The software and data in this repository are for the book Celestial Calculations: A Gentle Introduction to Computational Astronomy by J. L. Lawrence, PhD and published by The MIT Press. The book contains the chapters listed below, while the software in this repository are programs that demonstrate the book’s various concepts and algorithms.
Read endorsements for Celestial Calculations and purchase it from MIT Press at https://mitpress.mit.edu/books/celestial-calculations.
1 Introduction
Astronomy may well be the oldest science with archaeological findings from around the world demonstrating that the heavens have occupied mankind’s thoughts from the very dawn of civilization. With only primitive tools and a rudimentary understanding of mathematics, the ancient Greeks learned how to predict the position of the planets and even made early estimates of the distance to the Sun, Moon, and stars. Astronomy, however, has come a long way since those early beginnings. With the advent of the personal computer, amateurs today can make astronomical calculations and predictions that the ancients could only dream of.
Chapter Topics:
1.1 Accuracy
1.2 Other Notes
1.3 Layout of the Book
1.4 Program Notes
2 Unit Conversions
Astronomy requires measuring various physical quantities: length, temperature, distance, mass, etc. Being able to convert a measurement from one system of units to another, such as converting miles to kilometers, is a basic skill required in all of the sciences, including astronomy. This chapter defines some units that astronomers use to measure large distances and presents time and angle-related conversions that are required in the rest of the book.
Chapter Topics:
2.1 Some Preliminaries
2.2 Measuring Large Distances
2.3 Decimal Format Conversions
2.4 Program Notes
2.5 Exercises
3 Time Conversions
Defining and measuring “time” is not as simple a task as it may appear at first glance, yet time is one of the most fundamental quantities of interest in astronomy and the sciences. This chapter discusses this fundamental concept by describing multiple ways to define and measure a day, month, year, etc. Methods are presented for converting between various systems of time that are frequently encountered in astronomy.
Chapter Topics:
3.1 Defining a Day
3.2 Defining a Month
3.3 Defining a Year
3.4 Defining Time of Day
3.5 Calendar Systems
3.6 Julian Day Numbers
3.7 Some Calculations with Dates
3.8 LCT to UT
3.9 UT to LCT
3.10 UT to GST
3.11 GST to UT
3.12 GST to LST
3.13 LST to GST
3.14 Program Notes
3.15 Exercises
4 Orbits and Coordinate Systems
Astronomers use several different coordinate systems to uniquely describe the position of a celestial object with respect to some reference point. This chapter presents the methods required to convert from one coordinate system to another.
Chapter Topics:
4.1 Trigonometric Functions
4.2 Locating Objects on a Sphere
4.3 The Celestial Sphere
4.4 Ellipses
4.5 Orbital Elements
4.6 Equatorial Coordinate System
4.7 Horizon Coordinate System
4.8 Ecliptic Coordinate System
4.9 Galactic Coordinate System
4.10 Precession and Other Corrections
4.11 Program Notes
4.12 Exercises
5 Stars in the Nighttime Sky
The previous chapters presented basic information about time and coordinate systems. Those fundamental concepts are a necessary and sufficient foundation for being able to locate where stars and other deep space objects will appear in the sky for an observer. This chapter builds upon that foundation to calculate when a star will rise and set, and culminates in showing the equations necessary for plotting a chart of the nighttime sky for any observer at any given local time.
Chapter Topics:
5.1 Locating a Star
5.2 Star Rising and Setting Times
5.3 Creating Star Charts
5.4 Program Notes
5.5 Exercises
6 The Sun
The most prominent celestial object in the sky is the Sun. Without the Sun, life on Earth as we know it would be impossible. Due to its massive size and resulting gravitational pull, the Sun has a major impact on the orbits of all of the planets, asteroids, and other objects in our Solar System. This chapter begins with some basic astronomical facts about the Sun and then shows how to calculate its position in the sky for an observer, when the Sun will rise and set, and various other astronomical tidbits about our nearest star.
