Need equations, please

[Jim Eshelman]

I need some equations. Perhaps someone here (Derek?) has them? I used to know them by heart, back in the programmable calculator days of the late '70s, and I haven't had to use them in decades - and no longer know where the file folders are that have them.

I promise I'll make something fun and useful with them

I think these are all I need:

(1) Convert Tropical longitude and latitude to right ascension and declination (and the reverse).

(2) Convert RA and declination (and the other variables, e.g., RAMC and latitude) into PV longitude.

Thirdly, I think there is a generalizable version of the above which allows transformation between any two coordinates sets. This would be useful for experiments, e.g., calculating positions of planets projected against the meridian by great circles through EP-WP, to determine mundane aspects between horizon and prime vertical.

But the first two are what I really need.


My immediate plans are to create an Excel spreadsheet that, among other things, would let planet positions from one chart, in one era, be converted to a mundoscope within the context of a second chart from another era. Simple example: What are the mundoscope positions of your natal planets within your current lunar return? To get this, we need to precess your natal positions to the current SLR date, recalculate RA and Dec, then use this to calculate the prime vertical longitude for the RAMC and latitude of the current SLR.

Here is what the spreadsheet would look like: At the top, you can type in RAMC, geographic latitude, and current and birth SVP - perhaps obliquity of the ecliptic - all available from SF easily). You can set up a permanent spreadsheet for yourself, with your own positions, where one or two of these numbers are all you would ever have to change.

The body of the spreadsheet would have a row for each planet, in which you type the Sidereal longitude and latitude. (Make one for yourself and save it; or save it as a separate tab in the Excel spreadsheet.)

Immediately, it will give the Mundoscope positions (PV longitudes) of each planet.

To put it in the framework of another chart - say, your current SSR or SLR, you just edit the "current SVP" and RAMC fields and, bingo, you instantly have the Mundoscope positions of your natal planets inside the current SSR or SLR. (It's the only way you can REALLY tell how angular your natal planets are in the return chart, or whether there are mundane aspects between them. Everything we do at present is a trick to estimate it.)

There are also other uses. Instant relocation angularity... ways of calculating primary directions... and more.

If someone could just please provide me with the equations I've lost?

Thanks!

[Jupiter Sets at Dawn]

Like this?
(after Geroge Noonan)

α = RA
β = latitude
δ = declination
ε = obliquity of the ecliptic (23°27')
λ = longitude

(1) Convert Tropical longitude and latitude to right ascension and declination (and the reverse).

sin δ = cos ε sin β + sin ε cos β sin λ
tan α = -(tan β sin ε)/cos λ + cos ε tan λ
sin β = sin δ cos ε - cos δ sin ε sin α
tan λ = (sin ε tan δ)/cos α + cos ε tan α

[Jupiter Sets at Dawn]

(2) Convert RA and declination (and the other variables, e.g., RAMC and latitude) into PV longitude.

h = altitude
A = Azimuth
t = hour angle
φ = observer's latitude
θ = Local Apparent Sidereal Time

t = θ - α
sin h = sin φ sin δ + cos φ cos δ cos t
sin A = - cos δ sec h sin t

[Jupiter Sets at Dawn]

Thirdly, I think there is a generalizable version of the above which allows transformation between any two coordinates sets.

No. Maybe Derek knows.

[DDonovanKinsolving]

Mr. E., I have already constructed such a spreadsheet. I will post it as soon as possible. Perhaps tonight.

If you have a preference about how to make it available on the Forum, let me know in the meantime.

-Derek

[Jim Eshelman]

Thanks to both of you.

Derek, go ahead and post it as an attachment. I can extract it and repost it idlf necessary.

Very cool!

