Position of the Moon Equation

[Christian.]

Hello everyone
I am working on an equation to solve for the position of the Moon, which I intend to plug into a very lengthy solar/ lunar eclipse calculation. I am using the formula provided by Jean Meeus in the book Astronomical Algorithms. I understand how the table/ equation works but I am confused on if I include the lines in the table that have no coefficient as + sin(argument) or just not include it at all in the calculation. The instructions in the book either don’t explain what to do at this point or I am miss reading something. This is my first time reading an equation written this way. I will note that I have been to the math and physics/ astronomy professors at my university and they agree it is not that clear on what to do. I will add pictures of my current interpretation and the text itself. Can anyone help? Thank you.

Christian

 

[HallsofIvy]

Exactly what do you mean by "no coefficient"? Something like "\(\displaystyle sin(\theta)\)" has coefficient 1, NOT "no coefficient".

 

[Christian.]

What I mean by coefficient is the column “sigma L coefficient of the sine of the argument”. The last row of sigma L is blank, so do I include the argument or leave the argument out of the calculation? The way the formula works is that, you take the coefficient of the sine of argument and put it in front of the sine. Then within the sine function you place the sum of arguments. For example row 1 of the equation would be 6288774sin(1M’). Then you would add all the calculations. What’s confusing is that the instructions do not state if you include the arguments if there is not a value in the sigma L or sigma r column. The last row of the sigma L column is blank. Would I consider the blank spot as a 1 in front of sine?

 

[Dr.Peterson]

It doesn't make any sense for the default to be 1, so I'd expect it to mean 0 (though certainly that should have been stated).

But since most of the other numbers are much larger than 1, it probably wouldn't make much difference.

Are you sure there's nothing else stated, or used in an example, that would remove the doubt?

 

[Christian.]

It doesn't make any sense for the default to be 1, so I'd expect it to mean 0 (though certainly that should have been stated).

But since most of the other numbers are much larger than 1, it probably wouldn't make much difference.

Are you sure there's nothing else stated, or used in an example, that would remove the doubt?

I don't think this book is online. I purchased it from a publisher of astronomy and math books that specializes in these topics. There is no contact infromation for the author. There is nothing else stated in the instructions for using the equation tables. The reason that it matters is to accuratly calculate the regions of visibility of an eclipse, I need to know the Moons position in the sky up to 1 arcseconds, which could be the diffrence between a total eclipse or partial eclipse. This is the most accurate formula I have found for this calcuation which I will use this value to plug into an eclipse calculation from another book. Its very difficult to find this information. If the value of this coefficient is 0 then I would not have to include. If you ignore the blank space and just add sin(arguments) you get an decimal number.