This Month in Astronomical History: December
Jason Ybarra West Virginia University
Each month as part of this series from the AAS Historical Astronomy Division (HAD), an important discovery or memorable event in the history of astronomy will be highlighted. This month's guest author, Jason Ybarra of Bridgewater College, reflects on Reverend John Michell and his dark star — a hypothetical star whose escape velocity was equal to the speed of light. Interested in writing a short (500-word) column? Instructions along with previous history columns are available on the HAD webpage.
John Michell and His Dark Star
Star after star from Heaven's high arch shall rush,
Suns sink on suns, and systems systems crush,
Headlong, extinct, to one dark centre fall,
And Death and Night and Chaos mingle all!1
— Erasmus Darwin (1791)
These verses by physician and poet Erasmus Darwin, grandfather to biologist Charles Darwin, refer in part to John Michell’s dark star, a hypothetical star whose escape velocity was equal to the speed of light.2 The Reverend John Michell, a contemporary of Henry Cavendish and William Herschel, was born on Christmas Day (25 December) in 1724, 82 years after the birth of Sir Isaac Newton, who also happened to be born on Christmas Day.[A] Michell studied mathematics at the University of Cambridge, where after graduating he lectured in mathematics, Greek, Hebrew, and philosophy before being appointed to the Woodwardian Chair of Geology in 1761. At Cambridge he published A Treatise of Artificial Magnets (1750), proposing that magnetic forces follow an inverse square law, and the book Conjectures Concerning the Cause, and Observations upon the Phænomena, of Earthquakes (1759), on his study of the Lisbon earthquake of 1755. He designed the torsion balance that was eventually used by his friend Cavendish to measure the density of the Earth.3 In 1763 Michell left Cambridge to become a cleric, obtaining the position of rector at Thornhill in 1767. It was here that Michell focused his attention on astronomy.
Michell published his first astronomical paper in 1767 on the nature of double stars and the determination of distances to stars by parallax.4 Michell used statistical analysis to argue that most double stars are binaries and proposed a procedure for determining the mass of binary stars.5
In 1784 Michell published a paper considering the effect gravity might have on light leaving the surface of a star. Michell accepted Newton’s hypothesis that light consisted of particles and reasoned that if the particles of light were subject to Newton’s law of gravitation, then the speed of the particles would be reduced by the star’s gravitational pull. He then considered a star with a gravitational pull so strong that the light it emitted would return to its surface and become trapped.6
Although Michell was wrong about the effect gravity has on the speed of light, the idea of a body with a gravitational field so strong that even light cannot escape re-emerged in the early 20th century as a consequence of Einstein's general theory of relativity. In 1916 Karl Schwarzschild found a spherically symmetric solution to Einstein’s field equations with a coordinate singularity at R = 2GM/c2. In 1958 David Finkelstein showed that this Schwarzschild surface is unidirectional.7 By the 1960s these objects were named black holes.8
In his paper Michell also reasoned that the existence of these dark stars could be determined from observations of satellites orbiting around them. He wrote that
if any other luminous bodies should happen to revolve about them we might still perhaps from the motions of these revolving bodies infer the existence of the central one with some degree of probability...9
More than 200 years later, modern astronomers would use Michell’s method to infer the existence of the supermassive black hole at the center of our own Milky Way galaxy.10,11
[A]. Great Britain used the Julian calendar (Old Style) at the time. The Gregorian calendar was not adopted until 1752.
Figures
Fig 1 Paragraph from Michell’s 1784 paper describing his dark star.
References
1. Darwin, E. 1791, The Botanic Garden. A Poem in Two Parts. Part 1: The Economy of Vegetation, Canto IV, verses 373-376.
2. Crossley, R. 2003, Mystery at the Rectory: Some Light on John Michell. Yorkshire Philosophical Society.
3. Cavendish, H. 1798. Experiments to Determine the Density of Earth, Philosophical Transactions of the Royal Society of London, 88, 469–526.
4. Michell, J. 1767, An Inquiry into the Probable Parallax, and Magnitude of the Fixed Stars, from the Quantity of Light Which They Afford Us, and the Particular Circumstances of Their Situation, Philosophical Transactions of the Royal Society of London, 57, 234-264.
5. Montgomery, C., Orchiston, W., & Whittingham, I. 2009, Michell, Laplace and the Origin of the Black Hole Concept, Journal of Astronomical History and Heritage, 12, 90.
6. Schaffer, S. 1979, John Michell and Black Holes, Journal for the History of Astronomy, 10, 42.
7. ‘t Hooft, G. 2009, Introduction to the Theory Of Black Holes, Lectures presented at Utrecht University, http://www.staff.science.uu.nl/~hooft101/lectures/blackholes/BH_lecture…
8. Siegfried, T. 2013, 50 Years Later, It’s Hard to Say Who Named Black Holes, Science News
https://www.sciencenews.org/blog/context/50-years-later-its-hard-say-wh…
9. Michell, J., 1784, On the Means of Discovering the Distance, Magnitude, &c. of the Fixed Stars, in Consequence of the Diminution of the Velocity of Their Light, in Case Such a Diminution Should Be Found to Take Place in Any of Them, and Such Other Data Should Be Procured from Observations, as Would Be Farther Necessary for That Purpose, Philosophical Transactions of the Royal Society, 74, 35-57.
10. Ghez, A.M., Morris, M.R., Becklin, E.E., et al. 2001, The Keck Proper Motion Study of the Galaxy's Central Stellar Cluster: From Speckle Imaging and Velocities to Adaptive Optics and Accelerations, Dynamics of Star Clusters and the Milky Way, ASP Conference Series, Vol. 228.
11. Schödel, R., Ott, T., Genzel, R., et al. 2002, A Star in a 15.2-Year Orbit Around the Supermassive Black Hole at the Centre of the Milky Way, Nature, 419, 694.