Observatory Construction :: Maths to the Rescue!

[AweSIM]

I've been wanting to construct an observatory on top of my house for a long time and am finally almost ready to build one. I settled for a roll-off roof design with the observatory being almost 10 feet by 10 feet and 7 feet high. I'd park my telescope in a horizontal parking position. My main concern was that what if I construct the observatory room too small or too tall so that it blocks out a good portion of the sky that would otherwise be accessible to me without an observatory. This post is more of a blog about my journey thus far, in hopes that others might find it interesting or useful.

I came across an article online (don't remember the source, sorry) that showed how to show a custom horizon in Stellarium. I climbed onto the roof where the proposed observatory is supposed to be built and shot a 360 degree spherical panorama using Google Traffic app for Android. I exported the unwrapped 4096 x 2048 pixel image and edited it using Photoshop to make the sky transparent. An interesting problem I encountered in this process was that the horizon is not always in the middle of the image, so I needed to have a reference object in the same 360 degree panorama at the camera level. Being at the same level, it should touch the horizon, and this means that the top of this object should lie in the exact middle of the unwrapped image vertically. If it is not, the entire image can be shifted up or down till it is. Finally, I crafted a suitable "landscape.ini" file to reference the unwrapped image and define its Z-rotation and packed these assets into a zip file. Finally I imported it into Stellarium and viola! I could see my custom horizon perfectly. Stellarium now showed me views exactly as it would appear as if I stood at that spot myself. This step helped confirm if the spot I had chosen for my observatory was good or not (It was! Only 10 degrees above horizon was blocked, except south-east where almost 30 degress above horizon was obscured by trees).

However, the issue still remained whether the observatory, once constructed, would block significant portions of the sky or not, and there was no easy way to test this. So I decided to put my software development skills to the test to address this. The proposed observatory is about 10 feet by 10 feet in size and about 7 feet high, with the scope placed in the middle of the room. With the walls so close to the telescope, parallax plays an important role.

I created a quick programming project in TypeScript, included a good matrix maths base library, and created some 3D math classes on top of that to work with vectors, matrices and calculate ray-triangle intersections, etc. I created a basic 3D model of my telescope and mount such that the camera it looking out along the axis of the telescope, and can rotate like an equatorial mount along RA and DEC. I also created a very simple model of the proposed observatory with four walls, each made up of two triangles.

The code loops thru each possible value of RA and DEC and computes where the telescope is pointing in the sky. It then computes if there is a wall triangle in between the telescope and its target. If there is, the code converts the direction the telescope is pointed at into polar coordinates (alt-azimuth) and plots a point on a graph where horizontal axis is azimuth and the vertical axis is altitude. If there is no triangle between the telescope and its target, it means that the sky is visible in that direction.

This allows me to generate an 360 degree unwrapped panoramic image much like the horizontal I captured earlier. Using photoshop, I overlaid the custom horizon on top of the generated image to get the following image.

This image clearly shows that the walls of the observatory don't obscure any significant additional portion of the sky, and hence the design is perfect from the perspective of viewing angles. Furthermore, we can also create a custom horizon out of this image and import it into Stellarium.

Thank you for reading this. 😃

Edited October 17, 2020 by AweSIM

[fifeskies]

It looks like your ROR walls will be blocking most of the lights around you as well which is a bonus.

I actually made my walls high enough to block most of the distractions around me and made a fold down flap to the south where I could catch the few objects at low altitude I wanted to see sometimes.

Also helps to keep the breeze away from the telescope.

 

I made a custom horizon too when I was planning my ROR position , it helps a lot to visualise what you are going to get once it is finished.

[AweSIM]

@fifeskies you made some interesting observations and thank you for sharing your experience as well. You're right about the ROR blocking most artificial light sources in my neighborhood. But what surprised me the most was that even though the telescope will fit inside the room, it will still be able to see so close to the horizon.

For me, the most fun part was programmatically generating a horizon for the room itself. Also, now that I have the horizon image, I can also use it to program mount limits in EQMOD, although that might be an overkill. 🙂