Archive for Lagrangian Points

Lisa Pathfinder – better late than never!

Posted in Science Politics, The Universe and Stuff with tags , , , , , , , on December 3, 2015 by telescoper

Determined to post about something positive after yesterday’s act of collective idiocy by Parliament I find myself given a golden opportunity by today’s successful launch of the Lisa Pathfinder experiment by the European Space Agency.

As space missions go, LISA Pathfinder seems quite a modest one: it is basically a pair of identical 46 mm gold–platinum cubes separated by 38 cm. The idea is to put these test masses in free fall and measure their relative positions as accurately as possible.

After a false start yesterday, LISA Pathfinder was successfully launched in the early hours of this morning and is now en route to the First Lagrangian Point of the Earth-Sun system, about 1.5 million miles from Earth, at the location marked L1 in the diagram:


The contours show the “effective potential” of the Earth-Sun system, which takes into account the effect of rotation as well as gravity. The five Lagrangian points are the places at which tis effective potential is locally flat, i.e. where its spatial gradient vanishes. Any physics student will know that when the gradient of the potential is zero there is no force on a test particle. What this means is that an object placed exactly at any of the 5 Lagrangian points stays in the same position relative to the Earth and Sun as the system rotates. Put a spacecraft at one of these points, therefore, and it stays put when viewed in a frame rotating around the Sun  at the same speed as the Earth.

It’s not quite as simple as this because, as you will observe the Lagrangian points are not stable: L1, L2 and L3 are saddle-points; a  stable point would be a local minimum. However, around the first three there are stable orbits so in effect a test mass displaced from L1, say, oscillates around it without doing anything too drastic. L4 and L5 can be stable or unstable, in a general system but are stable for the case of the Solar System, hence the tendency of asteroids (the Trojans) to accumulate at these locations.

You may remember that WMAP, Planck and Herschel were all parked in orbits around L2. A spacecraft positioned exactly at L2 is permanently screened from the Sun by the Earth. That might be very useful if you want to do long-wavelength observations that require very cool detectors, but not if you want to use the Sun as a source of power. In any case, as I explained above, spacecraft are not generally located exactly at L2 but in orbit around it. Planck in fact had solar cells on the base of the satellite that provided power but also formed a shield as they always faced the Sun as the satellite rotated and moved in its orbit to map the sky. The choice of L1 for LISA Pathfinder was made on the basis of spacecraft design considerations as it will operate in a very different manner from Planck.

The reason for doing eLISA is to demonstrate the technological feasibility of a much more ambitious planned gravitational wave detector in space originally called LISA, but now called eLISA. The displacement of test masses caused by gravitational waves is tiny so in order for eLisa it is necessary (a) to screen out every effect other than gravity, e.g. electromagnetic interactions due to residual charges, to great precision and (b) to measure relative positions to great accuracy. That’s why it was decided to fly a cheaper technology demonstrator mission, to prove the idea is feasible.

LISA Pathfinder won’t make any science discoveries but hopefully it will pave the way towards eLISA.

It has to be said that LISA Pathfinder has had a fairly troubled history. I just had a quick look at some papers I have dating back to the time when I was Chair of PPARC Astronomy Advisory. Among them I found the categorical statement that

LISA Pathfinder will be launched in 2009.

Hmm. Not quite. It’s obviously running quite a long way behind schedule and no doubt considerably over its initial budget but it’s good to see it under way at last. There will be a lot of sighs of relief that LISA Pathfinder has finally made it into space! Now let’s see if it can do what it is supposed to do!