Eros and the solar parallax

Steven van Roode Michael Richmond By Steven van Roode and Michael Richmond

The year 2012 offers us the unique possibility to measure the size of the solar system with two classic and historical important methods: using the transit of Venus (in June) and the opposition of Eros (in January). By taking pictures of Eros at specified times from January 28 to February 3, analysing the pictures yourself using free and online software, and submitting the retrieved data, you can add to the determination of the distance to the astroid Eros! This page has all historical and methodological backgrounds and instructions for you to join this special outreach project.

Check out the submitted results so far and the depository of submitted images. You can also compute the distance to Eros (and the Sun) yourself by pairing observations in this Excel sheet.

→ January 1931: telescopes aimed at Eros
→ January 2012: re-enactment of the 1931 campaign
→ How to participate
→ Submit your data and photographs


January 1931: telescopes aimed at Eros

When the asteroid Eros came into opposition in January 1931, it was closer to earth than it had been since the opposition of January 1901. This close opposition was taken advantage of to find the distance to Eros with unsurpassed accuracy through parallax measurements. It was a welcome opportunity after it had dawned upon the astronomical community that the transits of Venus hadn’t fulfilled the high expectations with regard to the determination of the sun’s distance.

When a celestial body comes close to earth, and is viewed at simultaneously from two widely separated locations on earth, the observed positions of the body with respect to the background stars are a little different. If this so-called parallactic displacement is measured and when the distance between the two observing locations is known, the distance to the body can be computed through trigonometry. Once the distance between Eros and earth is established, the distance to the sun is also known from Kepler’s Third Law.

Eros is an asteroid discovered in 1898. It’s an elongated 33-km wide Mars-crosser asteroid, which means it periodically comes within the orbit of Mars. The highly elliptical orbit brings Eros to within 0.2 AU from earth’s orbit every 1.76 years. No other then-known asteroid came ever as close to earth as Eros. Such a close apparition made it an ideal object to perform parallax measurements. Close encounters like these, however, are quite rare. After the January 1931 opposition, Eros came close to earth again in January 1975. After this year’s opposition, the next time Eros comes close to earth will be in January 2056.

The preliminary work for the 1931 opposition already started in the 1920s. To be able to accurately measure the parallax angle, the position of all reference stars up to the 9th magnitude along the path of Eros (see picture to the left) had to be determined with high precision. A list of 419 reference stars was carefully prepared by the Rechen-Institut in Berlin. To account for atmospheric dispersion, also the brightness, spectrum and colour index of the stars was to be determined.

During the month January of 1931, numerous observatories measured the position of Eros with respect to the reference stars. This was done either visually, using micrometer measurements, or photographically, where the exposed plates were measured afterwards. The photographic method had some advantages over the visual observations. First, the photographic plates could be kept and measured carefully in peace and quiet. Secondly, the photographs of the sky could capture a wider star field, allowing more brighter reference stars to be on the exposure than would be visible in the narrower field of view of visual observations.

After reducing all observations, a solar parallax of 8″.790 was established. It was the most accurately known value for the solar distance up to that time, and this value would remain a standard until 1968, when radar measurements attained an even more accurate value for the distance to the sun.


January 2012: re-enactment of the 1931 campaign

In many respects the opposition of Eros in January 2012 mimics that of 1931. The shortest distance to earth, the time of the year, the path through the stars and the maximum brightness are all nearly the same. The only difference will be the observers: instead of professionals, Eros will now be photographed chiefly by amateurs like you.

The picture to the left (click to enlarge) shows how Eros and earth approach each other during the months November through January. Perigee, the shortest distance to earth, will be reached on January 31. Eros will then be 0.1787 AU from earth, peaking in brightness with magnitude +8.56. The picture to the right (click to enlarge) shows how the position of Eros with respect to the background stars changes between January 30 and February 1. The asteroid will slide south through the constellation Sextans during this time, heading away from Leo and towards Hydra, with a rate of nearly 2.8″ per minute, making its movement readily apparent. More excellent charts showing the path of Eros across the sky can be found on the website of Sky and Telescope (if you are living on the Northern Hemisphere) the Royal Astronomical Society of New Zealand (if you’re on the Southern Hemisphere). These maps may be useful to find Eros with your telescope or telephoto lens.

If Eros is observed simultaneously from two widely separated locations A and B, the asteroid will be seen at different positions between the background stars. This difference can be as large as 98″ on January 31. If the two observers both make a picture of Eros and the surrounding stars, the angular separation p between these two positions can be established by comparing the two pictures. This can be done by overlaying the two pictures, as in the image below on the right. In our project, however, you will measure the position (right ascension and declination) of Eros directly from your own picture. From the positions submitted by all participants, the angle p can subsequently be derived. With trigonometry, using the baseline between the observers and the measured angle p, the distance to Eros can be found. Udo Backhaus explains in a paper the math to compute the parallax of Eros yourself and provides an accompanying Excel sheet to perform these calculations on your own.


How to participate

So, you want to help us to measure the distance to the asteroid Eros? Great! Let’s look at the steps which are required. I’ll try to provide a little guidance, but please don’t think that this is the only way to do things.