[Jim Eshelman]

I've copied off the equations to a place I'll like find them in the future. (Thanks, JSAD, for the reminder that some of this is in Noonan - that's another skinny book I should try to grab from storage next round.) Yes, if you find the generalizable formula, that can be tweaked to move between any two concentric frameworks, we can do all sorts of cool stuff, from meridional longitudes to, perhaps, even galactic plane conversions - that would open up all sorts of vistas of things to confirm or knock down '

Derek, I look forward to your spreadsheet. No panic-level rush, I just suddenly got an inner nudge to do this after all these years (the Tom Mooney example I wrote up yesterday was the active motivation - I've been sitting for years agnostic about whether SLR interfaces should be taken ecliptically or mundanely, and the Mooney example so strongly speaks to mundane that I suddenly wanted a tool to be able to check routinely).

[DDonovanKinsolving]

Oh, drat. I can't get it off my phone into the browser.

Will have to send it later today when I have access to a friend's computer.

To get you started though, create a Solar Fire points file (I named mine Sidereal_Export) with these 19 points:

Moon through Pluto
Chiron
Vesta, Pallas, Juno, Ceres
North & South Nodes
Black Moon
Eris

Obviously, I wrote this with experimentation in mind.

It will be an Open Office Calc file.

In the SF Calculated Charts, highlight the natal chart (this is for the first time through).

Right-click and select Export Charts as Text.

In the new screen, under Select types of points, select Chart Points.

Under Select types of data, highlight Longitude and Latitude (only).

Under Field Delimiters, select Tabs.

Under Destination, select Export to Clipboard.

With this preparation and practice, you'll be ready to take the next step of importing the data. The example spreadsheet will be President Trump's. It contains glyphs, mostly from ET SYMBOL 3 which comes with SF, IIRC. There's a comet symbol from font Astolabe1, whose data would be entered manually.

As Mr. E. has anticipated, after the natal data has been imported and properly sorted, all subsequent input will be the Sidereal Time of the chart in question (SSR, SLR, or whatever),
Obliquity of Ecliptic, SVP of date, and geographic latitude.

The output will be the Campanus mundoscope of the natal planets precessed to date, in terms of house, degree and minute. (Sorry, any other way would have confused me. It helps when writing the values into the horoscope wheel.)

I've been up all night, and now it's beddie-bye time.

-Derek

[DDonovanKinsolving]

Oh, I should also say that precessed RA and Decl ARE calculated, but as intermediate steps toward the mundoscope.

[SteveS]

I get to learn something new that will help us see with return charts. I will have to get my friend to teach me how to use Excel.

[Jim Eshelman]

Oh, drat. I can't get it off my phone into the browser.

Will have to send it later today when I have access to a friend's computer.

No rush.

To get you started though, create a Solar Fire points file (I named mine Sidereal_Export) with these 19 points:

Interesting approach, eager to see it. I'd just contemplated typing in the longitude and latitude. Your way sounds faster and more efficient (I'll make sure that it also works to simply type the positions in Sign Degree Minute Second format. It should be usable, e.g. for mundoscopes, by people who don't have SF.)

It will be an Open Office Calc file.

I suppose I can open that in Excel and convert it? Surely that capability exits (it just isn't evident on an Excel "Open" dialogue.

Under Destination, select Export to Clipboard.

The output will be the Campanus mundoscope of the natal planets precessed to date, in terms of house, degree and minute. (Sorry, any other way would have confused me. It helps when writing the values into the horoscope wheel.)

No, that's perfect!

Get some sleep! This can wait. We're all going to benefit from this.

[Jim Eshelman]

I get to learn something new that will help us see with return charts. I will have to get my friend to teach me how to use Excel.

Yes, you should I use it for dozens of things around here.

This should be quite straightforward, though. We'll make it easy.

For those that don't own Excel, and don't want to spend the money for it, you can get a free web version if you have any Microsoft account, e.g., at Outlook.com. You can register a Microsoft account with any email address, but might (or not) want to get an Outlook.com address to anchor it. In any case, after you have an account on OneDrive.com or Outlook.com (same thing, different roads in), you'll have access to (slightly lower capability) web versions of all of Microsoft Office (Word, Excel, PowerPoint, OneNote, contacts, calendar, tasks, and more, plus a starter block of cloud storage space on OneDrive. That's all free.

