The Seventh Planet: A Gravity-Assist Tour of the Uranian System (2003)

The next in line: from its vantage point in orbit of Saturn, the sixth planet, the Cassini spacecraft catches a glimpse of Uranus, the seventh (blue dot, upper left). Image credit: NASA.

The four largest and most massive satellites of Jupiter are, in order out from the planet, Io, Europa, Ganymede, and Callisto. Io and Europa form a pair of roughly the same size, as do Ganymede and Callisto. Io has a diameter of 3636 kilometers, while Europa, the smallest of the four, is 3138 kilometers in diameter. Ganymede, the largest moon in the Solar System, measures 5262 kilometers across. Callisto, Jupiter's outermost large moon, is 4810 kilometers in diameter.

The presence of four large, massive moons enabled the Galileo spacecraft to carry out a complex tour of the Jupiter system between December 1995 and September 2003. Over the course of 35 revolutions around the giant planet, Galileo used gravity-assist flybys of the four moons to change its orbit.

By contrast, Saturn and Neptune each have only one large, massive moon. Saturn's moon Titan, the second-largest moon in the Solar System, measures 5152 kilometers in diameter, while Neptune's moon Triton is just 2706 kilometers across. The Cassini Saturn Orbiter, at this writing exploring the Saturn system, must rely on Titan for most of its gravity assists, which means that it must rely more often than did Galileo on its finite supply of rocket propellants to make orbital changes. A Neptune orbiter, with only Triton available for significant gravity assists, would face a similar challenge.

The four largest and most massive moons of Uranus are puny compared with Io, Europa, Ganymede, Callisto, Titan, and Triton. Titania, the largest, measures just 1578 kilometers in diameter. The others are: Ariel (1158 kilometers across), innermost of the four moons; Umbriel, 1169 kilometers wide; and Oberon, (1522 kilometers), outermost of the four. Titania orbits between Umbriel and Oberon.

To scale: the five largest moons of Uranus in order (left to right) out from the planet. Image credit: NASA.

Though often derided as small and dull, the reality is that the Uranian satellites are little known. Voyager 2, the only spacecraft to visit Uranus, imaged no more than 40% of any Uranian moon as it flew through the system in January 1986. Furthermore, the Cassini Saturn tour has revealed that even small outer Solar System satellites can be surprising: Enceladus, for example, just 505 kilometers wide and by all rights cold and dead, is hot enough inside that it blasts salty water into space from parallel cracks ("tiger stripes") at its south pole at more than 2000 kilometers per hour.

In a paper published in the Journal of Spacecraft and Rockets shortly before Galileo concluded its Jupiter satellite tour, Andrew Heaton of NASA Marshall Space Flight Center and James Longuski of Purdue University demonstrated that the Uranus system could support a complex Galileo-style tour. This was, they acknowledged, "contrary to intuition. . .because the Uranian satellites are much less massive than those of Jupiter."

A Galileo-style tour would be possible, they explained, because "the key to a significant gravity assist is not the absolute size of the satellite, but the ratio of its mass to its primary, and the mass ratios of the Uranian satellites to Uranus are similar to those of the Jovian satellites to Jupiter." Titania and Oberon form a large outer pair similar to Ganymede and Callisto, they noted, while Ariel and Umbriel form a small inner pair equivalent to Io and Europa. The "Uranian system is nearly a smaller replica of the Jovian system," Heaton and Longuski wrote.

To perform their calculations, they relied on "Tisserand graphs" developed at Purdue University in the late 1990s. Their mathematical tool was named for 19th-century mathematician Felix Tisserand, who had calculated the effects of planetary gravity on the motion of comets. Tisserand followed in the footsteps of Anders Johan Lexell, who in the early 1770s had sought to explain the sudden appearance and subsequent disappearance of a previously unknown comet. In 1770, Comet Lexell flew past the Earth at a distance of 2.3 million kilometers.

