Distance to Pluto from two pictures three days apart

[StupendousMan]

Earlier this month, I took some images of Pluto on two nights, separated by three days. Sky and Telescope's July 2010 issue pointed out that in early July, Pluto would pass in front of a dark cloud of gas and dust in the Milky Way, making the little dot of light a bit easier to find, so I gave it a shot with my 12-inch telescope and CCD camera. Success!

One can barely see the motion of Pluto during each individual night, using a sequence of images taken over 2 or 3 hours, but it's really easy to find the object when one compares pictures taken on the first night with pictures taken on the second night.

I was inspired by the apparent motion of Pluto against the distant stars to see if I could work out the distance between the Earth and Pluto, using my pictures and bit of trigonometry. With a bunch of simplifying assumptions, the answer is "yes, and it's not that difficult, either." So, I wrote a detailed description of the procedure and made up a little worksheet, thinking that perhaps some of my students might like to give it a try.

Before they see it, however, I'd like very much to receive comments and feedback and corrections from other people. So, I'm asking BAUT readers to look at the pictures, read the words, and, if they dare, give the calculations a try. You can find a web page with instructions at

http://spiff.rit.edu/richmond/ritobs...luto_2010.html

and the worksheet at

http://spiff.rit.edu/richmond/ritobs...worksheet.html

Please tell me what you think!

[Swift]

Cool idea StupendousMan. Just so you know, I got the error message "The page you are looking for is currently unavailable." from both links.

[StupendousMan]

Aargh. Thanks for that quick response. I've fixed the URLs in my original posting.

[RussT]

Hopefully, Celestial Mechanic (CM) will stop by with some Java

[Nereid]

Some quick comments:

* you might explain where the factor of "0.9425" comes from (this may be superfluous for your students, I don't know what they've already covered)

* "We can look up the speed with which the Earth moves in its orbit around the Sun in many places; its velocity is about v(Earth) = 30 km/sec." - mixing speed and velocity?

* Do you expect any of your students to ask "what if the Earth is ~90^o away from where you put it, in the very simplified view? wouldn't the triangle be a completely different one, and your calculation of the angle differ too?" Was Pluto, in fact, pretty much in the opposite direction (in the sky) from the Sun on those days?

* (scratch that last point, I see you cover it towards the end)

* nowhere do you mention any errors/uncertainties, starting with the data; might it not be a good idea to work that in somehow? For example, you quote 'the answer' to three significant figures (30.9, 29.8), which implies both precision and accuracy to < 1%.

Next: I'll have a go at running the numbers

Great exercise, BTW!

[StupendousMan]

Some quick comments:

* you might explain where the factor of "0.9425" comes from (this may be superfluous for your students, I don't know what they've already covered)

Done. The actual procedure involved measuring positions in pixel units for sixty or eighty stars,
looking up the positions for those same stars from one of the big astronomical catalog,
then performing a large least-squares fit to a linear geometric transformation ...
which is a lot more than I wanted to put into this exercise. I added a short paragraph
giving the general idea.

* "We can look up the speed with which the Earth moves in its orbit around the Sun in many places; its velocity is about v(Earth) = 30 km/sec." - mixing speed and velocity?

Sigh. Yes, I suppose so. The problem is that if I use the word "speed",
people will wonder why the formula have the letter "v" in them.
But any textbook or paper on the subject _will_ use the letter "v"
in formulae, not "s".

* nowhere do you mention any errors/uncertainties, starting with the data; might it not be a good idea to work that in somehow? For example, you quote 'the answer' to three significant figures (30.9, 29.8), which implies both precision and accuracy to < 1%.

Bringing up uncertainties opens a large can of worms, for which I have
no appetite right now. I guess I'll skip this idea, since my goal is
to lead students through the procedure, not get bogged down in
the details.

[Tobin Dax]

I think I might want to borrow this come spring semester.

Very nice, StupendousMan.