[Jupiter Sets at Dawn]

Or you can get Open Office, which is free. https://www.openoffice.org/download/

[DDonovanKinsolving]

Here is the Mundoscope Conversion Spreadsheet for Pres. Trump. (Converting it to Excel format: I've done this before, but it's not doing it now. I don't know why. On the friend's computer that I'm using for internet connection, Excel seems to be set to default, and it opens, but the cell-reference conventions are different in the two systems and so calculations don't carry from one page to another.)

As DDK and I discussed earlier, I've relocated a link to download this, and removed the attachment. You can find the link here.
http://solunars.com/viewtopic.php?f=9&t=1544
-- J.A.E.

First, let's go through how to use it as-is. The President is 71 years old, which is almost one full degree of precession. That can make a bit of a difference in marginal cases; and can make those of us who want it right no end of dissatisfaction with eye-balling it.

In Solar Fire, calculate the chart in question. It can be an SSR, SLR or a simple transit. Highlight the horoscope in the Calculated Charts box. Click on the View Reports icon. At the top of the report, find the values of LST (Local Sidereal Time), Ob (Obliquity of the Ecliptic), and Ayanamsa of date (SVP longitude). Manually enter these into the cells next to the labels LST, epsilon and gamma (I like the Greek letters), respectively. Change the Latitude, phi, if necessary. (I can't get the Greek letters into the Bulletin Board.)

The example provided is for the President's SLR on Dec. 17, 2017 at DC. Down the left, you will see the natal planets in longitude order. The name is spelled out, then its glyph (if you have the font), and then its mundoscopic (Campanus) longitude. Natal Uranus is first in regular zodiacal order, in the twelfth house 23°41' of the SLR. Natal Mercury is angular, at first house 10º18', etc.

For convenience, I've arranged the ten major planets and the two lunar nodes in one block, the four major asteroids in another block, Chiron, Eris and the Black Moon (the other focus in the Moon's elliptical orbit around Earth) in a third, and space for a comet last.

(to be continued)

[DDonovanKinsolving]

Some (such as myself) like to see a circular horoscope with mundane positions of the natal and cycle charts in usual inside-outside format. This can be done in Solar Fire, but remember what you do so that you can undo it when you're done (and almost assuredly, you WILL want to undo it).

First, create a points file with all planets and points de-selected. Name it (for example) None.

Create a Prime Vertical chart for the cycle chart. (Highlight the chart. Chart > Harmonic/Transform > Chart Type to Generate: Z-Analogue Prime Vert.)

Select Bi-wheel view. (View > BiWheel.) Mr. E. has provided a bi-wheel file that orients the chart by the outer wheel, Bireturn.wh2. It's not important in this case, but I leave it as the default bi-wheel anyway.)

SF prompts for Inner Wheel and Outer Wheel. Select the natal chart for Inner, the cycle chart [edit: that's the cycle chart's mundoscope, just created] for Outer, and click View.

The bi-wheel appears. Now come the parts you will want to remember to reverse, so record the settings you have if you are happy with them.

On the right-hand side of the display, at the very bottom, you will see three icons: a monitor, a printer and a printer with a plus sign. These are respectively, settings to control how you SEE the bi-wheel, settings to control how to PRINT the bi-wheel on a single page, and settings to control how to VIEW THE BI-WHEEL IN A SCROLLING MODE. For the time being, we'll assume you want to print the page, so click on the printer icon, in the middle.

You should see the outer wheel with the Campanus cycle chart positions in the outer wheel, and the zodiacal natal positions inside. This, of course, is meaningless. We'll fix that now.

With the mouse cursor anywhere inside the wheel, right-click. A context menu appears, which allows you to control certain features of the bi-wheel. Select the top item, Properties of BiWheel.