A previous post detailed how, in the early 1960s, Michael Minovitch used his own graphs and University of California, Los Angeles and Jet Propulsion Laboratory computers to calculate dozens of gravity-assist trajectories (see "For More Information" at the end of this post). His work laid the groundwork for many planetary missions, including the Mariner 10 Venus-Mercury flybys and Voyager 2's Jupiter-Saturn-Uranus-Neptune "Grand Tour." Minovitch did not, however, calculate satellite system tours; presumably this was because in the early 1960s so little was known of outer Solar System moons.

Heaton and Longuski described a three-phase, 811-day Uranian system tour. After launch from Earth in March 2008 and a gravity-assist flyby of Jupiter in September 2009, the Uranus tour spacecraft would fire its main rocket engine to capture into an elliptical Uranus orbit on Valentine's Day in 2018. This would mark the start of the first Uranus tour phase, which would be devoted to matching the plane of the Uranian equator, ring system, and moon orbits.

Images of Uranus and its ring system taken over four years using the Hubble Space Telescope in Earth orbit. South is to the left. The 2003 and 2005 images show features in the planets clouds; a southern hemisphere polar hood and, in 2005, a northern hemisphere storm. In the 2007 image, the planet's rings and equator are edge on to the Sun.

Uranus is tipped on its side relative to the other planets in the Solar System, and its moons have equatorial orbits. Heaton and Longuski wrote that the Uranian system would appear edge-on to the Sun in 2007, then would tilt gradually until the planet and its moons pointed their north poles at the Sun in 2028.

The Uranus tour spacecraft would capture into an initial orbit tilted 13.6° relative to the planet's equator and system plane. It would fly past Titania in May 2019 at a distance of 316 kilometers, allowing the largest Uranian satellite to "crank" its orbital plane. A total of nine similar Titania flybys over 261 days would place the spacecraft into the same plane as the Uranian equator, rings, and moons.

The second phase of the Uranus tour, the energy-reduction phase, would see the spacecraft reduce the size of its orbit, thus shortening its orbital period, while at the same time conducting a thorough exploration of the four largest Uranian moons. This would begin 287 days after the spacecraft captured into Uranus orbit with a flyby of Oberon at a distance of 414 kilometers and would proceed through eight Ariel flybys, five Umbriel flybys, three Titania flybys, and four additional Oberon flybys over the course of the next 395 days.

The spacecraft would pass nearest any world in the Uranian system during this phase. At the start of its 14th revolution about Uranus, almost exactly one Earth year (364.3 days) after arriving at the planet, it would pass just 54 kilometers over Umbriel's icy landscapes.

The southern hemisphere of Miranda: a mosaic of images from the January 1986 Voyager 2 Uranus flyby. Image credit: NASA.

Heaton and Longuski did not include the enigmatic moon Miranda on their list of close flybys because it orbits close to Uranus and, with a diameter of just 480 kilometers (only a little smaller than surprising Enceladus) is less than half the size of Ariel, the smallest moon they employed for gravity assists. Close proximity to Uranus and low mass would mean that Miranda's gravity could contribute little to shaping the Uranus tour.

Miranda has some of the most intriguing known surface features on the Uranian satellites — for example, Verona Rupes, a five-kilometer-high fault scarp that begins near the edge of the lighted area visible to Voyager 2. Presumably the Uranus tour spacecraft would image Miranda whenever its tour route took it relatively close by.

The third and final phase of the tour would commence 691 days after Uranus arrival with a 151-kilometer Umbriel flyby. The somewhat arbitrary goal of the third phase would be to place the Uranus tour spacecraft into orbit around Ariel. Through three additional Umbriel flybys and four Titania flybys over 120 days the spacecraft would nearly match Ariel's orbit about Uranus, reducing its maximum velocity relative to its target to slightly less than one kilometer per second. The Uranus tour spacecraft would then briefly fire its rocket motor to slip into orbit about Ariel.

Source

"Feasibility of a Galileo-Style Tour of the Uranian Satellites," A. Heaton and J. Longuski, Journal of Spacecraft and Rockets, Volume 40, Number 4, July-August 2003, pp. 591-596.

More Information

The Challenge of the Planets, Part Three: Gravity

Centaurs, Soviets, and Seltzer Seas: Mariner 2's Venusian Adventure (1962)

Touring Titan By Blimp & Buoy (1983)