From the Director

Rex

 

 

 

by Rex Parker, Phd director@princetonastronomy.org

Zoom AAAP Meetings for May 12 and June 09.
We hope that you are well and keeping your sense of humor and perspective despite the social and personal challenges of COVID. As you know, club meetings at Peyton Hall and Observatory activities at Washington Crossing Park remain suspended. While we see some positive signs, it is not clear when we will get back to gathering for meetings. So in response, we’re making plans to bring the May 12 and June 09 AAAP meetings to members on-line using the well-established Zoom platform. The Board reviewed available options and concluded that Zoom is the best choice for our next 2 meetings, based on wide-spread acceptance and familiarity, and functionality for groups our size.

For the May 12 meeting we will have a guest speaker, and structure the meeting more or less the same as we do in Peyton Hall. After the talk we’ll hold a members business meeting. So we’ll ask for your patience as well as participation in this experiment, and hope we all become more adept amateur astronomers through the experience. See Ira’s Program Chair section (below) for speaker information and for the Zoom details, and stay tuned for e-mails with more about using Zoom for these meetings. If you haven’t yet used Zoom and would like a pilot run ahead of the meeting, we can offer a practice session before May 12 – stay tuned for emails about this.

Officer Elections – Voting Link.
In order to conduct elections of officers in May, consistent with the by-laws, we sent a link to a specific survey on-line where you can vote on the slate of officers Results will be discussed at the May 12 meeting. If you haven’t yet voted please do so by going to this secure link.

Capital Expenditure Recommendation for Observatory Columns Repair.
The Board recommends the expenditure of up to $9500 for observatory columns (pedestals) repair.  The proposal will be discussed at the May 12 meeting and voted on at the June 09 meeting, each conducted by Zoom.  Our current Treasury balance is sufficient to absorb this amount;  as of March 31 the Treasury balance was slightly over $15,000.  Of course it will be wise for us to raise money in the near future to offset this expense.  I’d like to ask all members to give some thought on ways to generate additional funds .  One example is to donate to the club and apply for a matching gift, if your company or organization has a charitable donation program. We are a tax-exempt 501c3 organization.

The background on this proposal is that the concrete block pedestals that support the roll-off roof of the AAAP-owned observatory at Washington Crossing State Park are in need of serious repair, due to substantial deterioration of the mortar and blocks over time. We have concluded that prompt action is prudent. Options were reviewed by the Board and a few members with engineering and construction expertise over the last half-year, and these were discussed in previous business meetings. We recently obtained cost estimates from professional contractors. The best proposal, from CWC Masonry LLC, of Trenton NJ, is to completely rebuild four pedestals (demolishing and removing the old) on the existing concrete footers which are in good shape. The cost estimate is $8500; the request to authorize up to $9500 helps provide for unexpected issues during construction.

The Bylaws stipulate: … expenditure in excess of $1000 must be recommended by the Board of Trustees and the recommendation must be published in AAAP’s monthly newsletter together with the meeting date on which the expenditure will be voted. The expenditure must then be approved by a majority of the votes cast and not less than 30% of the paid membership. Members not attending the meeting may vote by mailed or e-mailed ballot provided that their ballot is received by the Secretary within 40 days of the meeting.

Next steps:

  • Discuss expenditure proposal at May 12 meeting (Zoom)
  • Members vote on expenditure authorization at June 09 meeting (Zoom)
  • Obtain Park administrative approval (pending)
  • Schedule contractor, execute job, and pay for the work

The Domain of the Amateur Astronomer.
The domain of the amateur sometimes overlaps with the professional. Such was the case with a fascinating Nature Astronomy report which made the mainstream media last week. Two amateur astronomers made the novel discovery of an unusual “teardrop” shaped star. The amateurs carefully analyzed data emerging from NASA’s Transiting Exoplanet Survey Satellite (TESS) and communicated their initial findings to astronomers at MIT and UT-Austin (reference – Handler, Kurtz, Rappaport, et al., Nat Astron, Mar 9 2020). The TESS data revealed unexpected brightness variations of a pulsating variable star named HD74423. The interpretation is that the star attained its ovoid shape due to gravity of a companion red dwarf star with a rapid orbital period, 2 days. The surprise was the dependence of brightness variation on exactly when the observation was made. Tidal forces in the system shift the orientation of the pulsation axis so that the main star forms a teardrop shape in synchrony with the binary orbital period. In their words, “the pulsation mode amplitude is strongly modulated at the orbital frequency; this is the first time that oblique pulsation along a tidal axis has been recognized”. But not the first time that an amateur astronomer contribution has been recognized.

We’re all waiting for the club’s Observatory to reopen. Meanwhile, hopefully you’re getting outside in your yard at home and observing using your own personal telescope. In many ways this is the most essential domain of the amateur astronomer. And here in central NJ we’ve been fortunate to get a few clear nights between spring rainstorms. Below, I offer a few images taken with my own amateur equipment, showing some of the magnificent Messier objects well-positioned now for observing in the early evening. I hope you can get outside to take in some of the views in your own telescope.

Messier 94, sometimes called the “Cat’s Eye Galaxy”, in the constellation Canes Venatici. Astrophoto by Rex Parker from home observatory in Titusville NJ; 12.5 inch telescope with ZWO CMOS camera.
Astrophoto by Rex Parker from home observatory in Titusville NJ; 12.5 inch telescope with ZWO CMOS camera.

Elliptical galaxies Messier 105 and NGC 3384, and spiral galaxy NGC 3389 in the constellation Leo. Astrophoto by Rex Parker from home observatory in Titusville NJ; 12.5 inch telescope with ZWO CMOS camera.

