22 March 2015

The Challenge of the Planets, Part Three: Gravity

It is strange that Lexell's Comet is not better remembered. Discovered by ace comet-hunter Charles Messier on the night of 14 June 1770, it passed Earth just two weeks later at a distance of only 2.3 million kilometers, closer than any other comet in recorded history. On the evening of 1 July 1770, its nucleus shown as brightly as Jupiter at its brightest, and its silvery coma was five times larger than the full moon.

Lexell's Comet then drew close to the Sun - that is, it reached perihelion - and was lost in the glare. Messier saw it next in the pre-dawn sky on 4 August. Having moved away from Earth and the Sun, it had become small and faint. Messier observed the comet with difficulty before dawn on 3 October 1770, then lost sight of it.

Comets are today named for their discoverer or discoverers, but in the 18th century it was the mathematicians who computed their orbits who got all the credit. Comet Halley is, for example, named for Edmond Halley, who computed its orbit and determined that what had seemed like a series of individual comets was in fact a single comet that returned again and again. Partly this was because in Comet Halley's case no one knows who discovered it; records of the comet's apparitions extend back at least to 240 BCE, but it almost certainly was noticed in Earth's skies much earlier.

Lexell's Comet was named for Anders Johan Lexell, who determined that it completed one elliptical orbit around the Sun in 5.6 years. This was for the time a remarkably short period for a comet, raising questions as to why it had not been observed before. Lexell hypothesized that the comet had previously had a large orbit with a perihelion close to Jupiter's orbit, but then had passed Jupiter at a distance of about 3.2 million kilometers in 1767. The giant planet had, he wrote, slowed it and deposited it into its new short-period orbit.

Lexell's Comet was due to reach perihelion again in 1776, but this occurred on the far side of the Sun as viewed from Earth and so was not observed. Astronomers eagerly awaited its next perihelion in 1781 or 1782, but nothing was seen. Again, Lexell offered an explanation: in 1779, as it neared the point in its new orbit where it was farthest from the Sun - its aphelion - the comet had again intersected Jupiter. This time, it had sped up and entered an unknown but probably long-period orbit. It might even have escaped the Sun's gravitational grip entirely. In any case, Lexell's Comet has not been seen since and is officially designated "lost."

The light-show of 1 July 1770 should have ensured that no one forgot Lexell's Comet, but both its close pass by Earth and its orbit changes soon faded from memory. If they had not, then Michael Minovitch's mathematical research in 1961-1964 might not have shaken the interplanetary mission planning world the way they did.

Minovitch, in 1961 a 25-year-old graduate student at the University of California - Los Angeles (UCLA), began his research while working a summer job at the Jet Propulsion Laboratory (JPL) in Pasadena, California. He calculated that a flyby spacecraft which passed behind a planet would be seized by the planet's gravity and in effect towed as the planet orbited the Sun. This would increase the spacecraft's speed. As it departed the planet's vicinity, it would keep the speed it gained. Conversely, a flyby spacecraft that passed ahead of a planet would be slowed. Minovitch viewed this as a new form of propulsion; he called the effect the planet's motion had on the spacecraft "gravity thrust."

Minovitch determined that a spacecraft could use gravity thrust flybys to travel from world to world indefinitely without use of rocket propulsion. It could even return to the vicinity of Earth, enter a close solar orbit, or escape the Solar System entirely. In all, he calculated about 200 different planetary-flyby sequences using charts he devised and computers at JPL and UCLA.

Many engineers who learned of Minovitch's results assumed at first that they violated fundamental physical law. It seemed that the flyby spacecraft would get something for nothing. This was, of course, incorrect: when the spacecraft was slowed, the planet gained a very tiny amount of momentum; when the spacecraft was accelerated, the planet lost a very tiny amount of momentum. Nature thus balanced its books. Minovitch, for his part, was not very skilled at first at explaining his discoveries; he seems to have understood the clean elegance of numbers far better than he did the fuzzy vagaries of human beings.

