asteroid velocity reprise
by Ted Frimet
I attended a presentation on asteroid occultation and IOTA, hosted at Montclair State University, by NJAG member Albert Carcich. I found Alberts lecture and slide presentation on measuring asteroid size and shape to be very appealing, and an deceptively easy topic to grasp. A thought quickly developed. Could I use the results of one chord, instead of many, to rough estimate an asteroid diameter? Probably not, I’ve been told. Of course, you would have to be at midline, during measurement and lucky. And lacking the negative reports of the “shadow boundaries” during an an asteroid eclipsing a star, the results would be sketchy at best. In fact, I have been told that it is inherently flawed. I agree. Not knowing my head from my tail, I reached out, once more.
I reached out to IOTA membership, and they were very helpful. I was hopeful that knowing how to calculate an asteroid Vt, that the occultation shadow velocity would prove out a ratio, that might divulge its hidden metrics. Either there were no takers, or my education was so lacking that I failed to materialize the math. Probably the latter. As such, I am vying to move forward. I have attempted purchases on the cheap, used copies of: The “Explanatory Supplement to the Astronomical Almanac” by J. Meeus and “Textbook on Spherical Astronomy” by R.M. Green. And Astronomical Tables of the Sun, Moon, and Planets, by J. Meeus. Regretfully, I am unable to locate a copy of the Supplement to the Astronomical Almanac, at a low enough cost. However the Tables, and Textbook should confound and confuse me for a least a few months to come! UACNJ member, Kris Kootale, will set aside another tome, for me to borrow – Meeus’ Astronomical Algorithms, next time we meet on observers duty for 2018 at Jenny Jump.
I will have a tool at my disposal. It is the Occult program. Since the many supported algorithms are very complex, they do not lend themselves to easily being implemented by hand. Certainly not by me! Using Occult, however, I will have a proven staple to compare any results I obtain, otherwise. I should be downloading and fidgeting with software, before any of my books arrive from the U.K., or elsewhere.
There is NOVAS code, available on the Navy’s MIL website for occultation study. However it has been decades since I’ve used Fortran, and I don’t think it a good idea to reverse engineer any C programs. There is, as good fortune even smiles on us all from time to time – a Github site where the code sits ready for compilation. Here, too, I will take a pass, having decided on taking the longer road to knowledge. I am as foolish in my math pursuits, as I am at the eyepiece of a telescope. Perhaps, during my travels I will write snippets of Visual Basic code in .NET with a fully functioning interface. I own that skill. That might even help the next traveler on their way. The next IOTA meeting, in Suffern – NY, is a full week before NEAF. I plan to attend both.
Last AAAP meeting I reached out to membership, voicing my concerns on the CLEA software model, Astrometry of Asteroids. Member Matthew Rapp’s suggestion was fully grounded when he recommended using the sample files to learn from. Being Mac based, and confusing the install with previous software that was buggy, I had my concerns. I was happy to find out that I didn’t need to create a Virtual Machine to install Astrometry. My current installation of Bootcamp, running Windows 10, was more than sufficient. I did, however find it necessary to move forward with the more advanced Astrometry toolkit, which provided me with access to star catalogues not found in the student version.
And now a pause for errata on last months essay, “How to Haul Tail”. I have since revisited the FITS files. I have taken notice that there are two places for observation times and dates in the FITS file format. Please take note that using either FITS header field results in same outcome of 2,208 elapsed seconds.
For asteroid Griqua image 0: First occurrence of the FITS field for date time group:
DATE-OBS= ‘2017-12-27T01:30:21’ /YYYY-MM-DDThh:mm:ss observation start, UT
Second occurrence of the FITS field for date time group:
DATE = ‘2017-12-27′ / Date at start of exposure, UT
TIME-OBS= ’01:30:06.154’ / Time at start of observation, UT
For asteroid Griqua image 7:
First occurrence of the FITS field for date time group:
DATE-OBS= ‘2017-12-27T02:07:06’ /YYYY-MM-DDThh:mm:ss observation start, UT
Second occurrence of the FITS field for date time group:
DATE = ‘2017-12-27′ / Date at start of exposure, UT
TIME-OBS= ’02:06:53.926’ / Time at start of observation, UT
Onwards! I wanted to refine my hunt for asteroids, by learning how to extrapolate their locations in an astrophotography image. Using the Skynet image frame center as the target “home” position was sufficient. The Skynet observers user interface easily communicated that information to me. I have noticed some drift, as the asteroid falls out of the field of view, during some endeavors. I decided that if I was going to continue to calculate and refine asteroid metrics, I was in need of a more precise measurement method. Using the Astrometry program, I can now select navigational, also known as, reference stars. The program effortlessly interpolates the asteroid location, in RA and DEC. It appears to be highly precise, and a decent tool for this student of Amateur Astronomy.
The same can be accomplished in Afterglow software, provided for in the Skynet interface. This post processing tool provides a window into the associated Digital Sloan Survey (DSS) images. You can select any point, on a corresponding frame and read off the correct RA/DEC coordinate. However, there is presently no way to overlay the asteroid image onto a DSS, as they are in two different non-corresponding proportions. You could “point and guess”, however I wanted something a bit more precise. Enter Toolkit for Astrometry.
