Visual Magnitude, Distance, and Absolute Magnitude

[thnkrx]

I am looking for the formula for determining Absolute Magnitude from a stars distance and Visual Magnitude.

(I used to know this...but then I went ahead and made a chart based on said formula, and then forgot the formula...decades ago - which makes this really annoying. I remember it as being simple, but for the life of me cannot recollect the exact steps).

Anybody know this? And care to walk me through a simple example? Say a star with a parallax of 0.04 (25 parsecs) and a visual magnitude of 7.0?

This is starting to drive me nuts.

 

[adrenalynn]

M=m-5log(d/10)

Absolute Magnitude = apparent magnitude-5log(distance/10) [distance/10 because absolute magnitude is the brightness of a star from 10 parsecs away]

7-5 log(2.5)

Google's calculator says:
7 - (5 log(2.5)) = 5.01029996

I'm in the hot tub at the moment - about the only place I don't have a scientific calculator.

 

[thnkrx]

Thanks!

Logarithms...that explains it.

My current cheapo calculator doesn't do those, which probably explains why I was driving myself nuts.

Is there a way to do the Logs on the regular three dollar calculator?

 

[adrenalynn]

Well, it's really just exponation. That said, I'd be surprised if it would do arbitrary exponation without doing logs.

You do know that you can type just about any ol' single variable equation into Google's search bar and it'll do the math for you, right?

http://www.wolframalpha.com is an online source from the folks that do Mathematica and will handle far more complex calculation than Google.

Also worth noting that Windows built-in calculator (start -> run -> calc [enter] Then View menu, then Scientific option.) will do logs.

A TI 30X or 30Xa can be had online for $7, $10-$11 locally (office-staples-depot-max or wallyworld or target). I see them used online for $2ish. That TI is really a pretty capable calculator. I give them out like candy to students that don't have a scientific calculator. They're really quite capable. The Sharp EL531 is arguably even better for the same money, but I don't see them locally as often. They support Direct Algebraic Logic which is handy for the calculator novice. They also have a massive number of functions that the TI doesn't. I'd recommend the TI through maybe Trig, but the Sharp would support you through Statistics at least.

 

[thnkrx]

Thanx again.

I stopped off at Wally World yesterday and picked up a Texas Instruments 30XA for a little over ten bucks, and after a bit of fiddling, was able to use it to do what I was after.

I don't remember using a scientific calculator when I put together my other chart (distance vs the difference between Visual Magnitude and Absolute Magnitude, in tenth magnitude increments, if that makes any sense), but I might have. I do seem to recollect that putting the chart together was a much easier approach than laborously recalculating absolute magnitude each time, but while real handy, that chart wasn't good enough for my current project.

Next step, figure out distance from the difference between Visual and Absolute Magnitudes. Probably right in front of me...now watch me trip over it.

 

[MeteorWayne]

Excel works great too!

 

[adrenalynn]

And, if you learn Excel, you could get it to generate a new chart for you. Or just type in the variables and have it do all the hard work. Or graph the relationship, or ...

I'll watch you trip over it. If your knees get too skinned up, we'll give you a few hints.

 

[thnkrx]

Actually once I get that far, yes, I do plan on plugging these formulas into a database program. As I remember, this database program can handle logs...but its been a long while since I used it as well, plus I had it installed on a long since dead computer.

Right now, I'm in the...second part of the feasibility stage, to see if what I have in mind will actually work. The first part went really well, this part...well, some of the variences are starting to make me wonder. I might have to do more research.

 

[thnkrx]

Ouch!

Ok...getting to the point where I could use that simple step by step formula for determining parallax when the Visual and Absolute Magnitudes are both known. Not quite to the point of driving myself nuts on this, but getting there.

Simple step by step directions please, as my last math class was decades ago...