Nevertheless, he had his champions. The most important was Maxwell Hunter, who met Minovitch at the American Astronautical Society's Symposium on the Exploration of Mars (6-7 June 1963) and quickly recognized the significance of his work. Before joining the professional staff of the National Aeronautics and Space Council (NASC) in January 1962, Hunter had worked at Douglas Aircraft for 18 years. He ended his career there as Chief Engineer for Space Systems. As part of the NASC, he was well placed to promote Minovitch's discoveries; the advisory body, chaired by Vice President Lyndon Baines Johnson, provided advice directly to President John F. Kennedy.

Hunter described Minovitch's "unconventional trajectories" in a report to NASC Executive Secretary Edward Welsh in September 1963. The report became the basis for a prominent article in the May 1964 issue of the important trade publication Astronautics & Aeronautics. Hunter permitted Minovitch to review a draft before the article went to publication.

In June 1964, a month after Hunter's article made the spaceflight world aware of Minovitch's labors, JPL began planning what became Mariner Venus/Mercury 1973, the first planetary mission to employ one of the trajectories Minovitch had calculated. The MVM '73 spacecraft would fly past Venus to slow down and enter a Sun-centered orbit that would take it past Mercury. The flight past Venus was labelled a "gravity-assist flyby" - Minovitch's "gravity-thrust" moniker never caught on.

At nearly the same time, high-energy propulsion systems, which had been deemed essential for travel to worlds beyond Venus and Mars, rapidly began to lose support. As described in the previous post in this "Challenge of the Planets" series, the leader among these systems was electric (ion) propulsion.

In 1962, JPL engineers had prepared a preliminary design for an automated 10-ton nuclear-electric "space cruiser" and proudly presented it at a conference attended by about 500 other electric-propulsion engineers. It was received with great enthusiasm. The system was still early in its development, but the JPL engineers expected that, with sufficient funding, they might develop it for interplanetary spaceflights in the 1970s.

By late 1964, however, such brute-force high-energy systems were increasingly seen as needlessly complex and costly (at least as far as the preliminary reconnaissance of the Solar System was concerned). NASA could instead use a relatively small booster rocket to place on an interplanetary trajectory a package comprising a small chemical-propellant propulsion system for course corrections, star-trackers for precise spacecraft position and trajectory determination, a cold-gas thruster system for turning the spacecraft, science instruments, a computer, an electricity-generating isotopic system or solar arrays, and a radio. By 1962 standards, such a package hardly qualified as a spacecraft, yet it remains the basic form of our proudest interplanetary flyby and orbiter spacecraft to this day.

Electric-propulsion supporters were loathe to give up their labors. In addition to developing small station-keeping electric-propulsion systems for Earth-orbiting satellites, they sought planetary exploration niches where electric propulsion could outshine gravity-assist trajectories.

Ironically, given the adventures of Lexell's Comet, the most significant niche they identified was comet rendezvous. Before the end of the 1960s, the 1985-1986 Comet Halley apparition became a particularly important target for electric-propulsion supporters. Their efforts to explore Comet Halley using electric propulsion will be described in forthcoming posts.

In the years that followed Mariner 10 (as MVM '73 came to be known), more of Minovitch's gravity-assist trajectories were put to use. Though often mistakenly attributed to JPL's Gary Flandro, among Minovitch's trajectories was the Jupiter-Saturn-Uranus-Neptune path of Voyager 2. (Flandro's oft-cited "grand tour" paper saw print in mid-1966, nearly five years after Minovitch began his research; in it Flandro gave credit where it was due by citing two of Minovitch's JPL internal reports.)

The Voyager 2 sequence of flybys has been touted as a once-in-176-years opportunity to visit all the outer Solar System planets during a single mission; Minovitch, however, was quick to point out that this claim is spurious. Jupiter, Saturn, Uranus, and Neptune are each massive enough to bend a passing spacecraft's path and accelerate it toward any other point in the Solar System at any time.

Voyager 2, with a mass at launch of about 726 kilograms, left Earth on 20 August 1977 atop a Titan IIIE rocket. It flew within 564,000 kilometers of Jupiter's trailing side on 9 July 1979; within 102,000 kilometers of Saturn's trailing side on 25 August 1981; about 82,000 kilometers from Uranus's trailing side on 24 January 1986; and within 5000 kilometers of Neptune on 25 August 1989. In all, its primary mission spanned just over 12 years.