Messier 3, globular cluster in in the constellation Canes Venatici. Astrophoto by Rex Parker from home observatory in Titusville NJ; 12.5 inch telescope with ZWO CMOS camera.

Posted in May 2020, Sidereal Times | Tagged , | Leave a comment

From the Program Chair

by Ira Polans, Program Chair

Monthly Meetings Resume–Virtually

Club Members,

As we, all practice safe social distancing; AAAP is resuming its meetings on Tuesday, May 12 at 7:30 PM using Zoom. (See below for more details).

Please read or print this email as there is a lot of information to review. Most of your questions are answered in this email.

Featured Speaker: Club member Bob Vanderbei is the May speaker and will give a talk on Astro Dynamics. Bob, like most avid astrophotographers, has already taken pictures of all of the interesting stars, nebulae, and galaxies visible in the northern night sky. So, a natural question is: What’s next? One common answer is to take much, much longer exposures to capture interesting faint stuff that wasn’t visible in one’s earlier images of the same target. Another common answer is to go (either physically or virtually) to somewhere in the southern hemisphere where there’s a bunch of cool stuff astro stuff that we can’t see up here in the north. A third answer, which is the one he likes the best, is to revisit objects we’ve already imaged and see if anything has changed. Sometimes things do change. With that in mind, Bob will discuss changes he’s seen and will talk about supernovae, variable stars, the Crab Nebula, the Dumbbell Nebula, and of course Betelgeuse. The image comparisons are surprising and the stories are interesting.

Members are welcome to invite friends and acquaintances by forwarding the link (contained at the end of this email). However, please be aware that we arelimited to 100 participants. Therefore, share your screen rather sharing the link whenever possible.

How to Join the May Meeting: For the meeting, we are going to follow a simple two-step process:

  1. At the end of this email is the information you need to join Tuesday’s meeting. You are welcome to share the link with friends and family. However, we are limited to 100 participants (connections).
  2. The night of the meeting just click on the link in the email and you will be taken to the meeting. You do not need a Zoom account or create one to join the meeting. Nor are you required to use a webcam. We will open the meeting at 7:10 so you have plenty of time to join.

NOTE: If you click on the meeting link and it doesn’t work, simply copy and paste it into your browser.

More Information on Zoom: The Zoom site has many training videos most are for people who are hosting a meeting. If you’re unsure how Zoom works you might want to view the videos on how to join a meeting or how to check your computer’s audio and video before the meeting.

Meeting Agenda

7:10 PM  Meeting Room Opens NOTE: You will not be able to join until the host opens the meeting room.

7:30 PM  Meeting Starts

Opening Remarks (Rex)

Speaker Introduction (Ira)

Featured Presentation (Bob Vanderbei)

Q&A (About 10-15 minutes)

Business Meeting

 

Virtual Meeting Procedures

  1. For this meeting AAAP is not monitoring chat.
  2. During our trial run, we found that being near your router improves performance. This is not a requirement to join the meeting.
  3. Please do not share your screen during the meeting
  4. Once the meeting room opens you may use the chat feature (if you know how to do this already) and your audio will be on. After the Introduction we will mute all participants and disable self-unmuting. You may continue to use chat if desired.
  5. During the Speaker’s Presentation, please turn off your own video as this helps the presentation run smoothly.
  6. Once the Q&A session begins, we will unmute everybody and enable self-unmuting.
  7. For the business meeting we are going to lock the meeting. This means that if you lose your connection we will do our best to readmit you.

 

Meeting Invitation

Members are welcome to invite friends and acquaintances by forwarding the link below. However, please be aware that we are limited to 100 participants. Therefore, share your screen rather sharing the link whenever possible.

Amateur Astronomers Association of Princeton is inviting you to a scheduled Zoom meeting.

Topic: AAAP May Meeting

Time: May 12, 2020 07:30 PM Eastern Time (US and Canada)

Join Zoom Meeting

https://zoom.us/j/98466394342?pwd=SHE0ZUZ1UVdwSHM3c3dEZWNVdjZKdz09

NOTE: If you click on the meeting link and it doesn’t work, simply copy and paste it into your browser.

Meeting ID: 984 6639 4342

Password: 674557

One tap mobile

+19292056099,,98466394342#,,1#,674557# US (New York)

 

Dial by your location

+1 929 205 6099 US (New York)

Meeting ID: 984 6639 4342

Password: 674557

Find your local number: https://zoom.us/u/ab1sLeKqrj

 

NOTES:

  1.  You do not need a Zoom account or create one to join the meeting.
  2.  You are not required to use a webcam. This means you can join using just an audio or phone connection.
  3. We will open the meeting at 7:10 so you have plenty of time to join
Posted in May 2020, Sidereal Times | Tagged , | Leave a comment

Minutes of the April 22, 2020 AAAP Board of Trustees meeting (online)

by John Miller, Secretary

  • This meeting was initiated via an online video conferencing.session lasting about one hour.

Attendees included:

Larry Kane, Assistant Director
Michael Mitrano, Treasurer
Rex Parker, Director
John Miller, Secretary
Ira Polans, Program Chair
David and Jennifer Skitt, Observatory Co-Chairs
Gene Allen, Public Outreach
Surabhi Agarwal and Ted Frimet, Sidereal Times Editors
AAAP members: Jim Poinsett, John Church, Bill Murray and Tom Swords.

