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Comets were once found by people willing to sweep the same patch of dark sky night after night, writing down everything that did not belong. Caroline Herschel was very good at it. She grew up expected to do only housework and ended with a Royal Astronomical Society gold medal. This post covers what she found, works out the orbit of one of her comets with Kepler's third law, and draws out habits any student can use.
Who was Caroline Herschel?
The MacTutor biography of Caroline Herschel records that she was born on 16 March 1750 in Hanover, in present-day Germany. Her mother strongly opposed her daughters doing anything other than household chores. In 1772 she joined her brother William in Bath, England. He gave her singing lessons, and she sang as first treble in oratorios such as Handel's Messiah. He also began teaching her English and mathematics.
William's hobby soon took over the household. MacTutor quotes her own account of feeding him by hand while he finished polishing a telescope mirror, because he would not take his hands off it. She recorded his observations and helped reduce them to usable results. Our profile of William Herschel and the discovery of Uranus covers his side of the story.
How did she find comets?
According to Royal Museums Greenwich, William made her a telescope of her own, and she used it to sweep the sky for comets. On 1 August 1786 she discovered her first, which made her the first woman to discover a comet. The next year her report appeared in the Royal Society's journal as An account of a new comet, in a letter from Miss Caroline Herschel. MacTutor counts eight comets found by her between 1786 and 1797.
Why was her salary such a big step?
In 1787 King George III granted Caroline a salary of 50 pounds a year as William's assistant. Royal Museums Greenwich notes that this made her the first woman in Britain to earn an income for the pursuit of science. It was official recognition that her work was a job, not a favour to her brother.
She also did the unglamorous work that keeps astronomy accurate. In 1798 she submitted to the Royal Society an index to John Flamsteed's star observations, together with a list of 560 stars that had been left out of his catalogue, MacTutor records. After William died in 1822 she returned to Hanover and, working independently, completed a catalogue of 2500 nebulae to help her nephew, the astronomer John Herschel.
Worked example: the orbit of comet 35P/Herschel–Rigollet
The JPL Small-Body Database entry for 35P/Herschel–Rigollet lists its discovery on 21 December 1788 by Caroline Herschel at Slough. It gives a perihelion distance q = 0.748 AU, an aphelion distance Q = 56.9 AU and an orbital period of 56,600 days.
How long does it take to go round the Sun?
The semi-major axis is the average of the nearest and farthest distances: a = (q + Q)/2 = (0.748 + 56.9)/2 = 28.8 AU.
Kepler's third law for orbits around the Sun, with T in years and a in AU: T² = a³.
T = 28.8^(1.5). √28.8 = 5.37, so T = 28.8 × 5.37 = 155 years.
JPL's 56,600 days divided by 365.25 is 155 years, a match. The same data give the eccentricity: e = (Q − q)/(Q + q) = 56.15/57.65 = 0.974, very close to 1, so the orbit is a long, thin ellipse. JPL's orbit solution places its last perihelion in 1939, so the comet will not return until the 2090s.
Common mistakes. Using the perihelion distance as a gives a period of under a year, which is obviously wrong for a comet that swings out beyond Neptune's orbit. Also remember Kepler's second law: the comet moves fastest near the Sun and spends most of its 155 years far out, too faint to see. Our post on gravitation and satellite problems has more orbit questions.
How was she honoured?
MacTutor lists the recognition that came, slowly. In 1828 the Royal Astronomical Society awarded her its gold medal for the nebula catalogue. In 1835 she and Mary Somerville became its first women honorary members. She was elected to the Royal Irish Academy in 1838, and on her 96th birthday, in 1846, the King of Prussia gave her a gold medal for science. She died in Hanover on 9 January 1848.
What can a student take from how she worked?
Start where you are. She grew up expected to do only household chores, and learned English and mathematics from her brother as an adult.
Keep records others can use. Her Flamsteed index was valuable because it let other astronomers find errors quickly. A clean error log does the same for your own revision.
Repeat the dull part. Comets came from many nights of sweeping. Most progress in problem solving also comes from steady repetition, not one brilliant evening.
Check the arithmetic twice. Much of her career was careful reduction of observations into numbers other people trusted.
If orbits still feel abstract, the Fermi Simulation Lab has interactive simulations for ideas that are easier to see than read, so you can watch how speed changes along an ellipse.
Try this next: look up Halley's comet's perihelion and aphelion distances, and use the same three steps to find its period.
