Tag: Johannes Kepler

How Far the Sun

How do we know our Sun is 93 million miles (150 million km) away1?

The ancient Greek astronomer and mathematician Aristarchus of Samos, who lived around 2,300 years ago, was probably the first person who made a reasonable attempt to determine the distance to the Sun.

Using a method of geometric analysis developed by Euclid (trigonometry had not yet been invented), Aristarchus measured the angle between the half-lit Moon and the Sun and determined that the Sun is 18 to 20 times farther away than the Moon.  Though he fell far short of the actual value of 389 due to the extreme difficulty of making accurate measurements using the instruments and methods available to him, Aristarchus showed the way for future generations of astronomers to determine the true distance to the Sun.

Determining the actual distance (and not the relative distance) to the Sun had to wait for Kepler’s Third Law of planetary motion that relates a planet’s orbital period to its distance from the Sun, the invention of the telescope, and Isaac Newton’s laws of motion and gravitation.

P^{2}\propto a^{3}

Distances within the solar system can be determined using trigonometry and parallax, which is the apparent shift of an object against the distant background stars as seen from different locations.

Hold your thumb at arm’s length and alternate between right and left eye open to see the parallactic shift.
Bring your thumb closer, and the shift is greater.

Measuring the parallax to a Sun-orbiting object (such as Mars) from two different locations on the Earth’s surface allows us to measure its distance and, thanks to Kepler and Newton, sets the scale for the entire solar system.  The true distance of each planet from the Sun can then be mathematically determined.  This was first accomplished in 1672, and has been done many times since, with ever-improving accuracy.

Observations of the position of Mars by Giovanni Cassini at Paris and Jean Richer at Cayenne
allowed the first determination of the distance to Mars using trigonometric parallax in 1672.

Today, we have even better methods to determine the scale of the solar system: timing radar reflections off of solar system objects, and measuring travel time for radio communications between Earth and spacecraft.  Both radar and radio signals travel at the speed of light, which is very well determined.

1Approximate average distance

Project Gutenberg

Over 56,000 historical books and other documents, most published prior to 1923, are available online for downloading or browsing at Project Gutenberg (https://www.gutenberg.org/), with more being added all the time. A quick search of the term “astronomy” yields the following:

The Discovery of a World in the Moone: Or, A Discovrse Tending To Prove That ‘Tis Probable There May Be Another Habitable World In That Planet (1638)
John Wilkins (1614-1672)

The Study of Astronomy, Adapted to the capacities of youth (1796)
John Gabriel Stedman (1744-1797)

The Martyrs of Science, or, The lives of Galileo, Tycho Brahe, and Kepler (1841)
David Brewster (1781-1868)

Lectures on Astronomy (1854)
The Wit and Humor of America, Volume V. (1911)
George Horatio Derby (1823-1861), writing under the name of John Phoenix
Marshall Pinckney Wilder (1859-1915), editor

Letters on Astronomy: In which the Elements of the Science are Familiarly Explained in Connection with Biographical Sketches of the Most Eminent Astronomers (1855)
Denison Olmsted (1791-1859)

The Uses of Astronomy: An Oration Delivered at Albany on the 28th of July, 1856 (1856)
Edward Everett (1794-1865)

Cosmos: A Sketch of the Physical Description of the Universe, Vol. 1 (1858)
Alexander von Humboldt (1769-1859)

Curiosities of Science, Past and Present: A Book for Old and Young (1858)
John Timbs (1801-1875)

Astronomy for Young Australians (1866)
James Bonwick (1817-1906)

Meteoric astronomy: A treatise on shooting-stars, fire-balls, and aerolites (1867)
Daniel Kirkwood (1814-1895)

Popular Books on Natural Science: For Practical Use in Every Household, for Readers of All Classes (1869)
Aaron David Bernstein (1812-1884)

Half-hours with the Telescope: Being a Popular Guide to the Use of the Telescope as a Means of Amusement and Instruction (1873)
Richard Anthony Proctor (1837-1888)

Astronomical Myths: Based on Flammarions’s “History of the Heavens” (1877)
John Frederick Blake (1839-1906)
Camille Flammarion (1842-1925)

New and Original Theories of the Great Physical Forces (1878)
Henry Raymond Rogers (1822-1901)

Recreations in Astronomy: With Directions for Practical Experiments and Telescopic Work (1879)
Henry White Warren (1831-1912)

The Sidereal Messenger of Galileo Galilei and a Part of the Preface to Kepler’s Dioptrics Containing the Original Account of Galileo’s Astronomical Discoveries (1880)
Galileo Galilei (1564-1642)
Johannes Kepler (1571-1630)
Edward Stafford Carlos ((1842–1927), translator

Sir William Herschel: His Life and Works (1880)
Edward Singleton Holden (1846-1914)

Popular Scientific Recreations in Natural Philosophy, Astronomy, Geology, Chemistry, etc., etc., etc. (1881)
Gaston Tissandier (1843-1899)

Publications of the Astronomical Society of the Pacific, Volume 1 (1889)
Astronomical Society of the Pacific (1889-)

A Textbook of General Astronomy for Colleges and Scientific Schools (1889)
Charles Augustus Young (1834-1908)

Time and Tide: A Romance of the Moon (1889)
Robert Stawell Ball (1840-1913)

Astronomy with an Opera-glass: A Popular Introduction to the Study of the Starry Heavens with the Simplest of Optical Instruments (1890)
Garrett Putman Serviss (1851-1929)

Pioneers of Science (1893)
Sir Oliver Joseph Lodge (1851-1940)

Great Astronomers (1895)
Robert Stawell Ball (1840-1913)

The Astronomy of Milton’s ‘Paradise Lost’ (1896)
Thomas Nathaniel Orchard, M.D.

