When comets pass close to a massive body like the Sun or Jupiter, they may break up due, at least in part, to the tidal forces encountered. Recall that tidal forces occur from differential gravity forces created on an object because of the difference in distance on either side of say, a comet from a planet or Sun. Several examples come to mind. In 1846, Biele’s comet split in two while passing close to the Sun. Comet XIV passed within 10 million miles of the Sun in 1947 and also split in two. In 1976 Comet West broke into four pieces near the Sun. More recently, Shoemaker-Levy 9 disintegrated into a 20+ fragments after passing too close to Jupiter, and returned the insult by spectacularly plunging into its aggressor.

In 1850, the French astronomer E. A. Roche (1820 – 1883) stated “no satellite can exist closer to a planet than 2.44x its radius or 1.44x from its surface.” The equation he developed for this distance, the Roche limit, is

where              L_R is the Roche limit, from the planet’s center

                       R_P is the planet’s radius

                  is the planet’s density

            is the satellite’s density

If a satellite or comet that is held together solely by its gravitational force (no tensile strength) passes within the planet’s Roche limit, it will break apart. A non-rotating liquid satellite without surface tension is an example. Note also that the limit depends on the relative densities of the two objects as well as the planet’s size. The Roche limit for Earth is approximately 20,000 km above the surface. The reason why artificial satellites within this limit don’t break apart is because they have significant tensile strength that overcomes Earth’s tidal force on the vehicles.

Deriving the Roche limit formula by equating the planet’s tidal force to the satellite’s self-gravitational attractive force gives a result slightly different from the standard formula shown above. Instead of the 2.44 constant, we get a 2.52 value. The standard formula takes into account the oblate spheroid deformation a satellite undergoes as it experiences the tidal forces.

We’ll examine the Roche limits for the Earth (radius 6,380 km, density 5.52), Jupiter (radius 71,500 km, density 1.33), Saturn (radius 60,300 km, density 0.69), and the Sun (radius 696,000 km, density 1.41). Comets are considered to be aggregations of ice and dust. Their significant porosity can result in nucleus densities of approximately 0.5. This structure makes them especially vulnerable to tidal forces. The density of asteroids varies widely, so we’ll assume an average density of 3.00. Most asteroids are structurally intact, giving them breakup resistance to tidal forces.

Earth’s Roche limit for comets is 34,700 km or 5.43 radii and for asteroids, 19,000 km or 2.98 radii.

Jupiter’s limit for comets is 242,000 km or 3.38 radii and for asteroids is 133,000 km or 1.86 radii.

Saturn’s limit for comets is 164.000 km or 2.72 radii and for asteroids is 90.200 km or 1.50 radii.

The Sun’s limit for comets is 2.4 million km or 3.45 radii and for asteroids is 1.3 million km or 1.90 radii.

The rings of Jupiter, Saturn, Uranus and Neptune are a creation of their Roche limits. Except for Saturn’s G and E rings which non-gravitational forces may maintain, the gaseous planets’ rings lie within their respective Roche limits.

In regard to comet breakups, it’s important to recognize that the combination of tidal forces, fragile structure, centrifugal force for rotating nuclei, plus thermal pressures near the Sun make them especially vulnerable to breakups. In 1992, Shoemaker-Levy 9 broke up as it passed within Jupiter’s Roche limit. The Shoemakers and Levy discovered the train of objects the following year. The cometary particles then crashed into Jupiter in July, 1994. In 1886, Comet Brooks 2 also encountered Jupiter’s Roche Limit, breaking in two. The Kreutz family of comets passes within the Sun’s Roche limit, breaking up or even colliding with our star. These comets are thought to originate from parts of the great comet of 372 B. C.

Let’s now imagine the inevitable. A million years from now, a comet may head directly towards Earth at 20 km/s. As it approaches our Roche limit (approximately 28,300 km from the surface), it begins to break up 23.6 minutes before impact. At about 120 km above the ground the pieces encounter a tenuous atmosphere. In the next few seconds before impact many more pieces are created from atmospheric shock. The impact area would cover many square kilometers, destroying everything within hundreds of miles. Hopefully, by then, we’ll have early detection and avoidance technology to prevent such a catastrophe.