The Object Properties menu appears. Points File 1 is the natal chart. Highlight this line. Observe toward the bottom: Select Points File 1 and below that is a box. Click on the indicator, > , to the left. You are taken to a directory of points files. Select the previously created points file None.pts.

You are returned to the Object Properties box. At this point you are free to adjust other items to your satisfaction, including selecting Bireturn.wh2. Click Save.

You are returned to the Printer View of the bi-wheel, and you should see that the Inside wheel is blank, yet its Chart Details are still present.

Print the page. You are now ready to manually write (yes, write) the planets and their mundane positions into the blank inner wheel. Since the natal planets have been pre-sorted by longitude in the sample spreadsheet of President Trump, you may start at the top of the list and work your way around sequentially.

Remember to reverse the settings so you don't print future bi-wheels this way inadvertently! Since you haven't made changes to Monitor View, it will look perfectly normal on the screen, as it is the default view.

(to be continued)

[DDonovanKinsolving]

Now we come to the most important part, using this sample as the basis for other charts.

First, make a copy of the file and work with that. Do not use or modify the original, because if you make a mistake you want a good original to go back to. This is basic, sound procedure generally when working with computers. It's good practice to copy and name the file to, say, the person's name.

In Solar Fire, set the default Displayed Points as Sidereal_Export (as described in an earlier post). Select the natal chart you will use, usually your own or someone else you do a lot of work with. Follow those instructions to the point where you have exported to the clipboard. You are now ready to bring the data into the copy of the spreadsheet.

Bring up the spreadsheet you're using and modifying. At the bottom you will see three tabs, Main, Calcs and Natal.

I'll digress for a moment and briefly explain each of these pages.

“MAIN” is the top page, where you will eventually do all your routine work of entering the changeable data, and you see the final results of the mundoscope.

Next down is “CALCS,” the workhorse of the spreadsheet. It takes the stable information from “NATAL” and the changing information from “MAIN.” It processes precession, displays precessed Right Ascension and Declination, and computes the Campanus Mundoscope. Don't mess with this unless you really know what you're doing. Since this is a project I return to now and again, it's not perfect, but it works. (E.g., What's that TRANSITS doing above the Comet line? Maybe a place for a transiting comet instead of a natal one?)

The final page is “NATAL” and this will be where we will be putting the focus on now. Once you have made changes here, you won't need to return to it. So click on that tab marked “NATAL” to go to it.

In cell O6 you see the instructions STEP 1: IMPORT HERE. Having exported successfully from Solar Fire, place the cursor in cell O8, right-click and Paste. A new box appears. The parts we are interested in are: Separated by – check "Tab"; Other options – check "Detect special numbers"; this is important, as this handles values close to zero and infinity, and we are always dealing with at least one value that's always zero, the latitude of the Sun. There is a graphic at the bottom previewing the results. There should now be nothing obviously wrong, as OO Calc now detects the properties and values of what you're pasting.

Click OK. The columns include the point name, the point abbreviation, the sidereal longitude and the declination. These are in the order Solar Fire determines, so now we have to put them in a new order that's more useful to us.

Select this range, from O8 to R26, and Copy it.

In cell J6, you see the instruction, STEP 2: SORT BY LONG. HERE.
So place the cursor in cell J8 and Paste. You will probably get a warning message that you are pasting into cells that already contain values. Of course, this is what you want to do, so say yes.

We will now sort this information into a more useful order. The pasted area, J8 to M26 should still be shaded; if not, select that area. In Open Office Calc, click Data > Sort. (If you're using another program, you must follow its procedure for selecting a sort range and telling it to sort.) In Open Office Calc, a Sort box opens, allowing you to define up to three sorting criteria. Since mathematically exact conjunctions are rare, we need define only one. (in the case of New Moons, or other conjunctions, I imagine you could add a sort by name.) In the first box, Sort by Column L Ascending. Click OK. The natal points are sorted by longitude.