Myths and Marvels of Astronomy (1896)
Richard Anthony Proctor (1837-1888)

The Story of Eclipses (1899)
George Frederick Chambers (1841-1915)

The Tides and Kindred Phenomena in the Solar System: The Substance of Lectures Delivered in 1897 at the Lowell Institute, Boston, Massachusetts (1899)
Sir George Howard Darwin (1845-1912)

The Royal Observatory, Greenwich: A Glance at Its History and Work (1900)
Edward Walter Maunder (1851-1928)

The Story of the Heavens (1900)
Robert Stawell Ball (1840-1913)

Other Worlds: Their Nature, Possibilities and Habitability in the Light of the Latest Discoveries (1901)
Garrett Putman Serviss (1851-1929)

Pleasures of the telescope: An Illustrated Guide for Amateur Astronomers and a Popular Description of the Chief Wonders of the Heavens for General Readers (1901)
Garrett Putman Serviss (1851-1929)

A Text-Book of Astronomy (1903)
George Cary Comstock (1855-1934)

Astronomical Discovery (1904)
Herbert Hall Turner (1861-1930)

A New Astronomy (1906)
David Peck Todd (1855-1939)

New Theories in Astronomy (1906)
William Stirling (1822-1900)

Side-Lights on Astronomy and Kindred Fields of Popular Science (1906)
Simon Newcomb (1835-1909)

The Children’s Book of Stars (1907)
Geraldine Edith Mitton (1868-1955)

Mathematical Geography (1907)
Willis Ernest Johnson (1869-1951)

Astronomical Instruments and Accessories (1908)
William Gaertner and Company (1896-)
now Gaertner Scientific Corporation

The Astronomy of the Bible: An Elementary Commentary on the Astronomical References of Holy Scripture (1908)
Edward Walter Maunder (1851-1928)

A Popular History of Astronomy During the Nineteenth Century, Fourth Edition (1908)
Agnes Mary Clerke (1842-1907)

Astronomical Curiosities: Facts and Fallacies (1909)
John Ellard Gore (1845-1910)

The Future of Astronomy (1909)
Edward Charles Pickering (1846-1919)

History of Astronomy (1909)
George Forbes (1849-1936)

Astronomy for Amateurs (1910)
Camille Flammarion (1842-1925)

Astronomy of To-day: A Popular Introduction in Non-Technical Language (1910)
Cecil Goodrich Julius Dolmage (1870-1908)

The World’s Greatest Books — Volume 15 — Science (1910)
Arthur Mee (1875-1943), editor
Sir John Alexander Hammerton (1871-1949), editor

The Science of the Stars (1912)
Edward Walter Maunder (1851-1928)

Are the Planets Inhabited? (1913)
Edward Walter Maunder (1851-1928)

Woman in Science: With an Introductory Chapter on Woman’s Long Struggle for Things of the Mind (1913)
John Augustine Zahm (1851-1921), writing under the name H. J. Mozans

A Field Book of the Stars (1914)
William Tyler Olcott (1873-1936)

An Introduction to Astronomy (1916)
Forest Ray Moulton (1872-1952)

Scientific Papers by Sir George Howard Darwin. Volume V. Supplementary Volume (1916)
Sir George Howard Darwin (1845-1912)
Ernest William Brown (1866-1938), contributor
Sir Francis Darwin (1848-1925), contributor

The gradual acceptance of the Copernican theory of the universe (1917)
Dorothy Stimson (1890-1988)

Astronomical Lore in Chaucer (1919)
Florence Marie Grimm

Lectures on Stellar Statistics (1921)
Carl Vilhelm Ludwig Charlier (1862-1934)

The Star People (1921)
Gaylord Johnson

Terrestrial and Celestial Globes Volume 1: Their History and Construction Including a Consideration of their Value as Aids in the Study of Geography and Astronomy (1921)
Edward Luther Stevenson (1858-1944)

Terrestrial and Celestial Globes Volume 2: Their History and Construction Including a Consideration of their Value as Aids in the Study of Geography and Astronomy (1921)
Edward Luther Stevenson (1858-1944)

Astronomy for Young Folks (1922)
Isabel Martin Lewis (1881-1966)

Astronomy: The Science of the Heavenly Bodies (1922)
David Peck Todd (1855-1939)

The New Heavens (1922)
George Ellery Hale (1868-1938)

Watchers of the Sky (1922)
Alfred Noyes (1880-1958)

Biography of Percival Lowell (1935)
Abbott Lawrence Lowell (1856-1943)