## Counting Stars

Looking in all directions, how many stars are there brighter than a particular visual magnitude? Here’s an empirical formula that gives an approximation. It can be used over the range mv = +4.0 to +25.0.

$\textup{S} = 10^{-0.0003\,\textup{m}^{3} + 0.0019\,\textup{m}^{2} + 0.484\,\textup{m} + 0.795}$

where S is the approximate number of stars brighter than apparent visual magnitude m in the entire sky

Apparent Visual Magnitude# of Stars
4.0552
4.1618
4.2690
4.3772
4.4863
4.5964
4.61,077
4.71,204
4.81,345
4.91,503
5.01,679
5.11,875
5.22,094
5.32,338
5.42,611
5.52,914
5.63,253
5.73,631
5.84,051
5.94,520
6.05,042
6.15,623
6.26,271
6.36,992
6.47,794
6.58,687
6.69,681
6.710,786
6.812,015
6.913,382
7.014,900
7.116,588
7.218,464
7.320,547
7.422,860
7.525,428
7.628,278
7.731,441
7.834,949
7.938,839
8.043,152
8.147,932
8.253,229
8.359,096
8.465,592
8.572,784
8.680,743
8.789,549
8.899,287
8.9110,055
9.0121,955
9.1135,104
9.2149,627
9.3165,662
9.4183,362
9.5202,891
9.6224,431
9.7248,181
9.8274,358
9.9303,200
10.0334,965
10.1369,938
10.2408,426
10.3450,768
10.4497,330
10.5548,514
10.6604,755
10.7666,528
10.8734,349
10.9808,780
11.0890,430
11.1979,963
11.21,078,096
11.31,185,610
11.41,303,349
11.51,432,229
11.61,573,241
11.71,727,456
11.81,896,035
11.92,080,230
12.02,281,392
12.12,500,983
12.22,740,574
12.33,001,863
12.43,286,675
12.53,596,976
12.63,934,877
12.74,302,651
12.84,702,734
12.95,137,742
13.05,610,480
13.16,123,951
13.26,681,371
13.37,286,180
13.47,942,053
13.58,652,916
13.69,422,957
13.710,256,640
13.811,158,721
13.912,134,260
14.013,188,640
14.114,327,575
14.215,557,134
14.316,883,749
14.418,314,236
14.519,855,805
14.621,516,082
14.723,303,122
14.825,225,420
14.927,291,933
15.029,512,092
15.131,895,815
15.234,453,520
15.337,196,142
15.440,135,142
15.543,282,516
15.646,650,811
15.750,253,128
15.854,103,131
15.958,215,053
16.062,603,700
16.167,284,449
16.272,273,253
16.377,586,632
16.483,241,673
16.589,256,016
16.695,647,847
16.7102,435,879
16.8109,639,337
16.9117,277,932
17.0125,371,840
17.1133,941,667
17.2143,008,417
17.3152,593,453
17.4162,718,451
17.5173,405,353
17.6184,676,315
17.7196,553,644
17.8209,059,737
17.9222,217,010
18.0236,047,823
18.1250,574,401
18.2265,818,743
18.3281,802,538
18.4298,547,061
18.5316,073,074
18.6334,400,717
18.7353,549,396
18.8373,537,665
18.9394,383,103
19.0416,102,189
19.1438,710,168
19.2462,220,923
19.3486,646,831
19.4511,998,631
19.5538,285,275
19.6565,513,790
19.7593,689,134
19.8622,814,048
19.9652,888,922
20.0683,911,647
20.1715,877,479
20.2748,778,904
20.3782,605,508
20.4817,343,852
20.5852,977,352
20.6889,486,170
20.7926,847,110
20.8965,033,523
20.91,004,015,228
21.01,043,758,439
21.11,084,225,707
21.21,125,375,873
21.31,167,164,044
21.41,209,541,573
21.51,252,456,065
21.61,295,851,393
21.71,339,667,742
21.81,383,841,658
21.91,428,306,130
22.01,472,990,684
22.11,517,821,499
22.21,562,721,546
22.31,607,610,744
22.41,652,406,140
22.51,697,022,107
22.61,741,370,568
22.71,785,361,232
22.81,828,901,853
22.91,871,898,516
23.01,914,255,925
23.11,955,877,722
23.21,996,666,815
23.32,036,525,723
23.42,075,356,932
23.52,113,063,265
23.62,149,548,260
23.72,184,716,557
23.82,218,474,290
23.92,250,729,483
24.02,281,392,450
24.12,310,376,189
24.22,337,596,778
24.32,362,973,766
24.42,386,430,550
24.52,407,894,751
24.62,427,298,570
24.72,444,579,131
24.82,459,678,812
24.92,472,545,544
25.02,483,133,105

How many stars are there in our Milky Way galaxy? Between 100 and 400 billion stars. Many stars are not very luminous, and can only be seen in the immediate solar neighborhood. That is one source of uncertainty.

How many galaxies are there in the observable universe? Something like two trillion (2 × 1012).

How many stars are in the observable universe? Something like a septillion (1024). A trillion trillion!