My apologies to everyone. This is where the procedure becomes very manual. No doubt, there is some instruction set that would make the next part easier and automatic. I can live with it as it is, but probably not others, so this spreadsheet is not really ready for wide release. I can tinker with it some more.

Guided by the numbers in column I, go through the list and copy and paste the longitudes (column Q) and latitudes (column R) and paste starting in column C so that Latitude also gets put into column D. Change the name and glyph in columns A and B as you go. If you mess up, there is a list of names and glyphs over in columns T and U. I think I intended to create some kind of Lookup Table to take care of all this, but Life Happened and I dropped/forgot it.

The idea is to copy the ten main planets' long. and lat. in longitude order, matched of course by the appropriate glyphs, then the four asteroids, then the 3 outliers. Once that tedious part is correctly done, copy the names and symbols and paste them into the appropriate places in pages MAIN and CALCS. This needs work also, so that changes here are carried over to them instead.

In fact, the more I think about it, the more annoyed I am that it's been left so obviously unfinished, so I promise to get this part up to snuff in short order.

Until then, the main part of Mr. E's request has, in my humble opinion, been provided.

As usual, feedback is welcome.

[SteveS]

Thanks Derek. When using Natal positions and correcting for precession, do we always use the residence location?

[Jim Eshelman]

Derek, thanks so much. I'll work through all this as I have time, but my first priority will be getting this working in Excel.

When I save it as an Excel file, it complains that it won't work right, but it then appears not to be broken. At least, a small change in a longitude produces a small change in the output, so at least it's still calculating something and updating. I'll have to drill on it.

(Why am I so intent on converting it? It's a personal ethic that has nothing to do with your work or, perhaps, even this site. I committed long ago to make no personal contribution to supporting the companies intent on disrupting Microsoft's hegemony. For me, it's platform platform platform. I will own no Apple-based device, nothing running a Google OS, etc. - my money won't support their efforts. If the phone market eventually narrows down to entirely iOS and Android, I'll actually have a hard choice to make, and may feel I have to stop having a cell phone - it's that big of a deal to me. So... whatever time and effort it takes me to convert this to a fully working Excel framework, I will happily do. And then I'll be back! <s>)

[Jim Eshelman]

As an update - simply by opening in Excel 2016 and saving back as an Excel file, everything seems (on minimal testing) to be working fine. I'll repost later after I do more exhaustive stuff, but anyone can do the same thing with an Open and a Save As.

[Jupiter Sets at Dawn]

(I can't get the Greek letters into the Bulletin Board.)

The name is spelled out, then its glyph (if you have the font)

What is Bulletin Board? Is it like Clipboard?
Which font?

[DDonovanKinsolving]

Thanks Derek. When using Natal positions and correcting for precession, do we always use the residence location?

No. Whichever place you've calculated the chart for, use that Sidereal Time and latitude in the spreadsheet. Take it from Solar Fire.

[DDonovanKinsolving]

... my first priority will be getting this working in Excel.

...

I committed long ago to make no personal contribution to supporting the companies intent on disrupting Microsoft's hegemony. For me, it's platform platform platform.

Mr. E., thanks and you're welcome.

My priority last night was to get directions up on the Forum, and then work on making the spreadsheet easier to use for people. I made
progress on that, I think, but need to take it through more testing and thinking.

From my cursory examination, it seemed to me that you should focus on the convention Excel has to reference other pages.

Not breaking Microsoft's hegemony is a personal ethic? That sounds so strange to me.

[DDonovanKinsolving]

(I can't get the Greek letters into the Bulletin Board.)

The name is spelled out, then its glyph (if you have the font)

What is Bulletin Board? Is it like Clipboard?
Which font?