→ Pick a time to photograph Eros
→ Acquire an image of Eros
→ Match the image to a catalog
→ Determine the RA and Dec of Eros
→ Submit the RA and Dec of Eros

1. Pick a time to photograph Eros
Because Eros is to be photographed simultaneously from different locations, some times should be agreed on at which Eros is visible in the night sky from widely separated populated regions. The three pictures below are showing earth as seen from Eros on three times on January 31. For clarity, the night side of earth has been made light, while the day side has been made darker. At 7:00 UT Eros will be highest in the sky for observers in North and South America, creating a long north-south baseline. At 18:00 UT observers in Asia and Australia will see Eros low in the sky, after sunset and before sunrise respectively. At 23:00 UT observers from Europe can team up with observers from Africa or India. Depending on your location, pick a time and start shooting Eros at these times on the nights between January 28 and February 3. To bypass any disadvantageous weather conditions, you can also take a series of pictures at 15-minute intervals, centred around the time assigned above.

2. Acquire an image of Eros
During this close approach between January 28 and February 3, Eros will have an apparent magnitude of about 8.56. That’s too faint to see with the naked eye, but it should be visible in binoculars and telescopes. There are several ways you might take a picture of the asteroid with a digital camera: you could use a telephoto lens and a tripod and simply point at the appropriate region of the sky, or you could attach the camera to a telescope.

Beware – this will probably take some practice. I suspect that most DSLRs with ordinary camera lenses will require exposure times of at least 20 or 30 seconds in order to record the light of Eros. Your camera might run into problems with such long exposure times; you can practice indoors in a dark room. Special CCD cameras made specifically for astronomical imaging should work very well, of course.

In order for you to determine the position of Eros in your image, you’ll need to be able to see at least 10 or 20 stars. The more stars in your image, the better the chances that you’ll be able to extract a good position for the asteroid. If you can’t see many stars in the image, try increasing the exposure time, or using a lens which yields a larger field of view.

As an example, here’s an image which does have enough stars to provide a good reference for matching. It’s an image taken with an astronomical CCD camera attached to the 0.9-meter WIYN telescope at Kitt Peak, New Mexico. The exposure time was 90 seconds, and an R-band (red) filter was placed in front of the camera. This picture is about 30″ wide and shows an asteroid – not Eros, but one called 2005 YU55.

2005 YU55

Be sure to record the time of your image carefully! Make sure to note the time when you begin the exposure to the nearest second. Try to synchronise your watch or clock to a time standard such as the WWV radio signals or the US Naval Observatory Master Clock. You’ll need to use the mid-point of the exposure as the time for future analysis. So, for example, if you open the shutter at 10:59:43, and leave it open for 30 seconds, the mid-point of the exposure will be at

10:59:43 + (30 seconds / 2) = 10:59:43 + 00:00:15 = 10:59:58

Later, you can convert the time from your local time zone to Universal Time. There are plenty of websites which can help you to perform this conversion – for example, EarthSky.org’s explanation.

3. Match the image to a catalog
Okay, so you have an image of Eros and a bunch of nearby stars. The next step is to match up the stars in the image to stars in an astronomical catalog. We can use the (RA, Dec) positions of stars in the catalog to figure out the orientation and scale of your image; and then, in the final step, we can use that information to determine the RA and Dec of Eros itself. Let’s focus on the matching process here.

Before we begin, make sure that your image is in one of the following formats: JPEG, GIF, PNG, FITS. Only these formats are understood by the astrometric software that we will use.
Matching little dots of light in a photograph to a table of positions in a catalog is a process with a long history. Astronomers have devised quite a few methods over the centuries to help them in this pattern matching. In some ways, it is more of an art or a puzzle than a science.

We will use a very helpful website called astrometry.net to do most of the work. Behind this website are some fast computers, lots and lots of stellar catalogs, and some clever algorithms. If you wish, you can read a technical paper which describes how the site works.

First, go to nova.astrometry.net and sign in. If you don’t already have an account with one of the many supported providers, you may have to create an account with one first.

Next, choose the “Upload” item.

which will send you to this page:

You can use the “Browse” button to choose the appropriate image on your computer into the empty box. Then, you have two choices.

Easy – Click on the “Upload” button and wait. It may take one minute or five minutes, but eventually the web page will refresh itself and show the results. If the page now looks like this, with the word Success, the matching software was able to figure out the identities of the stars in your image. You can skip to the next step now.

If “Easy” fails – then the astrometry.net page will eventually appear like this, with the word Failed. If this happens, you can try to give the matching software some extra information that may help it. Go back and “Upload” the image again, but this time, click on the “Advanced Settings [+]” item.

You should see a number of items which you can specify – it’s okay to leave most of them blank. The two which might help the software to measure your images are

  • Scale: If you can figure out the size of your image – how wide is it, in degrees on the sky? – choose the button which is the best match. You may also choose “custom” and then type your own upper and lower bounds to the size.
  • Limits: If you know where your camera/telescope was pointing during the exposure, you can type the RA and Dec in decimal degrees here. Be sure to convert the Right Ascension into decimal degrees. For example, if your telescope was pointed at RA = 10:33:00, meaning “10 hours and 33 minutes of RA”, then you can convert to decimal degrees like so:

    10 hours + (33 minutes / 60 minutes) = 10.55 hours

    10.55 hours * 15 (degrees/hour) = 158.25 degrees

Despite your best efforts, if the astrometry.net software fails, you may be out of luck. Perhaps you need to take pictures which show more stars, or have a larger field of view.