  • An extended topic concerned member-meeting solutions during the Covid-19 crisis. Various conference software solutions were discussed. Rex Parker decided on the Zoom product (being used for this conference). Ira Polans will submit details to the membership. Zoom Pro subscription is about $15. per month.
  • Michael Mitrano submitted the FY balance sheet as of 03-31-2020. It was recommended by John Miller that the report be emailed to the current membership. That was overridden by the Board in lieu of a later version.
  • An online survey (Survey Monkey) was accessed by Rex to poll AAAP members for the required vote for Board of Trustees election, as required by the club by-laws. The survey was emailed to the general membership by John Miller on April 23, 2020.
  • The status of the observatory supports repair was discussed. With Washington Crossing State Park closed, plans for repair are on hold. Rex will talk with the park manager regarding access, scheduling and related issues involving the AAAP. Rex also introduced a motion to increase the repair budget to $9,500 as a buffer.
  • Member Bill Murray reviewed a proposal concurrent with the NJ State Museum’s Planetarium. As a continuing partner with the planetarium, the proposal would coordinate small groups, managed by the planetarium to visit the AAAP observatory as special guests.

Posted in May 2020, Sidereal Times | Tagged , , | Leave a comment

Time

by David J. Kaplan

Time is more ancient than the stars.
It births evolution, yet limits life.
Time stops not for an unwound clock.

Posted in May 2020, Sidereal Times | Tagged , | Leave a comment

O, For a Dark Night Sky

by David J. Kaplan

The city’s night sky
Holds the moon aloft,
A dim orb.

Constellations—incomplete,
The drinking gourd dismantled
Cassiopeia banished.
Orion dismembered.

O, for a dark night sky,
Stars shimmering
In both mind and eye.

When meteors from heaven sent,
Toward Earth their voyage bent
With an arc as wide
As a child’s smile.

Posted in May 2020, Sidereal Times | Tagged , | Leave a comment

Solar observations – with a sextant

by Rafael C. Caruso, MD

On June 2019, a group of AAAP members met in Peyton Hall to attend a two-day celestial navigation course, which I found most enjoyable. The course was taught by Frank Reed, the navigation instructor who currently teaches all navigation classes offered by the Mystic Seaport in Mystic, Connecticut, a maritime museum well worth visiting.  

The objective of this short article is to describe an attempt to determine local latitude and longitude by an observation of the noon sun, and its elegant theoretical background.  These measurements are, in a way, a type of astrometry, the earliest form of astronomy. As this was my first such measurement, I opted to carry it out on from a stationary position on dry land rather than aboard a moving vessel (the fact that I do not own a yacht also played a role in that decision). The boardwalk in Belmar, New Jersey, provided a very convenient “deck” from which to observe the sun and the horizon on Saturday, November 16, 2019, a sunny and blustery day. 

1. Requirements

This determination required three equally essential pieces of information. The devices used in this case to obtain this information are shown in Figure 1.

1. A measurement of the sun’s altitude (H) above the horizon al local noon.

The nautical sextant allows an observer to align the images of sun and horizon, and measure the angle between them. A Freiberger drum sextant, manufactured in 1984 in what was then East Germany was used.  Its drum micrometer is calibrated in increments of 1 minute of arc, which allows estimating measurements to about 0.1 to 0.2 minutes of arc.

2. Precise timing of these measurements. 

A wristwatch with quartz movement, set to Universal time (UT) earlier on the same day, was used in this case. UT may be obtained from the US Naval Observatory Master Clock by dialing (202) 762-1401.  Since no assistant was at hand, a mechanical stopwatch was used to measure the time elapsed between each sextant measurement and its corresponding wristwatch reading. 

3. A knowledge of the sun’s coordinates at the time of measurement. 

The Nautical Almanac, an annual publication, lists the sun’s coordinates for every hour of every day of a given year, among much other information for celestial navigation. The Almanac is published jointly by the US Naval Observatory and the British Nautical Almanac Office. A free version containing the same information is also available online (https://thenauticalalmanac.com)

Sextant, timepieces, and Nautical Almanac.

Figure 1. Sextant, timepiece(s), and Nautical Almanac. This triad provides all the information required to find latitude and longitude (photo by the author).

2. Shooting the Sun

At the moment of local noon, when the sun reaches its highest altitude, the sun crosses the observer’s meridian. This fact is reflected in the etymology of the word, which is derived from “meridies”, Latin for “noon”. For an observer is in a mid-northern latitude, the sun is then due south (conversely, for an observer is in a mid-southern latitude, the sun is due north).

Diagram of a vertical section of the Earth.

Figure 2. Diagram of a vertical section of the Earth, showing the relative locations of an observer and of the sun’s geographic position (GP) when the sun in over the observer’s meridian. Redrawn with modifications from Prinet(1).

Figure 2 shows the position of an observer, depicted as a small circle on the surface of the Earth. Latitude and longitude are unknown to this observer, but we shall assume the observer does know that he or she is north of the equator.  As this measurement takes place in November, the point on the Earth’s surface where the sun is at the zenith (called the geographic position (GP) of the sun), is south of the equator. The blue line tangent to the Earth’s surface is his or her horizon, which is perpendicular to the observer’s zenith. Given the very large distance between the sun and the Earth, all the sun’s rays fall on the Earth essentially parallel to each other, both at the geographic position of the sun and at the observer’s position.  

All the observer does now is to use a sextant to measure the angle of altitude H of the noon sun with respect to the horizon, and to record the exact time of this measurement. As mentioned above, and particularly since the observer may have only an approximate knowledge of the time of local noon, an ideal way to do this to take sun sights starting while the sun’s altitude is still increasing (before noon) and continuing to do so every few minutes until it begins its decline (after noon).

3. Analyzing altitude data

Graph of the sun’s altitude.

