In mathematics, the integral of a function of several variables defined on a line or curve that has been expressed in terms of arc length (see length of a curve). An ordinary definite integral is defined over a line segment, whereas a line integral may use a more general path, such as a parabola or a circle. Line integrals are used extensively in the theory of functions of a complex variable.
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The COmet Nucleus TOUR (CONTOUR) was a NASA Discovery-class space probe that failed shortly after launch. It had as its primary objective close flybys of two comet nuclei with the possibility of a flyby of a third known comet or an as-yet-undiscovered comet. The two comets scheduled to be visited were Encke and Schwassmann-Wachmann-3, and the third target was d'Arrest. It was hoped that a new comet would have been discovered that would have been in the inner solar system between 2006 and 2008, in which case the spacecraft trajectory would have been changed if possible to rendezvous with the new comet. Scientific objectives included imaging the nuclei at resolutions of 4 m, performing spectral mapping of the nuclei at resolutions of 100-200 m, and obtaining detailed compositional data on gas and dust in the near-nucleus environment, with the goal of improving our knowledge of the characteristics of comet nuclei.
After ignition on 15 August 2002 of the solid rocket motor intended to inject the spacecraft into solar orbit, contact with the probe could not be re-established. Ground-based telescopes later found three objects along the course of the satellite, leading to the speculation that it had been destroyed. Attempts to contact the probe were ended on 20 December 2002. The probe accomplished none of its objectives.
The CONTOUR spacecraft had a total fueled mass of 775 kg, including 70 kg of hydrazine fuel and a Star 30BP booster with a mass of 377 kg. Power was provided by a body-mounted solar array designed for operation at distances between 0.75 and 1.5 AU from the Sun. It was three-axis stabilized for encounters and spin-stabilized during cruise mode between encounters. COUNTOUR's Command/Data-handling and Guidance/Control computers each used the Mongoose-V microprocessor. Communications were through a fixed 0.45 m diameter high-gain antenna to support data rates greater than 100 kbit/s at encounters. Data and images were stored on two 3.3 Gbit solid-state recorders with a capacity of 600 images. The spacecraft was equipped with four primary science instruments, the Contour Remote Imager/Spectrograph (CRISP), the Contour Aft Imager (CAI), the Dust Analyzer (CIDA), and the Neutral Gas Ion Mass Spectrometer (NGIMS).
CONTOUR launched on a Delta 7425 (a Delta II Lite launch vehicle with four strap-on solid-rocket boosters and a Star 27 third stage) on July 3, 2002 at 6:47:41 UT (2:47:41 a.m. EDT) into a high-apogee Earth orbit with a period of 5.5 days from Cape Canaveral Air Force Station. Following a series of phasing orbits, the Star 30 solid rocket motor was used to perform an injection maneuver on August 15, 2002 to put CONTOUR in the proper trajectory for an Earth flyby in August 2003 followed by an encounter with comet Encke on 12 November 2003 at a distance of 100 to 160 km and a flyby speed of 28.2 km/s, 1.07 AU from the Sun and 0.27 AU from Earth. During the maneuver the probe was lost. Three more Earth flybys would have followed, in August 2004, February 2005, and February 2006. On 18 June 2006 CONTOUR would have encountered comet Schwassmann-Wachmann-3 at 14 km/s, 0.95 AU from the Sun and 0.33 AU from Earth. Two more Earth flybys were scheduled in February 2007 and 2008, and a flyby of comet d'Arrest might have occurred on 16 August 2008 at a relative velocity of 11.8 km/s, 1.35 AU from the Sun and 0.36 AU from Earth. All flybys would have had a closest encounter distance of about 100 km and would have occurred near the period of maximum activity for each comet. After the comet Encke encounter, CONTOUR might have been retargeted towards a new comet if one is discovered with the desired characteristics (e.g. active, brighter than absolute magnitude 10, perihelion within 1.5 AU).