Sorry, I meant the Forum, Solunars.com. On my home computer, using Open Office it worked fine, since I was using native Courier New, but when I tried Copy/Paste here they wouldn't carry over. After some sleep and thinking about it, I can think of at least one other reason that might have happened, but there's nothing I can do about it right now. Maybe I should have tried opening the file on my friend's computer with MS Word.

[SteveS]

Thanks Derek.

[Jupiter Sets at Dawn]

Sorry, I meant the Forum, Solunars.com.

Oh. Shoulda twigged to that sorry.

Courier New, but when I tried Copy/Paste here they wouldn't carry over.

Sometimes some symbols work here, and others don't. This board works on BBCode, and it just depends on which fonts are available in the board styles that are installed.

[Jim Eshelman]

I am ready to put this to a practical example and test.

According to Bradley in Solar and Lunar Returns, Tom Mooney was born December 8, 1882, 4:09 AM LMT, Chicago, IL, and was given a full, unconditional pardon on January 7, 1939, when he was in San Quentin, CA.

Elsewhere on this forum, I wrote of his SLR for his release as follows:

In contemporary style, we can't miss the 0°00' Moon-Venus conjunction, though we have to admit it's quite background. Foremost, Mercury is within a degree of Ascendant and - one has to look for it - sesqui-square Pluto 0°23'. This was, indeed, a dramatic, life-altering signature!

Sun is barely foreground... The rising Mercury conjoins natal Sun, Mars, and Venus. I'm not sure about the Mercury-Mars, but the other two (especially Venus) are quite appropriate. Can we learn something about mundane vs. ecliptical from the deployment? Here is a list of the planets, their zodiacal degrees, and the degrees with which they rose. First, the ecliptical:

18°17' Sco r Mercury
20°22' Sco r Venus
21°05' Sco SLR Ascendant
22°34' Sco SLR Mercury
23°09' Sco r Sun
23°53' Sco r Mars

Next, giving the planets by the degree where they rise, rather than their longitudes:

18°39' Sco r Mercury
20°11' Sco r Venus
20°38' Sco SLR Mercury
21°05' Sco SLR Ascendant
23°09' Sco r Sun
24°16' Sco r Mars

This is great! Notice that, when taken mundanely, transiting Mercury is exactly conjunct natal Venus - the best aspect of the set for an unconditional pardon! It is next closest to his Sun (the second best), and farthest from natal Mars (the one that almost doesn't make sense). This is an important example that gives us a rare chance to look at the difference in mundane vs. ecliptical behavior in the SLR!

I was using the "show the longitude with which a planet rises" trick to estimate the actual mundane orbs, proximity of natal planets to the angle, transits to natal planets, etc. With Derek's spreadsheet, we have a way of calculating this directly, and therefore have a way of testing which approach gives us better results.

[Jim Eshelman]

So, taking the positions ecliptically, we have:

18°17' Sco r Mercury
20°22' Sco r Venus
21°05' Sco SLR Ascendant
22°34' Sco SLR Mercury
23°09' Sco r Sun
23°53' Sco r Mars

Taking pseudo-positions that are meant to infer mundane positions, we have:

18°39' Sco r Mercury
20°11' Sco r Venus
20°38' Sco SLR Mercury
21°05' Sco SLR Ascendant
23°09' Sco r Sun
24°16' Sco r Mars

Let's compare this to real calculations.
It's easy enough to calculate the mundoscope by our usual methods. This gives us:

(12) 29°16' - t Mercury
--------------Asc ----------
(1) 9°26' - t Sun

Using Derek's spreadsheet, I copy the RAMC (LST), obliquity, SVP, and geographic latitude of the SLR on the first page. I export Mooney's natal planet longitudes and latitudes to the spreadsheet and generally tweak the data as he recommended. Soon, the desired calculations appear on the Main tab, as follows. Remember, these are the precessed mundoscope positions of the natal planets within the framework of the SLR. (You can compare them against the actual two-wheel SLR for comparison; I recommend that you do. As above, I have put the house number in parentheses before the degree and minute values within the house.)

