# Reaction wheels and pointing satellites

The Kepler telescope, a satellite telescope in orbit around the Sun* designed to look for exoplanets, has come to the end of its original mission. The end of the mission was caused by the failure of ‘s reaction wheels, which are used to point the telescope. Reaction wheels are electric motors connected to metals discs, usually with masses between . As the speed of the motors are altered the conservation of angular momentum imparts a force on the spacecraft, causing it to rotate around its centre of mass.

The aboard the Lunar Reconnaissance Orbiter.

Reaction wheels are usually employed in groups of three, the x-, y- and z-axes, enabling the telescope to be pointed accurately in . Kepler was fitted with , with all , and each acting as a spare for the other three. After wheels (#2) failed in July 2012 the spacecraft was still able to operate normally, but reaction wheel #4 began malfunctioning in January 2013, and whilst the wheel returned to working order initially, it failed completely on, leaving the spacecraft now unable to move and point properly.

Reaction wheels aboard Kepler.

Reaction wheels are often confused with momentum wheels, but the two are very different. Momentum wheels are much heavier, and spin at much higher rates, and their role is not to point or steer the spacecraft but rather to use the gyroscopic effect to keep it in a fixed position when subjected to perturbing forces such as solar wind or radiation pressure. Satellites in orbit close around Earth can also use a device called a magnetorquer to control their position. By altering the flow of current through a set of coils (again usually three, with the spacecraft pushes against Earth’s magnetic field and the reaction force against this push causes the satellite to rotate.

* Technically an Earth-trailing heliocentric orbit.

# The Torino Scale

The Torino Scale is a system for categorising the risk presented by near earth objects (NEOs) such as asteroids and comets. On the Torino Scale NEOs are rated on a scale from zero to ten, based on a combination of the probability of an object striking earth and the kinetic energy of that object.

Because orbits are unstable and can change the scale only applies to potential objects less than one hundred years in the future. The diagram below shows the different Torino Scale categories, with a logarithmic scale on both axes and an approximate indication of the diameter of the asteroid on the kinetic energy axis.

The Torino Scale is separated into five categories:

• White (Torino Scale 0) – No hazard; “the likelihood of a collision is zero, or is so low as to be effectively zero”.
• Green (Torino Scale 1)Normal; “a routine discovery in which a pass near the Earth is predicted that poses no unusual level of danger … new telescopic observations very likely will lead to re-assignment to Level 0”.
• Yellow (Torino Scale 2-4)Meriting attention by astronomers; “current calculations give a 1% or greater chance of collision capable of localised [Level 3] or regional [Level 4] destruction”.
• Orange (Torino Scale 5-7)Threatening; at its most extreme “a very close encounter by a large object, which if occurring this century, poses an unprecedented but still uncertain threat of a global catastrophe”.
• Red (Torino Scale 8-10)Certain collision; “a collision is certain, capable of causing localized destruction [Level 8] … unprecedented regional devastation for a land impact or the threat of a major tsunami for an ocean impact [Level 9] … or capable of causing global climatic catastrophe that may threaten the future of civilisation as we know it, whether impacting land or ocean [Level 10]”.

As new data about an NEO becomes available the Torino Scale rating for an object can jump suddenly: the Chelyabinsk meteor had a kinetic energy of 0.4 megatons TNT equivalent, giving it a Torino Scale rating of zero, but had it been only a little bit more massive or slightly faster (one megaton) it would have suddenly jumped to an eight.

Currently NASA’s Jet Propulsion Lab’s Sentry system lists only one NEO with a non-zero Torino Scale rating. 2007 VK 184 has a Torino Scale rating of one, but the earliest possible collision date is in June 2048, so we don’t have to start worrying just yet.

# The Roche limit and planetary rings

As a satellite orbits around an object (a primary), the gravitational force on the side closest to the object is greater than that on the side opposite the object. This difference in gravitational attraction gives rise to a tidal force (so-called because it is what causes the tides on Earth). As a satellite approaches closer to the body it orbits this tidal force will eventually become greater than the gravitational forces holding the satellite together. The point at which this occurs is known as the Roche limit (named for Édouard Roche who first calculated it).

The Roche limit d depends on the radius of the primary RM, the density of the primary ρM and the density of the satellite ρm.

$d = 2.44\; R_M \sqrt[3]{\frac {\rho_M} {\rho_m}}$

If we take our Earth-Moon system as an example, with the radius of Earth being 6370 kilometres, the Earth’s density as 5520 kilograms per cubic metre and the Moon’s density as 3350 kg/m3 this gives us a Roche limit of 18 400 km. The Moon’s actual orbit is 385 000 km, so luckily we don’t have to worry about the Moon breaking up any time soon.

The Earth-Moon system, to scale. The area beyond the Roche limit is shaded red.

When an orbiting object passes through the Roche limit it begins to break up, with the material closest to the object moving faster than the material behind it. This eventually leads to the formation of rings.

# Whipple shielding

Space is full of micrometeroids and debris whizzing around at incredible speeds, thousands of metres per second. At these speeds even tiny objects have enormous amounts of kinetic energy and can cause serious damage on impact.

The image above shows what happens to a eighteen centimetre-thick aluminium plate when struck by a two-and-a-half gram twelve millimetre-wide aluminium ball travelling at nearly seven kilometres per second . You can see the large crater created, and spalling beginning to occur on the opposite side of the plate as the impact shockwave reflects off it.

To prevent damage to spacecraft thick and heavy shielding as shown above is clearly unsuitable; this is where the Whipple shield comes into play.

In its simplest form a Whipple shield is simply two thin layers of shielding separated by a gap. Impact with the first layer of shielding causes the projectile to vaporise, preventing it from penetrating the second layer. In this way two light and thin layers can have a much better shielding effect than one heavy and thick layer. (Other types of Whipple shielding also exist, using multiple layers or “stuffed” layers containing a substance like Kevlar.)

(L-R) A multi-layer and twin-layer Whipple shield.

In the example on the right-hand side it is easy to see the shielding effect in play – the projectile has punched a tiny hole in the first layer but failed to penetrate the second layer, causing only minor heat damage (from the plasma produced on impact).

# GPS in space

The global positioning system (GPS) run by the US Department of Defense makes it very easy to find your position anywhere on Earth, but what if you’re not on Earth? What if you’re in space? At the moment researchers rely on simple time of flight calculations using antennae spaced out across the Earth’s surface to work out where their probes are, but this method becomes increasingly inaccurate as the distance to objects increases. (As an example, the error in the position of an object at the orbit of the most distant planet, Neptune, is about 120 kilometres.)

A group led by Professor Werner Becker from the Max Planck Institute for Extraterrestrial Physics in Germany think they might have a way to make a “GPS for Space” using X-ray pulsars.

A pulsar (“pulsating star”) is formed when a massive star explodes in a supernova, compressing the star’s core into a highly magnetised fast-rotating neutron star that emits a beam of electromagnetic radiation. The period of rotation of a pulsar is very short (milliseconds to seconds), and the the invariance of the period of rotation of some pulsars rivals atomic clocks in their accuracy.

Because each pulsar has a characteristic period of rotation it is easy to identify a signal as having been received from one specific pulsar. By mapping the position of hundreds or thousands of highly accurate pulsars relative to each other, and comparing the signals received at a spacecraft’s location with the data for a reference location it should be possible to map an object’s position anywhere within our galaxy to an accuracy of five kilometres, an incredible degree of accuracy. This is a little bit like being able to measure your position on the surface of Earth to within the width of an atom or two!