Escape Velocity and Invisible Stars

One of the many implications of Newton’s gravitational theory almost inevitably led to the basic concept of what are today called black holes. While studying gravitational attraction, some of his immediate scientific successors considered what requirements would be needed to overcome that attraction. Newton’s formula showed why Earth remains in orbit around the Sun and does not fall onto the star; namely, the planet moves away from the Sun at just the right speed to match and balance its great gravitational pull. But what if Earth could suddenly move faster, some scientists wondered? Logically, it would then be able to overcome the Sun’s gravity and escape from the star’s grip.

The speed at which an object must move in order to escape the gravity of another object became known as its escape velocity. Earth’s escape velocity, for instance, is about seven miles per second, which means that a rocket or space shuttle must achieve that speed to escape the pull of Earth’s gravity. In contrast, a rocket blasting off from Jupiter at seven miles per second would not be able to escape that planet. This is because Jupiter is a good deal more massive than Earth and therefore has much stronger gravity. “The escape velocity is different for different worlds,” renowned science writer Isaac Asimov explains.

A world that is less massive than Earth . . . has a lower escape velocity from its surface. . . . On the other hand, worlds that are more massive than Earth have higher escape velocities than it has. It is not surprising that the giant of the planetary system, Jupiter, has the highest escape velocity. . . . From Jupiter’s surface, the escape velocity is . . . 5.4 times that from Earth’s surface.

During the 1700s, a few scientists gave considerable thought to this idea of more massive objects having higher escape velocities. One of these researchers was English astronomer John Michell, who carried out a detailed study of the properties of stars. It was by then clear that some stars in the heavens are more massive than the Sun. Michell did not know if there is an upper limit to a star’s size. But at least in theory, he proposed, stars with truly tremendous mass might exist, and if so, their gravities would be huge. Moreover, the escape velocities of such giant stars would be correspondingly huge.

That led Michell to ponder just how high a star’s escape velocity could reach. And taking this line of reasoning to its logical extreme, he wondered what might happen if the star’s escape velocity exceeded the speed of light 186,000 miles per second. In that case, he reasoned, even light could not escape the star. In a paper published in 1784, he wrote: “If there should really exist in nature any bodies whose . . . diameters are more than 500 times the diameter of the sun,” they would have enormous gravities and escape velocities. Thus, “all light emitted from such a body would be made to return to it by its own power of gravity.” And because the light cannot leave the star, “we could have no information from sight.” In other words, the star would be dark and therefore invisible to human eyes and telescopes. Appropriately, Michell called these objects “dark stars.”

Michell was not the only scientist of his day fascinated by the effects of extreme gravity. In 1795 French scientist Pierre-Simon Laplace arrived at the same basic conclusion independently. Someplace in the heavens, he wrote, there might exist

invisible bodies as large, and perhaps in as great number, as the stars. A luminous star of the same density [compactness] as the Earth, and whose diameter was two hundred and fifty times greater than that of the sun, would not, because of its [gravitational] attraction, allow any of its [light] rays to arrive at us; it is therefore possible that the largest luminous bodies of the universe may, through this cause, be invisible.

Based on this conclusion, Laplace called these hypothetical objects les corps obscures, or “invisible bodies.”

John Michell: the Forgotten Pioneer

The first person to realize that objects like black holes might exist English scientist John Michell is all but forgotten now, except by astronomers. In this excerpt from In Search of the Edge of Time, noted science writer John Gribbin summarizes Michell’s career and contributions to science.

Born in 1724, Michell . . . is still known as the father of the science of seismology [the study of earthquakes]. He studied at the University of Cambridge, graduating in 1752, and his interest in earthquakes was stimulated by the disastrous seismic shock that struck Lisbon [Portugal] in 1755. Michell established that the damage had actually been caused by an earthquake centered underneath the Atlantic Ocean. He became Woodwardian Professor of Geology at Cambridge in 1762, a year after becoming a bachelor of divinity. . . . Michell made many contributions to astronomy, including the first realistic estimate of the distance to the stars, and the suggestion that some pairs of stars seen in the night sky . . . are really “binary stars,” in orbit around each other. . . . The first mention of dark stars [i.e., black holes] was made in a paper by Michell read to the Royal Society . . . in 1783. This was an impressively detailed discussion of ways to work out the properties of stars, including their distances, sizes, and masses, by measuring the gravitational effect of light emitted from their surfaces.