Figure 3. Graph of the sun’s altitude as measured with a sextant (Hs) as a function of coordinated universal time (UT)

A graph of the measurements just obtained is shown in figure 3, a plot of altitude (Hs, which refers to altitude H measured with sextant s) as a function of universal time UT. Universal time is equivalent to Greenwich meridian time GMT for a civil day starting at midnight in the prime meridian. In the course of about an hour, from16:15 to 17:15, the sun’s altitude described an arc of an amplitude of 0.5 degrees, with a maximum at local apparent noon. The plot shows that local noon on November 16 occurred slightly before 16:45 hours UT, and that at that moment, the sun’s altitude read from the sextant scale was approximately 30.9 degrees (30° 54’ of arc). 

Celestial navigation textbooks 1-3 recommend tracing a smooth curve through the data points to determine the peak altitude at local noon by inspection. I opted to use a numerical approach, which I have not seen described in navigation manuals, though I assume has been used more than once in the past, since it is quite straightforward. As these data points describe a curve similar to a parabola, one can fit a parabolic function through them and find the function’s equation

Graph of the data points plotted.

Figure 4. Graph of the data points plotted in figure 3, after fitting a quadratic function (a parabola), and its equation. Fractions of UT hours are expressed as decimal fractions.

From the parabola, one can calculate:

a. The time of local noon, obtained from the time value corresponding to the peak or maximum of the curve.  In this case, local noon was at 16.693 hours UT (16h 41m 37s).

b. The sextant reading corresponding to this time, even if the sun’s altitude was not measured exactly then. This is just the highest Hs value of the curve, which is 30.91° (30° 54.5’).

Both values are similar to those estimated by inspection of the graph. The details of this calculation are described in Appendix 1.

Before using this value to calculate a geographic position, some corrections have to be applied to it, to account for the conditions in which the sextant measurement was made. The reasons underlying this requirement are listed in Appendix 2.  After these operations were carried out, the sextant altitude value Hs (30° 54.5’) was corrected to an “observed altitude” value Ho of 31° 6.5’. 

4. Calculating latitude

This calculation relies of the fact that the observer and the sun are on the same meridian at the time of local noon. As mentioned above, the observer knows that he or she is north of the equator, and knows that the November sun is south of the celestial equator. Therefore, their relative positions on opposite hemispheres are as depicted in Figure 5.  

Diagram of a vertical section of the Earth.

Figure 5. Diagram of a vertical section of the Earth, showing the three angles required for a calculation of latitude (ZD, dec, lat). Redrawn with modifications from Prinet(1).

This figure shows that the known value the sun’s altitude H above the horizon allows us to calculate the angle between the sun’s position and the zenith. This is called the zenith distance ZD, which is simply 90° – H. In our case, ZD is 90° – 31° 6.5’ = 58° 53.5’.  

The angle subtended by the larger arc drawn “inside” the diagram of the earth is also equal to ZD, since the sun’s rays are parallel for our purposes. The figure shows that this angle ZD can be visualized as the sum of two angles, the sun’s declination (dec) and the observer’s latitude (Lat).

(As an aside, it’s worth noting that the configuration of these three angles (ZD, dec, and Lat) may be different for other possible relative positions of observer and noon sun, but the latitude calculation always involves a combination of all three of them. I find that drawing a diagram of these angles is a more intuitive and less error prone approach than using any mnemonic).

Therefore, knowing the sun’s declination at local noon allows calculating the observer’s latitude.  This is where the Nautical Almanac becomes essential.

Excerpt of a page of the Nautical Almanac for 2019.

Figure 6. Excerpt of a page of the Nautical Almanac for 2019, which shows the sun’s coordinates for every hour of Saturday, November 16.

The relevant section of the Nautical Almanac page for Saturday, November 16, 2019 is shown in figure 6. The almanac lists sun declination values for every hour of the day.  Note that declination values are designated by convention as N(orth) or S(outh), rather than as the positive or negative values, the notation used in astronomy.   The table entries outlined in red indicate that declination was S 18° 46.0’ at 16:00 hs and S 18° 46.7’ at 17:00 hs.  What we need to know is the sun’s declination at 16h 41m 37s UT, which may be obtained by interpolation as S 18° 46.5’.  The observer’s latitude is therefore:

Latitude = ZD – dec = 58° 53.5’ – 18° 46.5’ = 40° 7’ North

6. Estimating longitude

Although there are more accurate celestial navigation methods for the calculation longitude, a measurement of the time of local noon may also be used to estimate longitude.  This estimation relies on the fact that the geographic position (GP) of the sun changes during the day (see figure 7). At local noon at longitude 0°, the sun’s GP is at some point on the Greenwich meridian. As the Earth rotates, the sun’s GP moves westward at a rate of 15° per hour, and completes a whole rotation of 360° in 24 hours. The angle between the Greenwich meridian and the meridian over which the sun’s GP has moved is called the Greenwich hour angle (GHA) of the sun.  This angle is measured westward from the Greenwich meridian, from 0° to nearly 360°. In the Western hemisphere, local noon occurs later than at longitude 0°, proportionally to the distance in longitude from the Greenwich meridian. Therefore, longitude is equal to the Greenwich hour angle of the sun at local noon2.  

Diagram of the Earth as a sphere, showing the Greenwich hour angle.

