Sunday, October 27, 2013

Motion of the Moon (or Moons) around the Earth

The next details to work out have to do with the Moon or Moons of your world. The Moon and Sun are responsible for the tides on Earth, and the cycle of the Lunar orbit has a large effect on life on Earth.

In addition to the influence of the Moon in an ordinary orbit, eclipses of the Sun or Moon are very impressive experiences and have played a role in history many times. Eclipses are tricky to model and I am not sure yet how to handle them so I am going to leave them out of the Quick Start for now. I hope to figure out a good model for them and will update this post after I do.

The period of your Moon's orbit around your world is the first thing to decide. You may or may not have a unit of time between a day and a year based on this period, but that is something to think about. This period will be the mean time from a phase -- full Moon for instance -- to the same phase in the next orbit. Depending on the orbit, this length can vary quite a bit as it does for the real Moon.

Until I have figured out how to handle eclipses there is not much point in determining other features of the Moon's motion. The orbit of the Moon is slightly inclined to the orbit of the Earth so that the Moon crosses the Earth's orbital plane twice per orbit. If the Moon is full (in other words, the Earth is directly between the Moon and Sun) at the very moment that the Moon is crossing the Earth's orbital plane, there will be a lunar eclipse. If the Moon is new (in other words, the Moon is directly between the Earth and Sun) at the moment the Moon is crossing the Earth's orbital plane, locations on the Earth directly behind the Moon from the Sun will have a solar eclipse.

Rotation of the Earth and Motion of the Earth Around the Sun

You may have already determined the length of the day and the length of the year in your world. If not, these are the first things to determine in creating the astronomy of your world. It is best to stay close to the values of the present day Earth if you want an Earth-like world. Throughout the Quick Start guide I will assume that an Earth-like astronomy is being generated, since picking values far from those of the real world may require a lot of astronomical knowledge to ensure a realistic outcome.

The first value to record is the length of the day in your world. How long is it from noon on one day until noon on the next day? If you have elliptical orbits (as we have on our Earth) this value will vary throughout the year, so pick the average value. You should also give some thought to how time will be measured in your world (keep in mind that sticking to a system close to ours will probably be easier on your players). You might want to read about historical timekeeping devices like sundials and waterclocks.

Next record the duration of one orbit of your Earth around the Sun relative to the stars. Assuming the direction of the rotation axis of the Earth moves very slowly (the Earth wobbles like a spinning top, with a circuit being made every 26,000 years or so) relative to the length of the year, this duration will correspond to 1 year in civic life since the seasons will repeat with this duration.

If your year length has a fractional day, you will need to modify some year lengths to keep your calendar in step with the seasons. The calendar we use today inserts a leap day every 4th year (most of the time - not always!) to keep the seasons in step with the calendar, but that is not the only way this can be done. Extra days can be inserted into the calendar when needed or at the whim of a ruler. These extra days may or may not be part of the count of days in a month. Multiple days can be added at once.

Now you should decide what the inclination of the Earth's axis is. Using a value close to the 23.4 ° value of the actual Earth's axis is probably best unless you want a climate very different from Earth's. It is this tilted axis that accounts for the seasons on Earth, with northern summer occuring when the north pole of the Earth is pointing toward the Sun, and northern winter occuring when the north pole of the Earth is pointing away from the Sun (the southern seasons are reversed since the south pole points in the direction opposite to the north pole). This value will be used later to find the path that the Sun, Moon and planets will appear describe in the sky of your Earth.

At this point you have enough information to begin working on a solar calendar, which will be very useful for societies to regulate agriculture, determine when it is safe to sail, roughly predict the weather and so on. You might want to wait until after you generate the data for one (or more) Moons to create your calendar in detail, but it is not too soon to start thinking about month names and deciding what you will do to keep the calendar synchronized with the seasons on your Earth. You can also think about having a unit of time less than a month but greater than a day, but again you might want to wait until you have thought about a Moon or Moons before determining this.

Saturday, October 26, 2013

Astronomical Creation for Fantasy Roleplaying Games - Introduction

The astronomical setting of the real world has a large impact on the environment and cultures of our world, and likewise the astronomical setting of a fantasy world should have a large impact on the environment and cultures of that world. While some campaigns go to an effort to determine a few astronomical details for the campaign world -- often to come up with a unique calendar such as the calendar of Greyhawk, or some information on the moons, as in Glorantha -- I think that much more can be done to add to the detail of FRPG campaigns with fairly little effort by developing a detailed astronomy.

Most people lack the astronomical knowledge to develop this sort of background for their campaign world, and it would be very difficult and time-consuming to set out to learn everything needed to do so. As I have been interested in astronomy since childhood, studied the subject in college, maintain an interest in celestial mechanics and ephemeris calculations as well as numerical simulation, and since I have played RPGs since junior high school, I think have a very good background to write a guide to creating the astronomy for a game setting.

While a thorough coverage of all aspects of astronomy as it relates to creating a convincing, realistic setting would require a lengthy book, I plan to begin with a Quick Start guide which will be a cookbook guide to creating an astronomy fairly similar to that of our Earth. Little astronomical knowledge will be assumed. The topics I think are most critical will be covered first. My plan is to post detailed instructions that won't require a great deal of astronomical knowledge or understanding, with some optional topics for those who are interested. I'll post the draft as I write it on the blog and gather feedback, and eventually will post PDF documents after revisions are made. I am also investigating writing software to assist in the creation of astronomical settings. Ideally, there will be simple web based CGI software for ease of use as well as source code for those inclined to read and modify code for their own use. Anyone interested in contributing to such software is encouraged to contact me and let me know.

The topics I plan to cover in the Quick Start are listed here:

  1. Rotation of the Earth and motion of Earth around the Sun
  2. Motion of the Moon (or Moons) around the Earth
  3. Rough sketch of the Ecliptic
  4. Detailed Diagram of the Ecliptic
  5. All Sky Star Map
  6. Inner Planets
  7. Outer Planets
  8. Calculating the Positions of Astronomical Objects