Chapter Topics:
6.1 Some Notes about the Sun
6.2 Locating the Sun
6.3 Sunrise and Sunset
6.4 Equinoxes and Solstices
6.5 Solar Distance and Angular Diameter
6.6 Equation of Time
6.7 Program Notes
6.8 Exercises
7 The Moon
The Moon is quite possibly the most widely studied celestial object in the universe. Its ethereal beauty has fascinated humans throughout the centuries and inspired countless poets and science fiction writers, the scientifically curious, and the romantically inclined. Setting foot on the Moon during the Apollo program not only represented the culmination of the collective dreams of mankind, but remains today as the crowning achievement in our eternal quest to explore. This chapter presents some of what we have learned about the Moon and shows how to calculate its position, its phase, and when it will be visible in the nighttime sky.
Chapter Topics:
7.1 Some Notes about the Moon
7.2 Lunar Exploration
7.3 Locating the Moon
7.4 Moonrise and Moonset
7.5 Lunar Distance and Angular Diameter
7.6 Phases of the Moon
7.7 Eclipses
7.8 Program Notes
7.9 Exercises
8 Our Solar System
The ancients were well aware that certain objects that appeared to be stars did not behave like other stars. The Greeks called such objects “wandering stars” and it is from the Greek phrase aster planetes that we get our word “planet.” As astronomers studied those “wandering stars,” and especially after the telescope was invented, they began to understand that numerous objects besides the Sun and Moon are relatively close to Earth. While our knowledge of the Solar System is ever increasing, much remains to be discovered. Much of what we know is due to the space probes that have only recently reached the planets. Even more will be learned when space explorers reach the planets and study them firsthand. We live in exciting times with regards to exploring our Solar System neighbors! To aid us “armchair explorers” in our own quest to study the Solar System, this chapter describes some of what is known about our Solar System and shows how to calculate the location of the planets as well as other interesting data about them.
Chapter Topics:
8.1 The Search for Planets
8.2 The Inner Planets
8.3 The Outer Planets
8.4 The Dwarf Planets
8.5 Belts, Discs, and Clouds
8.6 Locating the Planets
8.7 Planet Rise and Set Times
8.8 Planetary Distance and Angular Diameter
8.9 Perihelion and Aphelion
8.10 Planet Phases
8.11 Planetary Magnitude
8.12 Miscellaneous Calculations
8.13 Program Notes
8.14 Exercises
9 Satellites
Satellites are indispensable tools in the modern world. Among other uses, they monitor the weather, provide accurate worldwide navigation, help geologists discover new oil and mineral deposits, and help astronomers explore the cosmos. In the short time since Sputnik 1 was launched, thousands of manmade objects have been placed into orbit around Earth, including manned space stations. This chapter demonstrates that the same physical laws that govern the stars, planets, and other celestial objects also govern objects orbiting the Earth. There are, however, significant differences between satellites and celestial objects that must be accounted for due to the fact that satellites are so much closer to Earth and their apparent speed is so much greater.
Chapter Topics:
9.1 Vectors
9.2 Ellipses Revisited
9.3 Geocentric and Topocentric Coordinates
9.4 Satellite Orbital Elements
9.5 Categorizing Satellite Orbits
9.6 Locating a Satellite
9.7 Satellite Rise and Set Times
9.8 Satellite Distance
9.9 Other Flight Dynamics
9.10 Program Notes
9.11 Exercises
10 Astronomical Aids
While it can be immensely satisfying to personally calculate the location of a celestial object or other data, there are a variety of readily available resources and tools that can be used to aid both amateur and professional astronomers. Many of those resources and tools are available online through the magic of the Internet. This chapter presents some of the commonly encountered astronomical aids, such as star charts and ephemerides, and provides the Internet address for several useful online tools and data sources.
Chapter Topics:
10.1 Recommended Authors
10.2 Star Charts
10.3 Star Catalogs
10.4 Ephemerides and Almanacs
10.5 Astronomical Calendars
10.6 Online Resources
10.7 High Accuracy Resources