How do space probes navigate large distances with such accuracy? —T. STORM, BROADBEACH, QUEENSLAND, AUSTRALIA

Jeremy Jones, chief of the navigation team for the Cassini Project at the NASA Jet Propulsion Laboratory, replies:

Accurate navigation in space depends on three factors: estimating the probe's current position and velocity (the trajectory), predicting its future trajectory and adjusting the trajectory to achieve the mission objectives.

Estimating the current trajectory requires a model of the forces acting on the probe and measurements of the distance and speed of the probe. Because gravity is dominant, the primary force models are the planetary and satellite ephemerides, which specify the location of all major solar system bodies at any given time. Current planetary ephemerides are accurate to within less than a kilometer for the inner planets and less than 10 kilometers for Jupiter and Saturn. The orbits of Saturn's moons have been determined to within an accuracy of less than one kilometer for Titan and less than 10 kilometers for the other satellites.

Measurements of the range and speed of the probe are used to locate the probe relative to Earth. For all U.S. interplanetary probes, the antennas of the Deep Space Network provide the measurements. These antennas transmit radio signals to a probe, which receives these signals and returns them to the ground station. Navigators compute the difference between the transmitted and received signals to determine a probe's distance and speed. We can fix its radial velocity to an accuracy of 0.05 millimeter per second and its range to three meters. By using measurements spread over days to weeks, we can estimate the location of the probe to an accuracy of better than one kilometer.

The estimation process also results in improvements in the force models. The resulting estimates of the current position and velocity of the probe and the improved force models help to predict the probe's future locations. These predictions are then compared against the mission objectives to determine what corrections are required. Once the predicted attitude error is known, the last step is to determine when to use the probe's propulsion system to make the required correction. A typical mission will schedule a sequence of course adjustments to minimize propellant usage and maximize accuracy. Cassini schedules three corrections between Saturn satellite encounters and achieves a flyby accuracy of a few kilometers or less.

What causes ringing in the ears? —J. GIAMBRONE, CENTER MORICHES, N.Y.

James B. Snow, Jr., a physician, emeritus professor at the University of Pennsylvania, and former director of the National Institute on Deafness and Other Communication Disorders, offers this explanation:

Tinnitus (“to ring like a bell” in Latin), the medical term for ringing in the ears, is thought to occur when the brain areas involved in hearing spontaneously increase their activity; it is associated with virtually all disorders of the auditory system. It is not limited to ringing; it may also be perceived as whistling, buzzing, humming, hissing, roaring, chirping or other sounds.

The most common form of tinnitus arises from damage to the inner ear, or cochlea, caused by exposure to high volumes. Other causes include drugs such as aspirin, quinine and aminoglycoside antibiotics, cancer chemotherapeutics and other ototoxic agents, and infections and head injuries.

If the inner ear is damaged, input decreases from the cochlea to the auditory centers in the brain stem, such as the dorsal cochlear nucleus. This input loss may lead to increased spontaneous activity in the nucleus neurons, as if some inhibition had been removed. Imaging studies confirm increased neural activity in the auditory cortices of tinnitus sufferers. Their brains also show increased activity in the limbic structures associated with emotional processing. Other symptoms that sometimes appear alongside tinnitus—such as emotional distress, depression and insomnia—may have a common basis in some limbic structure, such as the nucleus accumbens.

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