The intrepid spacecraft then began its Interstellar Mission, which continues to this day. At this writing, Voyager 2 is more than 19 billion kilometers from the Sun; unless humans catch up to it and reverently bring it home, it will in centuries to come depart the Solar System entirely and wander among the stars.

Minovitch calculated Venus-Earth gravity-assist trajectories; these came in handy beginning with the loss of the Space Shuttle Orbiter Challenger (28 January 1986) and subsequent cancellation of the Shuttle-launched Centaur G-prime upper stage. The accident and stage cancellation grounded the Galileo Jupiter Orbiter and Probe mission, which had been set to launch to Earth orbit in May 1986 in a Space Shuttle payload bay then boost directly to Jupiter on a Centaur-G-prime.

The Space Shuttle resumed flights in September 1988. Galileo was launched in the payload bay of the Orbiter Atlantis (18 October 1989) and boosted from Earth orbit using a solid-propellant Inertial Upper Stage that was incapable of sending it directly to Jupiter.

Instead, Galileo flew by Venus (10 February 1990), Earth (8 December 1990), and Earth again (8 December 1992) before it built up enough speed to begin the trek to Jupiter. Galileo reached Jupiter on 7 December 1995. Over the course of 35 Jupiter-centered orbits, it explored the four largest Jovian moons using gravity-assist flybys to speed up and slow down. A final gravity-assist series caused it to orbit nearly 26 million kilometers from Jupiter and then perform a pre-planned death-dive into its atmosphere on 21 September 2003.

Current operational missions that used or will use gravity-assist flybys include (in no particular order) Voyager 1 (which flew by Jupiter and Saturn), the Cassini Saturn Orbiter (which carried out a Venus-Venus-Earth-Jupiter sequence of gravity-assist flybys), the MESSENGER Mercury orbiter (Earth-Venus-Venus-Mercury-Mercury-Mercury), the Rosetta comet-rendezvous spacecraft and Philae lander (Earth-Mars-Earth-Earth), the Juno Jupiter orbiter (Earth), and the New Horizons Pluto flyby spacecraft (Jupiter). Even the Dawn Vesta/Ceres mission, which relies on solar-electric propulsion, used a gravity-assist Mars flyby on 4 February 2009 to gain speed and reach the Asteroid Belt between Mars and Jupiter.


"Gravity Propulsion Research at UCLA and JPL, 1962-1964," R. Dowling, W. Kossmann, M. Minovitch, and T. Ridenmoure, History of Rocketry and Astronautics, AAS History Series Volume 20, J. Hunley, editor, 1997, pp. 27-106

Comets: A Chronological History of Observation, Science, Myth, and Folklore, D. Yeomans, John Wiley & Sons, New York, 1991, pp. 157-160

The Voyager Neptune Travel Guide, C. Kohlhase, editor, NASA JPL, June 1989, pp. 103-106

"Fast Reconnaissance Missions to the Outer Solar System Utilizing Energy Derived from the Gravitational Field of Jupiter," G. Flandro, Astronautica Acta, Volume 12, Number 4, 1966, pp. 329-337

"Utilizing Large Planetary Perturbations for the Design of Deep Space, Solar Probe, and Out-of-Ecliptic Trajectories," JPL Technical Report No. 32-849, M. Minovitch, December 1965

"Future Unmanned Exploration of the Solar System," M. Hunter, Astronautics & Aeronautics, May 1964, pp. 16-26

"Determination and Characteristics of Ballistic Interplanetary Trajectories Under the Influence of Multiple Planetary Attractions," JPL Technical Report No. 32-464, M. Minovitch, October 1963

Future Unmanned Exploration of the Solar System, M. Hunter, Report to the Executive Secretary, National Aeronautics & Space Council, September 1963

More Information

The Challenge of the Planets, Part One: Ports of Call

The Challenge of the Planets, Part Two: High Energy


  1. Excellent article. Of the planets in our solar system which would provide the fastest trajectory ?

  2. Jupiter offers the most opportunities for big velocity/direction changes, though any planet can be used for gravity-assist. Earth has been used more than any other planet.



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