Question

1. Describe the Deep Impact and Stardust missions and what they were designed to achieve?
2. Describe three ways in which our solar system would be different if orbital resonances had been important?

Answer 1

Deep Impact was a NASA space probelaunched from Cape Canaveral Air Force Station on January 12, 2005. It was designed to study the interior composition of the comet Tempel 1 (9P/Tempel), by releasing an impactor into the comet. At 05:52 UTC on July 4, 2005, the Impactor successfully collided with the comet's nucleus. The impact excavated debris from the interior of the nucleus, forming an impact crater. Photographs taken by the spacecraft showed the comet to be more dusty and less icy than had been expected. The impact generated an unexpectedly large and bright dust cloud, obscuring the view of the impact crater.

Stardust was the first spacecraft to return a cometary sample and extraterrestrial material from outside the orbit of the moon to Earth. In 2004, the Stardust spacecraft made a close flyby of comet Wild-2, collecting comet and interstellar dust in a substance called aerogel.

Two years later, the samples made it back to Earth in a return capsule that landed in the Utah desert. The Stardust mission samples indicated that some comets may have included materials ejected from the early sun and may have formed very differently than scientists had theorized.

The spacecraft, which was still operational, was later recycled for the Stardust-NExT mission, which flew by comet Tempel 1 on Feb. 14, 2011.

Mission Events

Feb. 14, 2011: The Stardust spacecraft, which had been recycled for a second mission called Stardust-NExT, flew by comet Tempel 1, marking the first time a comet had been visited twice by any spacecraft. (The Deep Impact spacecraft visited Tempel 1 in 2005 and released an impactor on its surface.)

In celestial mechanics, orbital resonance occurs when orbiting bodies exert regular, periodic gravitational influence on each other, usually because their orbital periods are related by a ratio of small integers. Most commonly this relationship is found for a pair of objects. The physical principle behind orbital resonance is similar in concept to pushing a child on a swing, where the orbit and the swing both have a natural frequency, and the other body doing the "pushing" will act in periodic repetition to have a cumulative effect on the motion. Orbital resonances greatly enhance the mutual gravitational influence of the bodies, i.e., their ability to alter or constrain each other's orbits. In most cases, this results in an unstable interaction, in which the bodies exchange momentum and shift orbits until the resonance no longer exists. Under some circumstances, a resonant system can be stable and self-correcting, so that the bodies remain in resonance. Examples are the 1:2:4 resonance of Jupiter's moons Ganymede, Europa and Io, and the 2:3 resonance between Pluto and Neptune. Unstable resonances with Saturn's inner moons give rise to gaps in the rings of Saturn. The special case of 1:1 resonance between bodies with similar orbital radii causes large Solar Systembodies to eject most other bodies sharing their orbits; this is part of the much more extensive process of clearing the neighbourhood, an effect that is used in the current definition of a planet.

A binary resonance ratio in this article should be interpreted as the ratio of number of orbitscompleted in the same time interval, rather than as the ratio of orbital periods, which would be the inverse ratio. Thus the 2:3 ratio above means Pluto completes two orbits in the time it takes Neptune to complete three. In the case of resonance relationships among three or more bodies, either type of ratio may be used (in such cases the smallest whole-integer ratio sequences are not necessarily reversals of each other) and the type of ratio will be specified.

A Lindblad resonance drives spiral density waves both in galaxies (where stars are subject to forcing by the spiral arms themselves) and in Saturn's rings (where ring particles are subject to forcing by Saturn's moons).

A secular resonance occurs when the precession of two orbits is synchronised (usually a precession of the perihelion or ascending node). A small body in secular resonance with a much larger one (e.g. a planet) will precess at the same rate as the large body. Over long times (a million years, or so) a secular resonance will change the eccentricityand inclination of the small body.

Several prominent examples of secular resonance involve Saturn. A resonance between the precession of Saturn's rotational axis and that of Neptune's orbital axis (both of which have periods of about 1.87 million years) has been identified as the likely source of Saturn's large axial tilt (26.7°). Initially, Saturn probably had a tilt closer to that of Jupiter (3.1°). The gradual depletion of the Kuiper belt would have decreased the precession rate of Neptune's orbit; eventually, the frequencies matched, and Saturn's axial precession was captured into the spin-orbit resonance, leading to an increase in Saturn's obliquity. (The angular momentum of Neptune's orbit is 104times that of Saturn's spin, and thus dominates the interaction.)

The perihelion secular resonance between asteroids and Saturn (ν6 = g − g6) helps shape the asteroid belt (the subscript "6" identifies Saturn as the sixth planet from the Sun). Asteroids which approach it have their eccentricity slowly increased until they become Mars-crossers, at which point they are usually ejected from the asteroid belt by a close pass to Mars. This resonance forms the inner and "side" boundaries of the asteroid belt around 2 AU, and at inclinations of about 20°.

Numerical simulations have suggested that the eventual formation of a perihelion secular resonance between Mercury and Jupiter (g1 = g5) has the potential to greatly increase Mercury's eccentricity and possibly destabilize the inner Solar System several billion years from now.

The Titan Ringlet within Saturn's C Ring represents another type of resonance in which the rate of apsidal precession of one orbit exactly matches the speed of revolution of another. The outer end of this eccentric ringlet always points towards Saturn's major moon Titan.

A Kozai resonance occurs when the inclination and eccentricity of a perturbed orbit oscillate synchronously (increasing eccentricity while decreasing inclination and vice versa). This resonance applies only to bodies on highly inclined orbits; as a consequence, such orbits tend to be unstable, since the growing eccentricity would result in small pericenters, typically leading to a collision or (for large moons) destruction by tidal forces.

In an example of another type of resonance involving orbital eccentricity, the eccentricities of Ganymede and Callisto vary with a common period of 181 years, although with opposite phases.