There are a couple of user interface “traps” in the Astrometry tool kit, however none of them are fatal. For instance, the interface may ask you to load a CD – as I have neither the CD and my Mac Book Pro doesn’t sport a CD ROM interface. I successfully click “no”, and flawlessly move on with the program. A sensitive area to some, however to me was just a passing inconvenience, is that some message boxes will populate with invisible content. I found a quick solution by employing two monitors. After moving the message box to the second, auxiliary monitor, the box properly populated, and I was able to click away my response. I subscribe the error not to the program, but to how it interfaces with my systems graphics card, and subsequent operating system. The interface issue lay with a “screen refresh” routine. Otherwise, please know that the program is intuitive, and easy to use.
Just like my first night out at Jenny Jump, versus skies that were not as dark, it is easy to get lost among the stars. My astrophotography of 1362 Griqua, being limited to 4 second exposures, would only express the brightest objects in frame. And using Astrometry, I would be bombarded by stars of 20th magnitude or more. What to do? Skynet to the rescue! Using the astrometric tools afforded by Afterglow, I selected the navigational stars that would help me in my asteroid hunt.
Deploying Astrometry. Shown below are the reference star results for magnitude = 22 or brighter. This is followed by the magnitude data for Griqua FITS 000, and FITS 007 at 4 seconds exposure. Note that Afterglow photometry, by itself, does not provide RA and DEC.
I then applied a magnitude limit of 16 to the Astrometry initialization file. And proceeded to select three or more reference stars. Below is the result for Griqua FITS 000, followed by FITS 007. Immediately below the reference star images you will find JPEGs from Skynet for comparison.
The Griqua asteroid, in both Skynet images appears to hold steadfast in center of frame.
This becomes an ideal test to recalculate and refine tangential velocity, using Astrometry coordinates.
Here are the Astrometry coordinates as reported for:
Griqua (0) =
RA = 0h 27m 52.99s Dec = -24° 59′ 22.5”
Original Griqua (0) observers data from Skynet:
RA/Dec: 00:27:52.198 | -24:59:39.468
and Astrometry, this time, for Griqua (7) =
RA = 0h 27m 55.43s Dec = -24° 58′ 51.8”
Original Griqua (7) observers data from Skynet:
RA/Dec: 00:27:54.559 | -24:59:11.705
Below is the sample astrometric solution for Griqua (0).
2018/02/17 4:26:17 PM
Image 1 – Astrometric Solution
Image File Name: GRIQUA_2335994_LUM_000S.FIT
Object: Griqua 1362
Observation Date: 2017 December 27, UT: 01:30:21
x = 515.4494, RA = 0h 27m 52.99s
y = 510.9753, Dec = -24° 59′ 22.5″
m = 15.07 (No Filter)
Estimated errors cannot be calculated!
N(=3) is minimum for selected solution type.
Estimated Error in Magnitude (Sigma): 0.03(3)
x = 512.0000, RA = 0h 27m 53.13s
y = 512.0000, Dec = -24° 59′ 23.1″
Plate Constants for Linear Solution:
Scale = 0.5865 “/pixel, Field Wd. = 10.01′, Ht. = 10.01′ Notes:
(X = a*x + b*y + c)
a = 2.8460361E-06, b = -6.0589289E-09, c = -1.5222572E-03
(Y = d*x + e*y + f)
d = -9.6308291E-09, e = -2.8407851E-06, f = 1.5439454E-03
(1) Star not used in astrometric solution.
(2) Star not used in magnitude solution.
(3) Magnitudes are unreliable due to errors in reference star magnitudes and passband differences.
Using last months essay, “How to Haul Tail”, I have followed the same procedure to calculate the tangential velocity of asteroid 1362 Griqua. However, this month, we substitute the Astrometric’s solution for the asteroid coordinates:
Griqua observation 0 – DEC
24 degrees 59 minutes 22.5 arc seconds
(24 x 3600) + (59 x 60) + 22.5 = 89962.5
Griqua observation 7 – DEC
24 degrees 58 minutes 51.8 arc seconds
(24 x 3600) + (58 x 60) + 51.8 = 89931.8
Griqua observation 0 – RA
0 hours 27 minutes 52.99 seconds
(0 x 3600) + (27 x 60) + 52.99 = 1672.99
Griqua observation 7 – RA
0 hours 27 minutes 55.43 seconds
(0 x 3600) + (27 x 60) + 55.43 = 1675.43
DEC difference = 30.7 arc seconds
RA difference = 2.44 seconds
I am keeping the time difference, from the already published essay, which was 2207.772.
I found an additional math error that I overlooked in the FITS file format, today. Without passing judgment on the essay precision – I calculated for both, and found a 3 second difference.
After “rounding” the angular velocity the answer ended up the same, as 0.021
2.44 x 15 x cosine (-25) = 33.171
sq root of ( ( 33.171 * 33.171) + ( 30.7 * 30.7 ) )
sq root of (1100.32 + 942.99)
sq root of (2042.81)
45.198 / 2207.772 = 0.021 (angular velocity)
Tangential Velocity = (Angular Velocity x Distance) / 206265
Vt = (0.021 x 287306800) / 206265
Vt = (6033442.8) / 206265
= 29.25 km/s
I have calculated that using Astrometry reference stars, and interpolated coordinates, 1362 Griqua, is moving at a higher measured velocity of 29.25 km/s versus last months calculation (using Skynet data) at 26.5 km/s.
Using an online calculator, we arrive at a solution that results in a 10 percent difference. I am inclined to believe that this is a sufficient precision shift. I will be dipping my hand in the Astrometric’s hunney pot, from time to time, now. Which will make future amateur asteroids analysis a sweeter preoccupation.