(5) 28° 32' Neptune
(6) 3° 29' Saturn
(6) 7° 26' Pluto
(7) 11° 11' Jupiter
(9) 19° 58' Uranus
(12) 3° 25' Moon
(12) 27° 23' Mercury
(12) 28° 50' Venus
(1) 1° 36' Sun
(1) 2° 37' Mars

Here I will rewrite the relevant parts near Ascendant, interweaving the transiting (SLR) planets:

(12) 27°23' r. Mercury
(12) 28°50' r. Venus
(12) 29°16' - t Mercury
--------- Asc 0°00' ---------
(1) 1°36' Sun
(1) 2°37' Mars

And, to make comparison easier, here are the pseudo-longitudes:

18°39' Sco r Mercury
20°11' Sco r Venus
20°38' Sco SLR Mercury
21°05' Sco SLR Ascendant
23°09' Sco r Sun
24°16' Sco r Mars

This proves the basic point I was estimating originally: The closest transit mundanely is transiting Mercury to natal Venus - he got really happy news. Ecliptically, SLR Mercury was just below Ascendant, partile conjunct natal Sun, nearly partile conjunct natal Mars, and farthest (over 2°) from natal Venus. Mundanely, this is reversed: SLR Mercury is 0°26' from conjunct natal Venus, over 2° from Sun, and over 3° from Mars. Venus is the one we wanted closest, Mars the one we wanted farthest, and the mundane accomplishes this.

What do we learn about the accuracy of our pseudo-longitude estimation system? Well, the Mercury-to-Venus orb is 0°26' actually, and 0°27' by my earlier estimate - which is pretty good! Mercury-to-Mars is 2°21' actually (by the carefully calculated mundoscope) and 3°38' by my earlier estimate, which is good for crude work, but not at all for precise work. It's better to have this new calculation tool.

This is the kind of thing I anticipate our using it for.

[Jim Eshelman]

This can be used for a single chart such as a natal, also. It is (among other things) a way to calculate the mundoscope if you don't have Solar Fire, but do have the longitude and latitude of the planets. In this case, of course, the four values at the top of the Main page are those of the birth chart.

(I hope Arena sees this. It will be of great value to her.)

I calculated my own natal mundoscope this way, and got the following table. (The three numbers of each line are the house, degree, minute.)

Mon 6 26 45
Sun 1 19 19
Mer 2 14 34
Ven 2 29 32
Mar 4 27 40
Jup 11 2 54
Sat 2 11 2
Ura 11 2 33
Nep 1 27 33
Plu 11 28 19

Now, here's the next cool part: To relocate it, I only need to change two numbers, and everything recalculates! Change the LST and geographic latitude to those of the new location, and, as fast as you can hit the Enter key, you have the new mundoscope positions.

Mon 7 23 21
Sun 2 19 12
Mer 3 14 53
Ven 3 28 51
Mar 5 23 59
Jup 11 29 19
Sat 3 13 17
Ura 11 28 56
Nep 2 28 46
Plu 12 24 5

[Jim Eshelman]

I will post Derek's original and my simplified version in a thread in the Solar Fire section (just to have some place to put it, though I suppose it could go under Angularity). I want to create a better version that takes simpler input for those who are adding longitudes and latitudes manually (this will be forthcoming).

[DDonovanKinsolving]

Thanks for simplifying the spreadsheet, Mr. E. Just the ten regular planets is good enough for basic work for everyone.

I'm still testing a revision of the elaborate original. I think the biggest ease-making step will be in making Macros, but I need to be sure that Sorting isn't jumbling equations.

When I get a chance, I'll also check it, but it looks like you've done enough cross-checking that any discrepancy would have stood out.

-Derek

[Jim Eshelman]

Yes, I liked the idea of sorting - thought I could do it in the very last step, and then realized it WAS (at that point) shuffling equations - so I let it drop for now.