Figure 7. Diagram of the Earth as a sphere, showing the Greenwich hour angle (GHA), increasing as the GP of the sun circles westward from the prime meridian. Redrawn with modifications from Karl (2)

To use this fact to estimate longitude, one also relies on the Nautical Almanac. The Almanac lists the GHA of the sun (and other celestial bodies) for every hour of each day. The Almanac excerpt in figure 6 shows that the sun’s GHA was 63° 49.2’ at 16:00 hours UT.  Since GHA is between 0° and 180°, longitude is West of the Greenwich meridian. What we wish to know is the GHA value at the time of local noon, i.e., at 16h 41m 37s. Since we know that GHA increases at 15° per hour, or 0.25° per minute, it has increased 10° 23.4’ in the 41m 37s after 16:00 hours.  Therefore, we can conclude that

Longitude = 63° 49.2’ + 10° 23.4’ = 73° 72.6’ = 74° 12.6’ West

7. Checking coordinate accuracy

At the end of this exercise, we have reached the conclusion that our coordinates are:

Latitude: North 40° 7’ 

Longitude: West 74° 12.6’ 

How accurate is this result? In these days, celestial navigation may be used as a backup if satellite navigation systems such as GPS fail, as it relies on different and independent information. But we may also use GPS as a way to check our celestial navigation results, using these more accurate values as the equivalent of “the answer on the back of the book” in a college math textbook.

The National Oceanic and Atmospheric Administration’s online solar calculator4 lists GPS coordinates of any selected location on Earth, in addition to giving solar position for any time at that location. For our location on the Belmar boardwalk, these coordinates are:

Latitude: North 40° 10.3’ 

Longitude: West 74° 0.9’

As one minute of latitude was historically equivalent to one nautical mile, our error of 3.3’ in latitude is approximately equivalent to a distance of 3.3 nautical miles. 

The length of one minute of longitude varies with latitude, from a maximum of about one nautical mile at the equator, to a vanishingly small distance at the poles.  At a latitude of 40°, a minute of arc spans approximately 0.77 nm. This implies that our error of 11.7’ in longitude is approximately equivalent to a distance of 9 nautical miles. The roughly three-fold difference between the longitude error and the latitude error is not surprising, since the method used here to determine longitude is not an ideal one, and gives only an approximate estimate of longitude.

The great circle distance between the celestial navigation coordinates and the GPS coordinates, obtained with a great circle calculator5, is 9.56 nautical miles. 

In this way, knowing an angle, a time, and having access to data which relate this angle to this time, it is possible to measure latitude and estimate longitude by the noon sun.  Celestial navigation is no longer the most advanced technique to find one’s position, but remains a beautiful achievement of the human mind, and provides a perception of the motions of the earth and sky that is most appealing for an amateur astronomer.

Appendix 1. Fitting a parabola

Numerical routines for fitting a parabola, or any other polynomial function, to data points are included in spreadsheet programs (e.g., Microsoft Excel, or the open source Libre Office), in graphing programs (e.g., Kaleidagraph), and in numerical analysis packages (e.g., Matlab, or the open source Octave).  The best fitting parabola for our data points is shown in Figure 4, in which fractions of UT hours are expressed not as minutes but as decimal fractions, which are required by the numerical routine used.  The curve-fitting program also yielded the equation of this parabola:

− 1.59 t2 + 53.02 t – 411.58

This equation may now be used to find the time of local noon, which is the time t for the maximum Hs value.   For this purpose, one can follow the usual approach to find a maximum of a function. This involves calculating the first derivative of the function: 

− 3.18 t + 53.02 

The maximum t value is obtained by setting the first derivative to zero and solving for t.

In this way, one can determine that local noon occurred at 16.693 hours UT (16h 41m 37s). Finally, one can calculate the sextant reading corresponding to the exact time of local noon. This is just the peak Hs value of the curve, and can be obtained by substituting the peak time (16.693) in the equation of the curve. This results in a value of 30.910° (30° 54.5’) for Hs.

Appendix 2. Applying corrections

This altitude value as measured with a sextant needs to be corrected, to account for the following facts: 

  1. A calibrated sextant may still have a minimal residual error in its angular measurement (which has to be added or subtracted from a reading).
  2. The observer is not at horizon level, but rather at a variable known height above it (in this case, on a modestly elevated boardwalk, 3.2 m (10.6 ft) above sea level).
  3. Aligning the lower limb of the sun with the horizon yields a more accurate measurement than aligning its center, which is the almanac-tabulated value.
  4. The atmosphere refracts rays of light from the sun. This effect is greater if the sun is close to the horizon, and minimal if it is close to the zenith.
  5. Sun sights are taken from the surface of the Earth rather than from its center. The resulting small parallax error is greater if the sun is close to the horizon.

Performing these corrections is considerably simpler that it may seem after reading this list. The observer is able to determine the angular measurement error (known as the index error) of his or her sextant (in this case, 0.3 min had to be added to the reading). The Nautical Almanac contains tables to perform the remaining four corrections. Alternatively, formulas for the same purpose are readily available, and may be entered on a spreadsheet program for ease of use. 

References

  1. Dominique Prinet, Celestial navigation using sight reduction tables Pub. No 249. Friesen Press, Victoria, BC, 2018
  1. John Karl, Celestial Navigation in the GPS age. Paradise Cay Publications, Arcata, CA, 2011
  1. David Burch, Celestial Navigation, a complete home study course. Starpath Publications, Seattle, WA, 2019
  1. NOAA National Oceanic and Atmospheric Administration. Online solar calculator (https://www.esrl.noaa.gov/gmd/grad/solcalc/)
  1. Ed Williams.  Great circle calculator (http://edwilliams.org/gccalc.htm)
Posted in May 2020, Sidereal Times | Tagged , , , , , , | Leave a comment

When, How and Why I Became Interested in Astronomy

by John Miller, Secretary

I was in my father’s den – the summer of 1965 – looking up something for a school assignment in our World Book Encyclopedia. Dad was also in the room tapping madly on his ancient Royal typewriter. It must have weighed 40 pounds.

