did some math

Another interesting journey...

I started a round of research to learn or verify how to measure double stars with the Meade Astrometric ocular with its illuminated reticule and its central Linear Scale with 50 divisions.

My experience is with the Celestron or baader planetarium Micro Guide (now discontinued) with 60 divisions. 

I had a bad feeling that my method and separation calculation would not work. I wanted to help Melody learn how to use hers but feared my technique would not apply.

"Let's start from scratch," I thought. 

Did some broad internet searches.

Landed in a Cloudy Nights thread started by Jeremy Perez no less. He was trying to learn his Meade Astrometric eyepiece. Perez developed his external protractor. People recommended Tom Teague's method and Bob Argyle's book. But in the end, it didn't reveal to me a formula.

Then I found a thread in the Stargazers Lounge. Davey T asked how to use his Meade (though he showed a reticule image for a Celestron) back in the spring of 2015. William aka Oddsocks gave a procedure referring to a star at zenith. A day later he backtracked. On reading Qualia's notes for a Micro Guide, he realised his instructions were wrong. But he had simply relayed the notes from Meade.

It is strange how you read something from a "respected" manufacturer and believe it must be correct...  I realised the published linear scale calibration method in the Meade document is garbage!

Oh my.

The Meade document is useful in other details but the linear scale calibration method can be ignored unless you are living on the equator

So I still did not have a formula.

But now I was getting more nervous for Melody's sake.

I read Qualia's blog post on measuring doubles and Jovian moons with the baader Micro Guide. Some pretty good notes.

Finally, I found a formula for calculating the drift’s scale constant.

S.C. = 15.0411 * T.avg * cos(Dec) / D

where:

• S.C. - Scale Constant
• 15.0411 - Earth’s rotation rate per hour in degrees
• T.avg - the given star’s mean average drift time
• cos(Dec) - cosine of the star’s declination
• D - number of division on the linear scale

I compared this to my formula:

ρ = D * T.avg * SidFact * cos(Dec) / 4

where:

• ρ - separation in arc-seconds, rho
• D - divisions or ticks on the LS, in decimal form
• T.avg - average drift time in seconds
• SidFact - sidereal time factor or 1.0027379
• cos(Dec) - declination of the star, in decimal form

Some marked differences that unnerved me. Oh boy.

Couldn't seem to find the source for my formula...

Still, there seemed to be something going on here. I could not see it at first... But after a lot of head-scratching and noodling and staring and some home-made spiced rum, I realised what it was.

The 15 (and change) value divided by 60 divisions gave 1/4 (close enough from an aeroplane). That was what I was using in my formula! Whew. They were essentially the same. That was a big relief. So I made a new universal formula considering everything.

S.C. = ( RotRate * T.avg * cos(Dec) * SidFact ) / D

And then you multiple that by the counted ticks on the scale to get ρ, of course.

I really like this new formula since it will work with any reticule regardless of the divisions and as it integrates the sidereal time factor too, which I also cross-checked.

That's produced by dividing 86400 (regular day in seconds) by 86164.0905 (a sidereal day in seconds).

Relieved.

Along the way I could not find an official PDF on the Meade site for the ocular. I could only find it on one of those suspicious manual sites...

But I finally saw it with my own eyes. Step 4: Aim the telescope at or very near (within +/- 5°) the zenith (perpendicular to the ground).

Later they said to take three timings. Ugh. More bad advice.

And there it was in writing, after the step-by-step procedure. Stars at or near the zenith move across the sky at 15 arc seconds per second (sidereal rate).

No. Wrong. Completely wrong.

Wow.

Oddsocks had called it. The true separation formula provided, ( T.avg * 15 ) / 50, would only work for observers at the equator.

So, again, the formula I made should be used:

S.C. = ( RotRate * T.avg * cos(Dec) * SidFact ) / D

This tells you how much real sky is between the tick marks on the Linear Scale.

Sorry. More work. And some trig. Sorry! But you'll get rather accurate results. I tested it in Stellarium with the Meade reticule view.

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In follow-up messages with Melody, I learned that the instructions in her eyepiece box were like the ones I had stumbled across. New eyepiece from a 2021 sale with old bad instructions. Wow. It's amazing to me is that after all these years Meade hasn't fixed it or issued new information. Terrible.