How to Determine Longitudinal DIstances

By Hersius

Introduction

These articles have continually promoted the believability of the fictional world that John Norman created for the Gor series. Part of the insistence on the verisimilitude of the fictional planet Gor is negative - the refutation of the distortion of distance found on many online maps. For example, the Tahari is not a miniscule blob hugging a supposed crook in the Voltai chain; the rainforests likewise do not comprise a small geographic inconvenience; and Torvaldsland does not span halfway across the northern forests. The other part is positive - the promotion of the simple ideas that when you have a planet of ballpark-definable size, then (1) you have only a set amount of territory in which to locate the places in the books; (2) the placements have constraints based on climate; (3) Norman’s climate-based geography is, in general terms, discoverable; (4) the placements have constraints based on their locales relative to each other; and (5) typographical errors in the texts do not nullify a self-consistent geographic scheme.

One starts, then, with an idea of the size of Gor. Gor is smaller than Earth, so you have less overall space on which to project places. In the March 2003 TGV I argued for the comparison to therefore be made with Venus, since the diameter of Venus is 95% that of Earth. You can pick a size either slightly larger or slightly smaller than Venus to conceptualize the size of Gor. For these articles, I chose a size narrowly smaller so that I would have a figure, expressed in pasangs, that was easy to work with mathematically. This allows for the imposition of longitude and latitude grids and so prepares the blueprint.

Next, since Gor is an Earth-like planet not in an ice age, the climate-based geography of Gor must correspond in general to the climate-based geography of Earth. In the February 2003 TGV I presented a latitude-based climate comparison of Gor and Earth based on information that would have been available to Norman at the outset of his creation of the Gor books. The comparison chart shown in the article strengthens the idea that Norman based his planetary geology on latitude-based climate ideas. This only makes since: the Tahari would not be expected to be found at polar latitudes, nor would a Vosk River that freezes in places in the winter be expected to be found in tropical locales.

Once climate zones can be placed on the planet, then specific places can be projected relative to each other. City A is southwest of City B; Town C is west of Town D; and, if we are lucky, Place E is 400 pasangs from Place F.

When you take into account that a planet has a curved surface, you then realize with a wince that you must use geometry to construct distances between planetary points. These articles have proposed distances and longitude - latitude coordinates for places using assumptions that have been openly held from the beginning. This month, you get to see the math and the resulting tables behind those projections.

The Formula

The formula for longitudinal distance is:

1 degree = 2 x pi x Radius x cosine of latitude / 360

Notice that 2 x pi x Radius is the circumference and that the circumference divided by 360 gives 1 degree around the circle. As a sphere or spheroid approaches a pole, the circle gets smaller. The circumferences of the smaller circles are found by introducing the cosine of the latitude into the equation.

As shown in the February TGV article, one degree of longitude at the equator of Venus is roughly 90 pasangs. I chose 85 pasangs to be the measure of one degree of longitude at the equator of Gor. Whatever distance is chosen determines the attributed distances from that time onward. As long has one has a starting point, one can derive distances, so not only can your mileage actually vary but you can determine by how much it varies!

Choosing 85 pasangs as the measure of one degree of longitude at the equator yields a planetary radius of 4,868 pasangs at the equator.

Rounding pi to 3.14 or using actual pi gives the final staple for the formula. A cosine table provides the final tool.

Here is an example problem to be solved:
What is the (curved surface) distance of 10 degrees of longitude at 60 degrees north (or south) latitude?

The solution:
1 degree of longitude = 2 x pi x Radius x cosine of latitude / 360
1 degree of longitude = 2 x 3.14 x Radius x cosine of latitude / 360
1 degree of longitude = 2 x 3.14 x 4868 x cosine of latitude / 360
1 degree of longitude = 2 x 3.14 x 4868 x cosine of 60 / 360
1 degree of longitude = 2 x 3.14 x 4868 x 0.5 / 360
1 degree of longitude = 42 if using 3.14 or 43 if using actual pi
10 degrees of longitude = 420 pasangs if using 3.14 or 430 pasangs if using actual pi

Application

Here are the tables used in these articles to determine longitudinal distances at different latitudes. If you prefer different starter numbers you can create your own similar tables using the above formula.

Down = Latitude, Across = Longitude

10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90

00 0850 1275 1700 2125 2550 2975 3400 3825 4250 4675 5100 5525 5950 6375 6800 7225 7650

05 0847 1271 1694 2118 2541 2965 3388 3812 4235 4659 5082 5506 5929 6353 6776 7200 7623

10 0837 1256 1674 2093 2511 2930 3348 3767 4185 4604 5022 5441 5859 6278 6939 7115 7533

15 0821 1232 1642 2053 2463 2874 3284 3695 4105 4516 4926 5337 5747 6158 6568 6979 7389

20 0799 1199 1598 1998 2397 2797 3196 3596 3995 4395 4794 5194 5593 5993 6392 6792 7191

25 0770 1155 1540 1925 2310 2695 3080 3465 3850 4235 4620 5005 5390 5775 6160 6545 6930

30 0736 1104 1472 1840 2208 2576 2944 3312 3680 4230 4416 4784 5152 5520 5888 6256 6624

35 0696 1044 1392 1740 2088 2436 2784 3132 3480 3828 4176 4524 4872 5220 5568 5916 6264

40 0651 0977 1302 1628 1953 2279 2604 2930 3255 3581 3906 4232 4557 4883 5208 5534 5859

45 0601 0902 1202 1503 1803 2103 2404 2705 3005 3306 3606 3907 4207 4508 4808 5109 5409

50 0546 0819 1092 1365 1638 1911 2184 2457 2730 3003 3276 3549 3822 4095 4368 4641 4912

55 0488 0732 0976 1220 1464 1708 1952 2196 2440 2684 2928 3172 3416 3660 3904 4148 4392

60 0425 0638 0850 1063 1275 1488 1700 1913 2125 2338 2550 2763 2975 3188 3400 3613 3825

65 0359 0539 0718 0898 1077 1257 1436 1616 1795 1975 2154 2334 2513 2693 2872 3052 3232

70 0290 0435 0580 0725 0870 1015 1160 1305 1450 1595 1740 1885 2030 2175 2320 2465 2610

75 0220 0330 0440 0550 0660 0770 0880 0990 1100 1210 1320 1430 1540 1650 1760 1870 1980

80 0148 0222 0296 0370 0444 0518 0592 0666 0740 0814 0888 0962 1036 1110 1184 1258 1332

85 0074 0111 0148 0185 0222 0259 0296 0333 0370 0407 0444 0481 0518 0555 0592 0629 0666

So, by this table, 60 degrees of longitude covers a whopping 5100 pasangs at the equator but only a mere 440 pasangs near the north and south poles at 85 degrees latitude. At the equator, that same 44o pasangs spans just over 5 degrees of longitude.