On the floor, next to his desk was a beautiful rectangular, burgundy leather case; small – about 15 by 8 inches. He had recently brought this home and I was fascinated by its contents. I will always remember his telling my older brother and me: “Keep five feet from this case. You’re always welcome to look inside, but never before asking me first.”

Of course, it was a new Questar 3 1/2” astronomical telescope. Gleaming like platinum and costing as much as a living room of new furniture. My father was an accomplished engineer out of Cornell. He knew this was a Stradivarius. He was also an avid sailor and well-educated in celestial navigation. Thus, an astronomical connection for me (but not my brother).

My uncle Tek (no one knows where the nick name originated), Dad’s older brother, owned a sprawling farm outside of Califon, NJ, about an hour’s drive from my hometown, Metuchen, NJ. “The Farm” (to which it was always referred) had livestock, a party-line phone – and a pristine open dark sky. Soon after acquiring the Questar, we went up to The Farm for dinner and to set up the scope for First Light.

It was late summer Clear as a bell. Lamb was roasting on the outside open spit. I remember my father and Tek (also a Cornell engineer) discussing how best to set up this little gem in the “outer field” (about 30 acres of horizon-to-horizon open sky) while simultaneously scratching there heads trying to figure out the Questar’s mysterious mode switches. I wasn’t watching their progress.

I was looking up.

In the past, I hadn’t really paid much attention to the sky. There was already light pollution in Central Jersey and none of my friends were much interested in astronomy. But that September night I couldn’t stop stargazing. We got the Questar set up on a sturdy table in the outer field. No vehicle noise. Not a light for miles. Just critters rustling in the grass. And more talk about the mysterious mode switches. And me – still mesmerized, looking up.

Dad knew some of the constellations, with their associated brighter stars and planets important to celestial navigation. It was a lucky night for a visit. The moon was in last quarter and late rising. Although, for this group, a quarter moon would have been a spectacular experience in the Questar.

Near the zenith was Vega, which my father recognized. And Polaris, which, of course, he knew well. There was a bright object low in the southeast. As with any well-prepared boatman, he had brought along his 7×50 binoculars. We would have been lost without them ! One of my Farm cousins had a beginner’s astronomy book (of course Chris, Tom, Peter, Mopsie and young Collie, Jupiter — yup, that was his name) were all out with us). The book listed a few prominent Messier objects, none of which any of us knew about. But we certainly wanted to explore.

The first target, if old memory serves, was Vega. Dad and Tek fiddled until they reached focus. They were most impressed. My cousins and I jockeyed for eyepiece (the famous Brandons) position and were sternly warned by both adults that any rough-housing near the Questar was absolutely forbidden. Back then, when our fathers set a command, we listened.

We found Altair and Polaris. I have no idea if we were able to split Polaris (Ab 2006 sep = 17.0”), but I doubt it. My father serendipitously ran across M 31 with the binocs (although it was easily naked eye). What a great to-do THAT caused. The book described M 31 and I recall we spent quite a bit of time on the galaxy. Mostly with the binoculars. I was slack-jawed and couldn’t wait to look up more about this object. Get me to a library ! But for me, the astonishment that sparked a life-long journey of curiosity and discovery was to come a little later in that field.

That bright object rising the the south east was…Saturn.

It took a while for the grown-ups to get the planet in the Questar FOV. But when they did, my father, generally a pretty reserved person, let out a shout. I don’t remember what he said, but I’ll never forget his tone of excitement and delight. When it was my turn at the Brandon, I was stunned. Sure, I’d seen lots of pictures of Saturn. But none of them looked like this. Not a one. This was live! This was real ! This eleven-year-old was hooked. Deeply and permanently.

I built a small library over the following year or two and was allowed to use the Questar under close supervision. I learned that binoculars were a Godsend for learning the sky and (at that early stage) effective for finding some of the brighter DSOs. Plus, I was very lucky to have a father who (loving the physical sciences himself) completely encouraged a youngster’s curiosity.

At 13, I still didn’t have my own telescope (I had use of a QUESTAR, for God’s sake).

But I wanted my own. Akin to a teenager wanting his own car. My paternal grandparents, who lived a few miles away, agreed to gift me the money. At the local hobby shop, I bought the standard novice scope of the era. You guessed it: a Tasco 60mm, f/12 refractor. Rickety, with a dangerous eyepiece screw-in solar filter, a 25mm and 10mm (undoubtedly Huygens) and a Barlow. The universe was mine.

At home, observing was challenging, Most of the property was filled with giant oaks, except for the front yard, which was filled with giant street lights. I kept copious observing notes and researched every new object I discovered. The ultimate astro uber-nerd. For a year or so, I treated that shaky scope like the Hale 200” at Palomar (which many years later I would climb aboard). A buddy I’d known from elementary school gained an interest in astronomy and bought a Sears refractor. So I had a comrade in arms. 1968. Just entering Junior High School there were new distractions. Girls (problem is they didn’t find me much of a distraction), and school work, much more of it and more difficult.

But astronomy was deeply ingrained and could be shoved to a corner – but not for very long. Then another hobby began gnawing at me as a direct result of my love for the sky.

Photography.

Like today’s public pushing their cell phones against an eyepiece, one night I pushed my Dad’s Leica IIIc against the terribly achromatic eyepieces (although all those exposures were B&W).

Of course photography was film-based (I mostly used Kodak Tri-X). You had to wait a week or more to see the results of those moon shots. While doing all that waiting, I started doing some terrestrial shots. And more terrestrial work.

So, for the first time since that Saturn epiphany, I was deeply smitten by a second hobby. And I seemed to be pretty good at it. I never pursued astro photography. I bought my first DSLR (a Miranda SX}, with removable penta prism, just in case astro photography came back into the —– picture. No more waiting. I convinced my parents to build a custom darkroom.

