not much different to 12 days ago.

I don't have much to compare my results to as there hasn't been any further data added to the BAA VSS database by other observers since the 10th December, though one BAA VSS member did say that he had measured it to be visual magnitude 7.7 on the 21st December (via baavss-alert).

All text and images © Duncan Hale-Sutton 2022

CH Cygni 25th November 2022

We again had some clear weather last Friday the 25th November. The moon was 2 days past new and not a problem. I went out to observe the variable star CH Cygni. At 18.29 UT I discerned that CH was a bit brighter than star A (=6.5mag.) on BAA chart 089.04 but much fainter than star L (=5.7 mag.). My estimate was L(3)V(1)A which made it magnitude 6.3.

I think this result was right and that CH was the brighter side of star A, however, observations on the 23rd and 24th of November put this star at magnitude 6.7 and 6.9 which is much fainter. I am not worried by this because I am pretty sure of what I saw.

All text and images © Duncan Hale-Sutton 2022

TX and AH Dra 23rd November 2022

It looked like we were going to get a good dark sky last Wednesday, the 23rd November, but it didn't last. It was new moon and I went out early evening to observe the variable stars TX and AH Draconis. I planned to get estimates for the brightness of these two stars, go indoors and then come out again later to look at some other stars but it clouded up.

I was using the new version of the BAA star chart (106.04) and at 18.20 UT I found that TX was brighter than star K (=7.0 mag.) but fainter than star N (=7.7 mag.) but not by much. My estimate was K(2)V(1)N which put it at magnitude 7.5.

Going on to AH at 18.28 UT I found that it was about midway in brightness between star 6 (=7.8 mag.) and star 8 (=8.4 mag.) making it 6(1)V(1)8 or magnitude 8.1.

All text and images © Duncan Hale-Sutton 2022

Derivation of the obscuration percentage during a partial eclipse

After the partial solar eclipse on the 25th October I came up with a formula for how to calculate the percentage area of the sun that is covered by the moon (the percentage obscuration). I now want to show how I derived this formula.

I have assumed that the sun and the moon have the same apparent diameter during an eclipse. This won't necessarily be true but will be a reasonable approximation. So in the above diagram we will assume the moon is the circle to the left and the sun to the right. Where the two circles intersect represents the area where the moon eclipses the sun. If we can calculate the area of the sun to the left of the chord AB then the area of the intersection of the two circles is just twice this by symmetry.

Firstly, as ADC is a right-angled triangle we have that AD/AC is sin t. Let AC be the radius r and let AD be x. So (x/r) = sin t. If the chord length AB is l then l = 2x.

We can see that the area of the sun to the left of the chord AB is the area of the sector of the circle AEBC (the piece of cake) minus the area of the isosceles triangle ABC. The ratio of the angle 2t to the angle 2pi (pi being the constant 3.14...) is the same ratio as the area of the sector to the area of the circle (t being measured in radians). Thus the area of the sector is tr^2 (where r^2 represents r squared).

The area of the triangle ABC is half the base AB times the height DC. Half AB is x and DC is rcos t, so the area of the triangle is xrcos t. So the area of the sun to the left of the chord AB is tr^2 - xrcos t and the area of the intersection of the two circles is 2(tr^2 - xrcos t).

We can now calculate the obscuration fraction as the ratio of this intersection area to the area of the sun. We can see this is (2/pi)(t - (x/r)cos t). But (x/r) = sin t, so the obscuration fraction is (2/pi)(t - sin t cos t). But sin t cos t = (1/2)sin 2t. So the obscuration fraction becomes (1/pi)(2t - sin 2t). If we let 2t = w, then the obscuration fraction is (1/pi)(w - sin w) or as a percentage (100/pi)(w - sin w) as we stated before. Note that to find w we use that w = 2t = 2arcsin (x/r). But x = l/2 and r = d/2 where d is the diameter of the sun. So w = 2arcsin (l/d). Thus measurements of the chord l and diameter d give the angle w and hence the obscuration.

There is another measure of the depth of the partial eclipse and that is the magnitude. This is the fraction of the sun's diameter that is occulted by the moon. In the above diagram you can see that the portion of the diameter of the sun that is covered by the moon is twice the distance ED. Now ED is EC - DC which is r - rcos t = r(1 - cos t). So twice ED is 2r(1 - cos t) and so the magnitude is just (1 - cos t) which in terms of w is (1 - cos (w/2)). By convention the magnitude is usually quoted at maximum eclipse.

