Astronomy & Celestial Mechanics
the sky, computed
Concept

Momentum dumping — where it appears

Removing angular momentum that a spacecraft's reaction wheels have absorbed from outside torques, by applying an external torque while the wheels slow down. Thrusters do it with propellant; magnetic torquers do it against a planet's field.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

Also named here as reaction wheel — the same set of essays touches all of them, so they are one junction rather than several.

An oscillation that does not matter, on a ramp that does. Stored angular momentum in a reaction wheel over 160 days at 550 kilometres, with a capacity of 25 newton metre seconds. The total environmental torque is 1.75e-4 newton metres, of which 35 per cent is taken to survive averaging over an orbit. The fast oscillation is the part that does not survive: it has the 95.6-minute orbital period, reaches 0.10 newton metre seconds, and returns to where it started every revolution, so it consumes capacity and nothing else. The ramp under it is the secular part, and its slope measured between two instants a whole number of orbits apart is 6.117e-5 newton metres, which is the secular torque and is how the figure checks itself. The wheel fills in 4.7 days and has to be emptied 33 times in the span drawn. Every attitude-controlled spacecraft in the collection lives on this sawtooth, and the vertical drops are the only part of it that costs anything: the store can be moved between wheels for nothing, and taken out of the vehicle only by pushing against something outside it.

The spin that has to be put somewhere

A spacecraft holding an attitude is not resisting a force. It is absorbing a slow, one-directional trickle of angular momentum from the gradient of gravity across its own body, from sunlight, from the last of the atmosphere — and every store it has for that trickle fills up.

spaceflight · Attitude control The pitch wheel, dumped into the field at four inclinations. Momentum stored in the pitch wheel of an Earth-pointing satellite at 500 km, over 3 days, under a steady pitch torque of 0.2 μN m, with coils of at most 0.2 A m² dumping it into the Earth's field under a law of gain 0.0005 per second. Without coils the store grows in a straight line to 51.8 mN m s. In orbits inclined at 0°, 28.5°, 51.6°, 97.4° it ends at 7.51, 1.18, 0.54, 0.40 mN m s. In the equatorial orbit the field lies close to the pitch axis, so only a small share of the stored momentum is across the field where the coils can remove it, and the store climbs until that share, times the gain, matches the torque.

The one axis the field will not take

A satellite that keeps one face towards the Earth can empty its reaction wheels into the Earth's magnetic field with coils, using no propellant. Its own rotation, once an orbit, cancels every steady torque except those about one axis, the pitch axis normal to the orbit. In an orbit near the equator the field lies along that same axis, and a coil cannot push about the direction of the field.

spaceflight · Attitude control

Named alongside it

The objects these essays reach for when they reach for this one.

Angular momentumAttitude controlMagnetorquerReaction wheelSaturationAtmospheric dragGravity gradient torqueInclinationMagnetic fieldMoment of inertiaPointing stabilitySecular variation

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