Spacecraft attitude control

Gravity-gradient stabilization

Gravity-gradient stabilization (a.k.a. "tidal stabilization") is a method of stabilizing artificial satellites or space tethers in a fixed orientation using only the orbited body's mass distribution and gravitational field. The main advantage over using active stabilization with propellants, gyroscopes or reaction wheels is the low use of power and resources. It can also reduce or prevent the risk of propellant contamination of sensitive components. The idea is to use the Earth's gravitational field and tidal forces to keep the spacecraft aligned in the desired orientation. The gravity of the Earth decreases according to the inverse-square law, and by extending the long axis perpendicular to the orbit, the "lower" part of the orbiting structure will be more attracted to the Earth. The effect is that the satellite will tend to align its axis of minimum moment of inertia vertically. The first experimental attempt to use the technique on a human spaceflight was performed on September 13, 1966, on the US Gemini 11 mission, by attaching the Gemini spacecraft to its Agena target vehicle by a 100-foot (30 m) tether. The attempt was a failure, as insufficient gradient was produced to keep the tether taut. The technique was first successfully used in a near-geosynchronous orbit on the Department of Defense Gravity Experiment (DODGE) satellite in July 1967. It was first used for low Earth orbit and tested unsuccessfully for geosynchronous orbit in the Applications Technology Satellites ATS-2, ATS-4 and from 1966 until 1969. The lunar orbiter Explorer 49 launched in 1973 was gravity gradient oriented (Z axis parallel to local vertical). Long Duration Exposure Facility (LDEF) used this method for 3-axis stabilization; yaw about the vertical axis was stabilized. An example of gravity-gradient stabilization was attempted during NASA's TSS-1 mission in July 1992. The project failed because of tether deployment problems. In 1996 another mission, TSS-1R, was attempted but failed when the tether broke. Just prior to tether separation, the tension on the tether was about 65 N (14.6 lbs). (Wikipedia).

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From playlist Applied Machine Learning 2020

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From playlist Functions of Several Variables - Calculus

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From playlist gradient_descent

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