 

I now want to consider the more complicated obscuration calculation when the moon and the sun are not the same apparent diameter on the sky. The above figure shows the exaggerated situation. We again assume that the disc on the left is the moon and that on the right is the sun. It can be seen that the obscured area of the sun AEBF consists of two 'lens' shaped areas either side of the chord AB. We have already calculated the first AEBD. This is (r^2/2)(w - sin w) with w = 2arcsin (l/d). By a similar argument the lens shaped area AFBD is given by (R^2/2)(W - sin W) where W = 2arcsin(l/D) (D=2R). So the total area eclipsed is (1/2)(r^2(w - sin w) + R^2(W - sin W)) and as a percentage of the area of the sun this is (50/pi)(w - sin w + (D/d)^2(W - sin W)). Here W = 2arcsin((d/D)(l/d)).

All text and images © Duncan Hale-Sutton 2022

TX and AH Dra, CH Cyg, Z and RY UMa on the 30th October 2022

We had some more clear weather here on Sunday the 30th October. The moon was nearly at first quarter but it would set at 20:04 UT. The sky transparency wasn't great but I decided to go ahead with my observations anyway. The constellation of Draco was in the west but still high enough in the sky to make estimates of the semiregular (Srb) variables TX and AH Dra.

Beginning with TX on chart 106.03 with my 7x50 binoculars I could make out star P at visual magnitude 8.4. TX was fainter than star K (=7.0 mag.) and star N (=7.7 mag.) but brighter than P. At 21:16 UT I saw that TX was much closer to N in brightness than star P, so I estimated it at 1 point from N and 3 points from P (i.e. N(1)V(3)P). This put it at magnitude 7.9 to 1 decimal place.

I then moved on to AH Dra which is south of TX. At 21:40 AH was fainter than star 1 (=7.1 mag.) but brighter than star 8 (=8.4 mag). In fact it was probably middle way between these two stars and this was confirmed by comparison with star 6 (=7.8 mag.). So my estimate was 1(1)V(1)8 which made AH visual magnitude 7.8 to 1 d.p.

Whilst I have been writing up this observing session I have noticed that there is a new chart for TX and AH Draconis. Chart 106.03 has now been redrawn and is now 106.04. The only difference that I could spot was that the star labelled 1 is now magnitude 7.0 rather than 7.1. I will use the new chart in my next session.

Cygnus was also reasonably well placed so my next target was the ZAND+SR variable star CH Cyg. This was easy to estimate as its brightness indistinguishable from star A and was thus magnitude 6.5.

Finally, the constellation of Ursa Major is beginning to rise again about 11pm having swung round under the pole, so I could have a go at Z and RY UMa. At 22:34 UT Z UMa was brighter than star D (=7.9 mag.) but was equal to B meaning that my estimate was magnitude 7.3. At 22:43 UT RY UMa was fainter than star 1 (=6.7 mag.) but was brighter than star 4 (=7.7 mag.). In fact its brightness was indistinguishable from star 2 which made it magnitude 7.4.

All text and images © Duncan Hale-Sutton 2022

Partial Solar Eclipse 25th October 2022

We had a partial eclipse of the sun on Tuesday 25th October. From our location near Norwich first contact with the moon was to begin at 10:07, maximum coverage was to occur at 11:00 and last contact at 11:55 (all times BST). I had a flu jab appointment at 11am and so I didn't have much time to set anything up. In the end I decided to use my 8x24 binoculars to project the image (twice!) onto a sheet of white paper. The first image I took was at 10:39 and the last at 10:47. The best of them was this image at 10:45 (15 mins before maximum):-

I quite like the fact that this looks like two eyes looking down. Looking at this image I think that the "bite" taken out of the sun is much less than 25% of the total area of the disk. To see this imagine dividing the sun into four equal quarters of cake. The bite can be seen to roughly sit in one of those quarters but it by no means covers the whole quarter. However, I do reckon that the bite covers more than half of that 25% (i.e. more than 12.5%). So perhaps 15 or 16%. I must try and calculate it. London was predicted to be 15.2% at max.

I have now (18th November 2022) done some work on calculating the obscuration (the percentage area of the sun that is covered by the moon as it is called). Have a look at this diagram below:-

The shaded area represents the area of the sun that is eclipsed by the moon. I have assumed that the moon and the sun appear to be the same angular diameter on the sky. I have found that the percentage obscuration is given by 100 (w - sin w) / pi where the angle w is in radians. To find w you need two measurements; the length of the chord PP' (which we can call l) and the diameter of the sun (which we call d). Then w = 2 arcsin (l/d). 

In the above picture of the eclipse I chose the left-hand projected image which was more well defined and circular and measured l to be 209 pixels and d to be 311 pixels. This gave the obscuration to be 15.2%. But I think this is a coincidence that it is close to the London value!

All text and images © Duncan Hale-Sutton 2022