Ologrin, the protagonist of LHOSA, advances from a childhood fascination with the sky to becoming the leading expert in his world on the movement of celestial bodies. It is a fair question from the in-depth reader to wonder if his discoveries and conclusions are realistic accomplishments in a late bronze-age society.
From the beginning, Ologrin knows that his world is round. It is not a stretch to accept that a civilization which had rebuilt itself to the bronze-age level would have re-discovered this fact, though certainly not everyone would understand it. Eratosthenes’ famous proof obtained by observing the different lengths of shadows cast by the sun from two different latitudes is credited to Master Crake in Ologrin’s world. Ologrin does his master one better by calculating the distances to celestial objects, but then discovers his conclusions about the immensity of the numbers involved are a hard sell, with political consequences. The question is, could Ologrin realistically have figured out how to make these calculations, and if so, how close could he get to the “truth.”
Ologrin notes at one point that he has estimated the Sojourner to be 28 gross leagues distant. (A league in LHOSA is 3 miles). Thus, he has calculated it to be just over 12,000 miles away. Is it realistic to think he could have made these calculations?
The Polfre retained knowledge of trigonometry (called angular maths in the book) which Ologrin masters. He would have been able to measure the angular width of the Sojourner (0.66 degrees). He also would have known it was at least somewhat farther away than the radius of his world, a number provided by Master Crake’s famous calculation: about 3100 miles. But that alone would not have allowed him to figure out how much farther away.
If, however, he had access to documents describing (lunar) eclipses of the Sojourner, specifically, the time it took for an eclipse to start and end, he could have deduced how much larger the shadow of his world was than the Sojourner. That would have given him enough information to calculate the distance to the Sojourner as multiples of his world’s radius, and thus determine its distance.
I have a computer program that allows me to create artificial solar systems and watch how different objects relate to each other. In order to generate the orbital frequency necessary to create its contrary rising and setting effect, I discovered the Sojourner would need to be about 9100 miles distant and make 2.08 orbits for every revolution of the world. Ologrin’s over-estimation of a distance of 12,000 miles suggests he over-estimated the Sojourner’s angular diameter. He was limited by the precision of his tools.
Ologrin’s calculation of his sun’s distance (48 gross times farther than the Sojourner, he says, which equals 82.9 million miles) is very nearly spot on. (Ologrin’s sun and world are a bit smaller than ours, and thus are a bit closer together than ours.) He could have made this calculation by determining the angle between himself and the sun when the Sojourner was exactly half full (thus at a right angle to the sun) as this would have given him two angles and one side of a right triangle. However, to be so spot on would have meant his measurements would have been extraordinarily accurate, or perhaps just lucky.
Finally, Ologrin determines the distance to the Red Eye to be 18 times the distance to his sun. Absent a quality telescope able to resolve the Red Eye as a measurable disk, he would not have had any way to figure this out himself. So how did he know it? Simple: I told him. He needed to know because you, the reader, need to know, because there is something mysterious about that slow-moving object, something you will learn more about in upcoming volumes.
LHOSAWORLD 