Early in 1969, at 15, my astronomy buddy, Eric Sohmer and I enrolled in a 10 session Saturday astronomy class at New York’s Hayden Planetarium. Our parents were initially against the idea of our going into the city, but we were good salesmen. Yes, of course we skipped some classes and went exploring another universe: Manhattan. We kept our wits about us and never ran into any problems. So THIS is 42nd Street ! Huh.

By this time I had been a loyal subscriber to Sky & Telescope. Remember those ads? Jaegers; Edmund Scientific; Optical Craftsmen (oh my !); Unitron. And, of course – Criterion and it’s mouth-watering RV-6. That full page ad lit my eyes on fire (again, what a nerd). That needed to be my next scope.  But, alas, my parents said no to all my imploring and justification. No room in the two-bay garage. Sure.

Many years later, I lived in the town of West Hartford, CT where Criterion Manufacturing was headquartered. But by then it had recently closed down.

At each NEAF I’ve attended, I still visit the vintage scope booth and admire the one or more RV-6s on display.

High school led to more terrestrial photography and new interests in physics (Henry Anzak – thank you for understanding how to bring physics alive for us !) and theoretical astronomy and cars and going “steady” and…

Tenth grade and my first trip to a newly-discovered astronomy club in Princeton; the Amateur Astronomers Association of Princeton. It was 1970. My father drove a friend and I down for the advertised lecture. That friend was Vince DaGrosa, who had a cursory interest in astronomy.

Fifty years later we’re still friends. Vince recently joined the AAAP. I guess he really had to study the options of joining. I stayed with the AAAP until 1976 (when college began) and re-joined in 1998. The 22 year hiatus was due primarily to living elsewhere around the country for business. From that year forward I again immersed myself in astronomy and astrophysics – and lucky enough to get to know many Princeton University astronomers and physicists over time. As luck and fate would have it, one evening an emeritus professor made a short “request” visit at the beginning of a AAAP monthly meeting.

That person was none other than David Todd Wilkinson.

Wilkinson was a world-renowned pioneer in the field of cosmology specializing in the study of the cosmic microwave background radiation (CMB). He was looking for volunteers to assist with a project, coordinated with Harvard’s Oak Ridge Observatory, It was an optical SETI endeavor and would require the refurnishing of the long-unused Fitz-Randolph Observatory, housing a 0.9 meter Perkin Elmer Cassegrain. All new software was written and installed by the physics department wizard Norman Jarosik. A complex photometer array called the “OSETI Box was co-designed and built by both groups. The project was active from 2001 to 2004. Sadly, David died from cancer after a long battle. He was one of the nicest human beings I’ve ever met. That project was a singular highlight in my astronomy life.

We also used the refurbished observatory to occasionally invite the public for open-house viewing. These events were extremely popular. Unfortunately, despite many debates, after David’s death, neither the Department of Astrophysics nor the Physics Department had any interest in maintaining the facility. It was mothballed and later scheduled for the wrecking crew. The scope was sold or donated to a school about 2015. The observatory still stands.

A long, fun and rewarding journey. From a field on a family farm, to Tascoland, later, an 8” Newtonian, an adventure climbing aboard the majestic and legendary Hale 200” on Palomar Mountain, Princeton classes (General Astronomy; Exoplanets; General Relativity; Cosmology), many NEAFs, countless “star parties” and a library of books.

Oh yes. And the experience has come full circle, dear reader.

Two years ago, I bought my very own ——

QUESTAR !

Posted in May 2020, Sidereal Times | Tagged | Leave a comment

When, how, and why I began my interest in astronomy

by Victor Davis

As a general rule, I tend to value earned experiences more than accidental ones. That’s a pretty common view, it seems to me. The exhilaration of a summit view is heightened by appreciating the effort it took to get there. The view from a parking lot is less sublime than the vista from an untrammeled vantage point miles from the trailhead and reached by scrabbling uphill across fields of talus and scree. My car climbed Mount Washington (though I never collected the ubiquitous bumper sticker), but it’s the experience of hiking the Franconia Ridge that I particularly remember. These events took place, as you might imagine, many years ago when I was more agile and before my heart muscle had to be re-plumbed. 

Among these miniature adventures was a cross-country car trip nearly 50 years ago. I took off with a friend in his beat-up Chevrolet on a 6-week tour from our homes in Ohio to the West Coast and back. We had little agenda beyond spending a few weeks sponging off relatives; his in Montana and mine in northern California.  We subsisted mainly on a diet of cheeseburgers and french fried mushrooms, an unfortunate addiction that led more or less directly to my re-plumbing experience mentioned earlier.

I no longer remember the sequence of our travels, but at some point we ended up, as many tourists do, at the south rim of the Grand Canyon. Then as now, the visitors’ overlooks swarmed with people (also black flies), and though only about one percent of canyon visitors expend the effort to hike its trails, my friend and I decided to be among the enlightened few to “walk” down to the Colorado River and back. In one day. At midday in August. Signs warned of the foolhardiness of expecting to accomplish what seemed a modest 16-mile stroll (with a 4,400 foot change in elevation) in a single day and without proper preparation. No matter; we knew better than the ignorant rabble who turned back at the first rest area that it was important to wear long pants and to stay hydrated. We filled our one-quart water containers to the very top, and headed off down the Bright Angel Trail. The scenery was stunning, each of many switchbacks bringing into view a landscape different from the last, and just as beautiful. We were pretty baked by the time we got to the river, but that made its cold water that much more appealing. We played along the river for a few hours, splashing around and clambering over two-billion-year-old rocks. Then, with an exuberance and confidence available only to the profoundly ignorant, we headed back up the trail. 

