How far are the stars?

Rabbi Levi ben Gerson, also known as Gersonides, lived from 1288-c.1344. He was from a family of scholars: his father, Gerson ben Solomon of Arles, was the author of the Sha'ar ha-Shamayim, an encyclopedia of natural science, astronomy, and metaphysics.* Levi is credited with first mentioning, and possibility inventing, Jacob's Staff. (He references Genesis 32:10 when he describes the device; this is likely the origin of the name.)

At a time when religion, philosophy, astronomy, astrology and science were overlapping (and in some cases, interchangeable), Gersonides' greatest work, which was philosophical, contained his greatest contribution to astronomy. He put twelve years (1317-28) of effort into the Milhamot Adonai ("Wars of the Lord"), whose six books dealt with 1) the soul, 2) prophecy, 3) & 4) god's knowledge of facts and providence, 5) astronomy/astrology, and 6) creation and miracles. Gersonides firmly accepted astrology and the celestial hierarchy of powers inherited from neo-Platonists and pseudo-Dionysius (far too complex to go into here), but he also brought mathematics and observation to his work with extraordinary results for the time.

Postage stamp honoring Gersonides.

Gersonides rejected the Ptolemaic system of epicycles to explain the erratic motion of planets affixed to their crystal spheres surrounding the Earth. According to Ptolemy, epicycles explained the changing size of planets; he said, however, that Mars varies by a factor of six; Gersonides' observations told him that Mars's apparent size varies only two-fold. Gersonides used the Jacob Staff and a camera obscura (pinhole camera) to make careful observations over several years. For Gersonides, 48 crystalline spheres were needed to explain the apparent motion of various heavenly bodies. This expansion of the "physics" of the Ptolemaic model was nothing, however, compared to the actual physical expansion he proposed.

Careful observation with the Jacob Staff, the camera obscura, and math made Gersonides declare heavenly objects to be much farther away than previously calculated. Ptolemy claimed the distance to Venus was 1079 Earth radii; Gersonides estimated it to be 8,971,112 Earth radii away. Ptolemy said the fixed stars were 20,000 Earth radii away; Gersonides estimated them to be at a distance 10 billion times greater.

Pope Clement VI had the "Wars of the Lord" translated into Latin in 1344, making it available to the west. Its impact was minimal, however; we know of a few scholars who were influenced by it, and Kepler asked a friend to send him a copy in the 17th century. But it took Copernicus two centuries later to "confirm" to Western civilization's satisfaction that Gersonides was on the right track.

*As I have mentioned about medieval encyclopediæ before, they were often compilations of previous works; this one drew from Claudius Ptolemy's Almagest and the Morah Nebukim, or "Guide for the Perplexed" of Maimonides. A 1547 edition of ben Solomon's work can be had from Kestenbaum & Company.

Jacob's Staff

Have you seen a modern surveyor using a single vertical rod with an instrument on top to measure property lines? That pole is nicknamed a "Jacob's Staff." Hundreds of years ago, however, the term "Jacob's Staff" was used to refer to more than one type of instrument; it's the other instrument that I want to discuss today.

A recreation of a Jacob's Staff.

The other instrument was also called a cross-staff, or a fore-staff, or (around the Mediterranean) a balestilha. It comprised a staff with cross-pieces designed to allow the user to determine angles of distant points. By aligning it with, say, Polaris (the North Star), a sailor could determine the angle between the star and the horizon. Matched against known measurements, the sailor then knew his latitude.

Knowledge of geometry and arithmetic also allowed the user to determine other measurements. If the height of a distant tower were known, that number and the angle known via the staff allowed you to determine your distance from the tower. Alternately, if you knew your distance from the base of a tall object, finding the angle from you to the top of it helped you determine how tall it was.

The Jacob's Staff had another name as well when used with heavenly bodies: radius astronomicus.

From an early book on navigation.

Where did it come from? The earliest description we have of the device is in the astronomical works of Gersonides (Levi ben Gerson, 1288-1344), who describes it as:

... a staff of 4.5 feet (1.4 m) long and about one inch (2.5 cm) wide, with six or seven perforated tablets which could slide along the staff, each tablet being an integral fraction of the staff length to facilitate calculation, used to measure the distance between stars or planets, and the altitudes and diameters of the Sun, Moon and stars. (Book of the Wars of the Lord)

Although some ascribe it to a contemporary of his, an astronomer named Jacob ben Machir (1236-1304). This might also explain its common name, since no other convincing etymology has come forth. The invention of the more precise sextant in the 18th century rendered the Jacob's Staff a quaint relic, and the name, when used, came to refer only to the simpler measuring stick we still see today.