Parallax Limitations: Measuring Distances Miles Away

[nmsurobert]

I'm setting up a lab for my astro students relating to parallax. We will be using some pretty simple tools. Measuring tape and a protractor with a straw fastened to it. I know that calculating distances with tools like these work in the classroom but what if I wanted to calculate the distances of something that was several miles away. Like, a mountain peak. Would this still work?
I haven't attempted to do it myself. I thought I would ask before I went through the trouble of trying to set this up only find out that it doesn't work out or that I'm missing something. I know that the baseline has to be wider. For something across the room, a baseline of 9 ft will do. But I imagine that wouldn't work for something that is ten miles away. The angle would be too narrow. Is there ratio that exists for how wide a base line should be for a certain distance? Any feedback would be helpful. Thanks!

 

[scottdave]

You should be able to do tte math, but maybe try with a map to see what would be minimum distance to get a decent angle difference.

 

[nmsurobert]

You should be able to do tte math, but maybe try with a map to see what would be minimum distance to get a decent angle difference.

Now that I read your post, doing the math should be pretty simple lol. Thanks.

 

[stefan r]

You must have a mountain 10 miles away. Use that as the non-varying background. Find a point source feature on the mountain, probably the peak but could be any spot that is easy to describe and less than 1 arcminute diameter. Compare that point to Andromeda galaxy or Deneb. Use a flag pole, goal posts, power line pole or a pointed building feature(antenna, steeple etc) as the object you are measuring the distance to.

It might be better to remain confined to the classroom. That forces the idea that you can only make your measurement inside a confined spread. You would need an upper floor room with windows and an unobstructed view of the horizon. You have a 4 meter spread in the windows so you get a 2 meter astronomical unit equivalent. A parsec equivalent is around 400km away. An object 7 km away should have less than 1 minute of arc paralax. That is the limit for 6/6 (20/20) vision. So no student with 6/6 vision or worse could see any change in a 7km object even if they had tools that sensitive enough to measure minutes of arc. Using a protractor and the window frame is unlikely to get better than single digit degrees. So your foreground objects should be within tan 1°, within 60 meters of the windows.

You could have them do the measurements at the windows but do them yourself with similar tools and a camera. Draw the protractor into the images on your computer. That gives you a printout with a measurement so you can test if a student can calculate the distance when given a specific angle.

 

[scottdave]

Like @stefan r pointed out, the resolution of measurement will be a limiting factor. Nice walkthrough.