Monthly Archives: October 2013

Proving Heliocentrism with a Small Telescope

David Hogg has a blog post about measuring the speed of light with Kepler.  This is actually closely related to an idea I’ve wanted to blog about for a while now.

As the Earth orbits the Sun, the stars seem to change position.  The analogy often used to explain this is that you imagine you are in the back of a moving pick-up truck, and you want to catch rain (which is falling straight down with no wind) in a deep bucket.  You should not hold the bucket vertically, because you are moving laterally and rain will hit the side of the bucket.  For optimal rain catching you should tip the bucket in your direction of motion by an angle equal to the arctangent of your velocity divided by the speed the rain is falling.  By “leading” the rain like this you will get maximum rain in the bucket, because no rain will hit the sides of the bucket: it will all fall straight to the bottom.
Likewise, as telescopes collect light from stars overhead, we have to “lead” the photons by an angle equal to the arctangent of the Earth’s velocity through space divided by the speed of light.  If one could measure this effect, one would be measuring the speed of the Earth around the Sun in units of the speed of light.  Equivalently, one would prove that the Earth orbits the Sun, and even measure its speed.
Now, this is actually hard.  Radio telescopes point this well, so handle this effect, but most optical telescopes don’t worry about it too much because you just get close to your desired coordinates and then find your object (or nearby objects) to correct for the inevitable pointing errors.
To really do this right, you would need to know about an absolute position on the sky, and then measure the motion of stars with respect to that position as a function of time of year.  Over the year, they should seem to move by 30 arcseconds (1/120 of 1 degree — that’s a lot to an astronomer) in an ellipse with respect to that point.
The problem is the absolute pointing — how can you find a spot on the sky to that precision over the course of a year?  Also, stars move through the night, so you’ll have to very carefully observe at the same sidereal time every night, which is tricky.  Also, differential refraction in the atmosphere is a function of time and wavelength… the whole problem is hard.
EXCEPT…
There is one spot on the sky where this works.  The North Celestial Pole — the point in the sky directly above the Earth’s rotational axis.  By exposing a camera for a long time (hours) while pointing at this part of the sky, one can find the North Celestial Pole because the stars will form star trails around that point.  As the year progresses, the center of these trails will seem to change — really the apparent positions of the stars are moving because of aberration as the Earth goes around the sun.
TRAILS.JPG
Now, there are complications:
  • Finding the coordinates of the apparent NCP in an image of star trails is not standard image analysis — you’ll need some sort of custom Hough transform or something.
  • Atmospheric refraction will complicate things, so you should chop between multiple filters to remove it
  • Polar mounted telescopes usually can’t point to the NCP (although if you can rotate the MOUNT it would work, because you’re going to turn off tracking)
  • Some stars may show parallax or proper motion — correct or remove them
  • The precession of the equinoxes ALSO causes the NCP to appear to move (in this case it really is the NCP that’s moving, not the images of the stars!)  You’ll have to track things for multiple years to disentangle the aberration (an annual ellipse) from the precession (a secular, almost linear trend).  This problem is analogous to disentangling proper motion and parallax for images of stars.

So, it’s a multi-year project to demonstrate an effect that everyone knows exists.

But if you do it, you’ve measured the velocity of the Earth’s orbit around the sun and proven that Copernicus was right!
Someday I’ll write and execute the observational lab…

George Herbig (1920-2013)

George Herbig passed away peacefully yesterday at home in Honolulu.  He was 93.

George was my grand adviser, of a sort.  When Geoff Marcy was earning his PhD at Santa Cruz Steve Vogt was his formal adviser, and George worked closely with him, teaching him spectroscopy and his philosophy of observational astronomy.

hh563-5.jpgMost students will encounter George’s name when they learn about Herbig-Haro objects.  These “objects” are the bow shocks formed when a bipolar outflow from a forming star forms a jet of material that collides with the gas and dust in the interstellar medium.  George determined that they were the products of star formation and elucidated their true nature.

I met George Herbig exactly once, when he was about 85 years old.  He was observing at Keck Observatory the night before I was on with Geoff Marcy, and I stopped by the control room in Waimea to say hi.  

I asked what he was observing, and he told me he didn’t know!  Someone had found something strange, so he had gotten a night of HIRES time to see what it was.  He was taking the first spectrum as we chatted.  In retrospect, I think this was part of his campaign to study V1057 Cyg.

As the first spectrum came up, he zoomed in on a line and took a cut.  When the spectrum came up, I instantly recognized a P Cygni profile, and asked if that was it was.  He said “apparently so!”  In retrospect, he must not have been surprised to see it, but I think he was emphasizing his philosophy of being ready to be surprised, and not presupposing you know what a strange (and time variable!) object will look like next.

The next night, I was going through the California Planet Survey HIRES checklist.  HIRES has a set of “standard” configurations for typical observing modes, and sometimes other astronomers use these for something other than planet hunting (the nerve!).   Our checklist makes you check off every “knob” that can be “turned” on the HIRES GUI and be sure it’s set properly, even though most of this is perfunctory — many of the settings are rarely changed except in rarely-used configurations, and some of the settings are pretty obscure or obsolete and are essentially never changed in any mode.  

So I was surprised when a rarely changed item on the list needed addressing before I could check it off.  I was doubly surprised when a second rarely-addressed item needed me to move an element in the spectrograph back to its “CPS standard” value.  Then there was a third one.

George had tuned every-single–setting on HIRES to be exactly what he wanted it to be.  I’m not sure how many astronomers there are that would have a preference for every setting on HIRES.  Maybe just him and Steve Vogt (who built it!).  George was as expert an observer that ever lived.

George’s adviser at Berkeley was Harold Weaver.  Harold celebrated his 90th birthday in 2007, and, last I saw of him in 2007 or 2008, was still going to work in his office at Berkeley on a daily basis.

Geoff Marcy sent members of his old group at Berkeley this email to inform us of the sad news, and included this note about him:

George received his Ph.D. from UC Berkeley in 1948.
George took me observing at the 120-inch telescope every month for four years.  He patiently taught me spectroscopy and he led me through many projects.   Among them were studies of the binary nature of the central stars of planetary nebulae, the hydrogen emission-line variability of T Tauri stars (on the Crossley telescope), Zeeman measurements of Sun-like stars, and the binary frequency of T Tauri stars.  For that last project, George urged me to make ever more precise radial velocity measurements of stars.  I’m still working on it.
Most of all, George taught me to work carefully, to double-check all measurements, and to draw physically meaningful interpretations that don’t stray too far from the data.  George’s approach to research influenced all of my work.
Last year, Dave Soderblom and I visited George, at 92, at his home.  He asked about everyone at Santa Cruz and Lick Observatory.  Then, he eagerly brought out three or four research papers he was still working on, encouraging us to solve enigmas he found in the spectra.

Herbig.jpeg

Geoff Marcy, David Soderblom, and George Herbig, in June 2012 at George’s home in Honolulu