Trojans and Hildas in the asteroid zone

When the $6 billion+ James Webb space telescope is launched by NASA in 2018, where will they put it?
Quoting NASA: ‘The Webb won’t be orbiting the Earth – instead we will send it almost a million miles out into space to a place called “L2.”‘

So we have two questions: where is ‘L2′, and what does it have to do with asteroids? It’s a point approximately 1,500,000 kilometres (930,000 miles) beyond the Earth, such that a straight line can be drawn from L2 through Earth to the Sun. In fact the telescope will go into a ‘halo orbit’ to avoid Earth’s shadow, i.e. move around the exact L2 point.

https://en.wikipedia.org/wiki/Halo_orbit

And where do the asteroids come in? Well, the ‘L’ in L2 stands for Lagrange, the Italian-French mathematician who first predicted the existence of five special points in a planet’s orbit now known as Lagrange (or Lagrangian) points.

We’ll leave most of the technical explanations aside, but NASA says:

‘There are five special points where a small mass can orbit in a constant pattern with two larger masses. The Lagrange Points are positions where the gravitational pull of two large masses precisely equals the centripetal force required for a small object to move with them’ (*L1 – L5)

This graphic shows the positions:

[image credit: Wikipedia]

While the L1, L2 and L3 points are considered to be unstable, L4 and L5 are stable.
NASA calls the L2 point ‘a wonderful accident of gravity and orbital mechanics.’

http://www.nasa.gov/topics/universe/features/webb-l2.html

Jupiter, by far the largest planet in the solar system, has large groups of asteroids around both its L4 (3900 +) and L5 (1900 +) points, known collectively as trojans – although the (leading) L4 group are the Greeks and the (trailing) L5 are the Trojans. As these asteroids are located on or close to the line of Jupiter’s orbit, they share its orbit period and are permanently confined to their L4 and L5 zones, as shown here (the white dots are the main asteroid belt).

[image credit: Wikipedia]

Some other planets also have a few trojans. Even Earth has at least one – 2010 TK7:

http://www.bbc.co.uk/news/science-environment-14307987

So we have groups of asteroids here ‘behaving’ in a structured and predictable way, namely in a 1:1 mean motion resonance with Jupiter. Nearby can be found more such definable patterns, within another asteroid group called ‘the Hilda family’. These are in a 3:2 mean motion resonance with Jupiter, since they orbit the Sun three times per two Jupiter orbits. At any given moment during their individual elliptical orbits, they collectively form what’s known as the ‘Hildas triangle’, shown here:

[image credit: easysky.de]

Their orbits are configured so their conjunction with Jupiter occurs close to their perihelion point, meaning at the time when they have the Sun between themselves and Jupiter. Thus they don’t run the risk of getting too close to Jupiter and being swallowed up by its enormous gravity. Generally they don’t interfere with the nearby Trojans as the latter are at higher inclinations.

An animation of the orbit of asteroid 153 Hilda can be found here:

http://en.wikipedia.org/wiki/Hilda_family

The main asteroid belt between Jupiter and Mars reveals another interesting feature, namely the Kirkwood gaps. These are locations where there are no, or hardly any, asteroids at all whereas either side there are plenty. The reason for the gaps stems from the fact that they lie at ‘resonance points’ with Jupiter, mainly where 2:1, 3:1, 5:2 or similar high-resonance orbit ratios would occur.

This chart shows clearly where the gaps are:

[image credit: Wikipedia]

Our final examples of specific asteroid behaviour lie further out in the solar system, near Neptune. Here we find the Trans-Neptunians, bodies that orbit in a 3:2 resonance with Neptune itself (2 orbits per 3 Neptune). This group includes dwarf planet Pluto and its ‘twin’ Orcus, and are often known as Plutinos.

http://en.wikipedia.org/wiki/Plutino

A further category on the same lines contains the so-called ‘Twotinos’, which as the name tries to suggest are bodies ‘whose orbit has a 1:2 resonance with the planet Neptune’ (Wikipedia).

Much more can be said about asteroids, but the point here is simply to show that resonance plays a key part in the solar system for many of these relatively small bodies. It can even be their passport to long-term survival in the system.

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‘The easiest way to understand Lagrange points is to adopt a frame of reference that rotates with the system’ says NASA.
More about the Lagrange points from NASA here, with clear graphics:

http://map.gsfc.nasa.gov/mission/observatory_l2.html

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Footnote – a recent (30 Jan. 2014) science paper says:
‘Asteroid Belt More Diverse than Previously Realized’

http://scitechdaily.com/asteroid-belt-diverse-previously-realized/

Source: http://tallbloke.wordpress.com/2014/02/08/trojans-and-hildas-in-the-asteroid-zone/