Frolicking overlong at the river had the unintended benefit of sparing us the worst heat of the day. Nevertheless, the uphill climb was brutal. And nightfall came unbelievably quickly. Did I mention that our water supply was woefully inadequate? So there you have it: two inexperienced, barely-fit hikers, exhausted and dehydrated, hiking a steep and precarious trail in the dark.  At some point, and many details are mercifully lost to memory, we virtually collapsed along the trail. Lying flat on the ground, I looked up at the sky.

I’d never –and I mean NEVER – seen anything like it. I briefly entertained the idea that I was hallucinating. Stars shone everywhere. A few bright planets dazzled. There was this amazing gauzy band spanning the sky from one canyon rim to the other. What the heck was that? Every minute or so, a meteor streaked across the sky. A Perseid? It was all so beautiful, so dynamic, that I couldn’t stop watching. It was unforgettable, a sight I’ve tried to recapture, usually with disappointing results. What would I have to give up to enjoy such a view from where I live? That’s a pretty slippery slope. 

In subsequent years I have gone out of my way to experience astronomical sights and events, and to seek the company of others whose enthusiasm and expertise surpass my own. These efforts have enriched my life. But, my first experience of a starry night in a dark sky is what got me hooked on astronomy. When the hour gets past 10 pm and the temperature drops below about 50 degrees, remembering the rewarded efforts of these experiences is what gets my butt out of its comfy chair.

high-contrast photo of my nutty friend climbing around the bottom of the Grand Canyon

high-contrast photo of my nutty friend climbing around the bottom of the Grand Canyon

Posted in May 2020, Sidereal Times | Tagged , | Leave a comment

Rekindling My Love of Astronomy

by David J. Kaplan

I was born in the South Bronx. My parents each had two jobs, so we as kids were pretty much on our own. Saturday mornings my mother gave me fifty cents, pinned a label inside my coat with my name, address and telephone number. “If you get lost, ask a cop for directions.”

My friend Gary and I would take the subway, which was 10 cents, and travel all over the city. Transfers were free. We would take the Staten Island ferry for a nickel, go to the Bronx Zoo, it was free, or the Botanical Gardens, also free.

But our favorite destination was the Hayden planetarium and the Museum of Natural History, also free. We’d weigh ourselves on scales calibrated to how much we’d weigh on several of the planets and the moon. We’d exam giant meteorites, and wonder at the latest missiles sent aloft during the formative years of artificial satellites such as Explorer I.

Of course the sky show in the domed theater was the biggest attraction and for two kids whose imaginations were as infinite as space that was the hit of the day.

Before leaving the planetarium a visit to the gift shop was also a must. If we purchased anything on our limited budget, it was a giant postcard with images of Saturn and Jupiter, always a winner on Monday’s show and tell in our public school classroom.

Another of my friends received, for his 11th birthday, a three inch reflector telescope. Now that was a big deal. One evening we carried it to the rooftop of his apartment building and observed the moon. What a thrill!

Talk about imaginations as infinite as space. While observing the moon, it appeared as though something was heading toward it. It had a trail like the exhaust of a rocket ship. And then, it appeared as though it went behind the moon and reappeared on the opposite side. We thought we had made some extraordinary discovery. We ran downstairs to my friend’s apartment and (at 10 o’clock at night) called the Hayden Planetarium, excitedly telling the person who answered the phone of our great discovery. He replied, “I’m only the night watchman.”

So much for our great discovery.

In 1967, I was doing research for CBS News, the Special Events Unit. We we’re covering the launch of Apollo 8. The executive producer approached me and in an off-handed manner said, “See if you can find a sculpted globe of the moon. We’ll use it as a prop.”

It seemed a slight chance. I called several agencies in the Soviet Union. Hey, it was on CBS’s dime. I knew they had the first images of the far side of the moon and thought someone might have had the same idea, sculpting a model of the moon. Nyet, nyet and more nyets.

After speaking with folks at space agencies in Europe and having no luck, a colleague suggested I call Dr. Thomas Nicholson, an astronomer at the Hayden Planetarium, who later became its director. “Sure, there are two guys in the Bronx who just finished sculpting a model of the moon.”

What an extraordinary find. Graciously, they allowed us to use their sculpted moon (1,000,000:1) in inches. Every rill and crater, straight wall. It was all there.

We invited Dr. Nicholson to come to our studio and assist the lighting director. The moon was lit to duplicate how the astronauts would see it on their approach.

I would say that entire experience rekindled my love of astronomy.

David J. Kaplan

Me, the young guy, with Robert Wussler the Executive Producer, The Flight of Apollo 8

Posted in May 2020, Sidereal Times | Tagged | Leave a comment

keep your distance

by Victor Davis

artist alteration

keep your distance. “at least the diameter of a saturn-mass black hole’s event horizon” – Artists alteration, 2020 – Ted Frimet, no copyright held.

assuming zero angular momentum and zero charge

I thought you might include in the newsletter, this social distancing advice for the astronomically inclined, which leaves the calculation as an exercise for the viewer.

Here are the relevant numbers:

Formula for the Schwartzschild radius of a black hole: R=2MG/c^2 (discounting charge and spin)

Gravitational constant (G): 6.67 X 10^-11 m^3/kg.s^2

Mass of Saturn: 5.68 X 10^26 kg

Have fun. My ZWO camera, which my wife ordered as a Christmas/Birthday gift for me, is finally due to arrive tomorrow! I figure that means dreary weather for the next month at least.

Your optimistic astro-buddy,

Victor

Posted in May 2020, Sidereal Times | Tagged , | Leave a comment