4. Determine the RA and Dec of Eros
At this point, you should have taken an image of the sky and used the astrometry.net site to match the stars in it to an astronomical catalog. There’s just one more step before you will have the (RA, Dec) position of Eros.

First, you’ll need to download the “astrometrically calibrated” version of your image from astrometry.net Go to the “Dashboard” item on the main web page, and click on “My images.” You should see a page with thumbnails of the images you have submitted. Click on one which was successfully matched to bring up a page like this:

On the right-hand side, you should see a line labelled “New FITS image” (I’ve circled it in red). Click on the link – “new-image.fits” in my example – and save the file to your computer’s disk.

What is it? It’s a version of your image in a rather obscure format called “FITS”, which is used exclusively by astronomers. If you really want to know more about this format, you can read NASA’s HEASARC pages on FITS. The basic idea is to combine the data for an image (the pixels) with a set of information about the image. FITS files consist of a header, composed of ordinary ASCII characters, followed by a the pixel data. If you wish, you can open the image with an ordinary text editor. If you make the editing window exactly 80 characters wide, you’ll see something like this:

SIMPLE  =                    T / Fits standard
BITPIX  =                   16 / Bits per pixel
NAXIS   =                    2 / Number of axes
NAXIS1  =                 2000
NAXIS2  =                 2000
EXTEND  =                    F / File may contain extensions
BSCALE  = 1.000000e+00
BZERO   = 0.000000e+00
ORIGIN  = 'NOAO-IRAF FITS Image Kernel July 1999' / FITS file originator

For our purposes, the important portion of the header is the part which contains the information added by astrometry.net; the first few lines of this section should look sort of like this:

COMMENT --Start of Astrometry.net WCS solution--
COMMENT
CTYPE1  = 'RA---TAN-SIP' / TAN (gnomic) projection + SIP distortions
CTYPE2  = 'DEC--TAN-SIP' / TAN (gnomic) projection + SIP distortions
WCSAXES =                    2 / no comment
EQUINOX =               2000.0 / Equatorial coordinates definition (yr)
LONPOLE =                180.0 / no comment
LATPOLE =                  0.0 / no comment
CRVAL1  =        36.6191898397 / RA  of reference point
CRVAL2  =        16.8128921849 / DEC of reference point
CRPIX1  =        1013.09495192 / X reference pixel
CRPIX2  =        1071.39555876 / Y reference pixel
CUNIT1  = 'deg     ' / X pixel scale units
CUNIT2  = 'deg     ' / Y pixel scale units

This section (which goes on for many more lines) contains information which can be used to convert the (x, y) position of any pixel in the image into the corresponding (RA, Dec) position on the sky. If you had a calculator, some instructions, and a little time, you could do it all yourself.

Fortunately, there’s a better way: let the astronomical image display program ds9 to do all the hard work. Just download the program onto your computer: it’s free, and versions exist for Linux, MacOS, and Windows. Once it’s installed, run the program. Use the “File” menu item at upper left to open the FITS image. You can use the “Zoom” menu item to adjust the display so that all or only a portion of the image is shown, and the “Scale” menu item to change the contrast. If you hold down the right mouse button and move the cursor, you can also modify the display. Here’s my image in ds9 after I played with the zoom and scale:

Note the small window at top right. The yellow arrows and letters indicate the direction of “North” and “East” on your image. Most astronomical charts show North up and East to the left (unlike maps on Earth, which show North up and East to the right).

Now, here’s the best part: because astrometry.net added its section to the FITS header of this image, ds9 will automatically compute the (RA, Dec) position of the cursor as you move it through the image! All you have to do is move the cursor so that it sits on top of Eros in your image, and then you can read its position from the “FK5″ boxes in the ds9 widnow.

Let me illustrate. In my image, the asteroid is the brightest object close to the center of the image. So, first, I’ll zoom in:

Then, as I move my cursor over the asteroid, I can use the small window at top right – which shows an enlarged version of the image near the cursor – to make sure I center the cursor on the asteroid. Now, up near the top of the ds9 window, note the word “FK5″. Next to it are two boxes. The first contains the Right Ascension of the pixel at the location of the cursor, and the second contains the Declination. In my image, the asteroid 2005 YU55 is located at

RA = 02:26:29.99 Dec = +16:47:50.28

5. Submit the RA and Dec of Eros
Once you have these values for asteroid Eros in your image, you are ready to submit your data. Please fill out the following form (you can copy and paste the data from ds9). If you would additionally share your photograph of Eros, you can also email us the original JPEG, GIF or PNG file separately, which will then show up in our depository of pictures for everyone to see.

.

.

From the ds9 program,
. Paste the value or insert it in parts: h m s.
. Paste the value or insert it in parts: ° ″.

, or to be precise, at : : UT.

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