Just a quick post to remind you (as if you needed it) that, in about 5 minutes’ time at 10am BST, the ESA spacecraft Rosetta will begin its encounter with a comet (actually Comet 67P/Churyumov-Gerasimenko).
As it approached its target, Rosetta took this picture that revealed the comet to be a rather peculiar beast, rather like a rubber duck:
Here’s a more recent, closer, view:
Rosetta’s journey began on 2 March 2004 when Rosetta was launched on an Ariane 5 from Europe’s Spaceport in Kourou, French Guyana. Since then, the spacecraft has orbited around the Sun five times, picking up speed through three gravitational “slingshots” at Earth and one at Mars, to enter an orbit similar to that of its target, said comet 67P/Churyumov–Gerasimenko, which is in an elliptical 6.5-year solar orbit that takes it from beyond the orbit of Jupiter at its furthest point, and between the orbits of Mars and Earth at its closest to the Sun.
To perform its rendezvous Rosetta has to match the pace of the comet – currently about 55 000 km/h – and travel alongside it to within just 1 m/s between them. This has required a complex and delicate series of manoeuvres:
The spacecraft will then travel alongside the comet as it approaches the Sun. In November 2014 the Philae probe will be deployed and will land on the comet surface. Rosetta will follow the comet to its closest distance to the Sun on 13 August 2015 and as it moves back towards the outer Solar System. The nominal mission end is December 2015.
I bet there’s quite a lot of stress in the ESA control centre in Darmstad, Germany, as the probe’s epic journey nears its end, not least because telemetry is lost while the burn happens. Those ten years in space will count for little if something goes wrong now. Good luck everyone involved!
You can watch a live feed of the encounter here.
UPDATE: after an agonizing wait – it takes 23 minutes for telemetry to reach Earth from Rosetta – the spacecraft has entered orbit correctly. Well done everyone!
UPDATE: click here for an amazing collection of images of the comet.
UPDATE: Relief at ESA HQ as The Clangers finally emerge to greet the Rosetta Spacecraft:
. Their (Eulerian) positions at some later time 
are taken to be![\vec{r}(\vec(q),t) = a(t) \vec{x}(\vec{q},t) = a(t) \left[ \vec{q} + b(t) \vec{s}(\vec{q},t) \right].](https://s0.wp.com/latex.php?latex=%5Cvec%7Br%7D%28%5Cvec%28q%29%2Ct%29+%3D+a%28t%29+%5Cvec%7Bx%7D%28%5Cvec%7Bq%7D%2Ct%29+%3D+a%28t%29+%5Cleft%5B+%5Cvec%7Bq%7D+%2B+b%28t%29+%5Cvec%7Bs%7D%28%5Cvec%7Bq%7D%2Ct%29+%5Cright%5D.&bg=000000&fg=B0B0B0&s=0&c=20201002)
coordinates are comoving, i.e. scaled with the expansion of the Universe using the scale factor 
. The displacement 
between initial and final positions in comoving coordinates is taken to have the form
is a kind of velocity potential (which is also in linear Newtonian theory proportional to the gravitational potential).If we’ve got the theory right then the gravitational potential field defined over the initial positions is a Gaussian random field. The function 
is the growing mode of density perturbations in the linear theory of gravitational instability.
In the Dark 