And, just so you know, our universe is probably much larger than the volume that we can observe.

How does the Universe love thee? Let us count the stars…

References

“How many stars are in the sky?”, Space Math, NASA Goddard Space Flight Center, accessed February 29, 2020, https://spacemath.gsfc.nasa.gov/weekly/6Page103.pdf.

Wikipedia contributors, “Galaxy,” Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/w/index.php?title=Galaxy&oldid=942479372 (accessed February 29, 2020).

Wikipedia contributors, “Milky Way,” Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/w/index.php?title=Milky_Way&oldid=942977760 (accessed February 29, 2020).

## Marfa Lights

Yes, I’ve seen the Marfa lights. Bernie Zelazny and I were coming back from doing a star party for a culinary group at El Cosmico in Marfa on April 7, 2011 when we decided to stop at the Marfa lights viewing station just off of US 67/90. For the first couple of minutes (Thursday evening around 11:00 p.m. or so) we saw nothing, but then, sure enough, a slowly moving white light appeared near a small tower with red lights, providing a good point of reference for the motion. The light gradually changed brightness, sometimes brighter, sometimes dimmer, moving left to right, then disappeared. Soon, another would appear: sometimes higher, sometimes lower, usually moving to the right, but sometimes to left. My first thought: distant headlights. Sometimes, more that one could be seen at the same time.

Quickly, I ran back to my car to get the 15 x 70 binoculars and binocular mount (an Orion Paragon Plus) and set them up to view the Marfa lights, which by now were happening frequently. When viewing each Marfa light through these powerful binoculars, the first thing I noticed is that I was not able to focus! No matter how I changed the focus of the binoculars, I could do no better than to see a round amorphous blob of light.

Next, I decided to see if any of the fixed distant lights would focus. First the red tower lights. Nope, red blobs. Then a distant ranch light to the left of the light dome of Ojinaga/Presidio. Nope, a while blob. Then, another distant ranch light. Another white blob. Then some distant headlights on US 67/90 near Marfa heading toward Alpine. The headlights were too far away to resolve, and in the binoculars they, too, were an unresolvable white blob. Next I moved the binoculars up a few degrees to look at some stars. Perfect focus! Back down to the ground lights and Marfa lights: out of focus blobs!

So, it appears to me that some atmospheric phenomenon is defocusing and distorting terrestrial lights in the distance. Perhaps some sort of superior mirage. I think the most likely explanation for the Marfa lights is distant vehicle headlights.

Next steps in the investigation of this curious phenomenon: Use a micrometer eyepiece in a low-power rich-field telescope to measure the angular sizes of the Marfa light blobs, as well as the angular sizes of the blobs from identifiable terrestrial lights. Determine the distance to the terrestrial light sources in the daytime (if possible) using triangulation. Better yet, determine the great circle distance to each terrestrial light source by obtaining GPS coordinates of each of those light sources, and the Marfa lights viewing station. Even better would be to shine a mobile light source at the Marfa lights viewing station from various GPS-determined locations at different distances on an evening when the Marfa lights are visible. Determine if the size of each known light blob is a function of distance. Using this information, estimate the distance to the Marfa light sources.

Also, note whether the angular size of each Marfa light is related to its altitude above the horizon.

More ideas: Take a series of 30-second digital camera exposures over the course of an evening to determine if the Marfa lights take preferred paths. The results might support or refute the vehicle headlights hypothesis. Determine if the Marfa lights paths change from night to night or during the course of one night.

Finally, I’d suggest using the same kind of wide-field spectroscopic equipment used to obtain meteor spectra to determine the spectral characteristics of the Marfa lights. This would tell us much about their chemical composition, temperature, and origin.

## Forever Stamps

The United States Postal Service has issued a number of enticing forever stamps in recent years, and I’ve begun accumulating stamps faster than I use them. Sound familiar? If so, why not use them for extra postage items—even if you end up spending a little more than is required.

The current value of a forever stamp is 55¢. If you have a postal scale at home to weigh the envelopes you want to post, this handy guide will show you how many forever stamps to use for envelopes of different sizes and weights. (Mail within the U.S. only)

##### Standard Envelopes (≤11.5″ long, ≤6.125″ high, ≤0.25″ thick)
• 0 to 1 ounce: 1 forever stamp
• 1 to 4 ounces: 2 forever stamps
• 4 to 8 ounces: 3 forever stamps
##### Large Envelopes(11.5-15″ L, 6.125-12″ H, or 0.25-0.75″ T)
• 0 to 1 ounce: 2 forever stamps
• 1 to 4 ounces: 3 forever stamps
• 4 to 7 ounces: 4 forever stamps
• 7 to 9 ounces: 5 forever stamps
• 9 to 12 ounces: 6 forever stamps
• 12 to 15 ounces: 7 forever stamps

If you are mailing a standard envelope that has one or more of the characteristics in DMM 101.1.2, add an ounce to the measured weight to cover the non-machinable surcharge.

If you are mailing a large envelope that is rigid, is non-rectangular, or is not uniformly thick, then take your envelope to the post office to mail because you will have to pay parcel prices.