As I write this very quick post, Philae has just successfully separated from Rosetta and is on its way to comet 67P. We’re going to attempt to land on a comet. I’ll repeat that…. WE’RE GOING TO ATTEMPT TO LAND ON A COMET!!
Go science! Go engineering! Not the glamour (or human risk) of the moon landings, agreed, but technically far more difficult (although the Apollo crews didn’t have the benefit of computers any more powerful than a modern day car!).
The difficulties come from the mission’s remoteness and the time it takes for commands to arrive, and lack of gravity to help anchor the lander, called Philae.
They (Rosetta, Philae and comet 67P) are currently 28 light minutes from Earth. Even the simplest conversation takes an hour. No immediate correction will be possible.
I’d like to focus on the second difficulty. That of gravity. The first thing to note about gravity is that it’s weak. May not seem like it if you hurl yourself out of a plane, but it’s by far the weakest force in nature. The masses required to generate appreciable forces are large. Luckily, the physics is easy.
In this case Mr Newton works just fine and we can leave Mr Einstein’s spacetime bending theories out of it. So, how much will Philae weigh on the surface?
At this point, we need to clear up the conflation of weight and mass that is common in society. Mass (again leaving Mr Einstein at home) doesn’t change with gravity. If you’re 80Kg on Earth, you’d be 80Kg on the comet. Weight (the effect of gravity on that mass to produce a force) is what changes. This is measured in Newtons (N), not Kg (the unit of mass).
It’s a lucky coincidence that on the surface of the Earth, to get your weight in Newtons, just multiply your mass by 10. (9.8 if you’re counting calories!).
Back to Philae:
To find out it’s weight (force) on the surface of 67P, we need to know:
G (gravitational constant, who knows why?…) = 6.673×10−11 N(m/kg)2
M (Mass of comet 67P) = 1013 kg (10 Trillion Kg)
m (Mass of Philae) = 102 kg (100 Kg – similar to a human)
r (the distance between Philae and 67P’s centre of mass) = 2Km (2,000m is 67P’s approximate radius)
Plug these number into the above equation….. and Philae’s weight (the force it is exerting on the comet, and the comet is exerting on Philae) is 0.015 Newtons.
Let’s pop it back into Earth conflation speak…… here, on Earth, it weighs the equivalent of roughly 1 gram. The paperclip of the title.
Now imagine getting the leverage to attach something large but weighing 1 gram to a comet…. using a robot built 10 years ago….. with a 28 minute delay on commands…..
Pretty tricky! No wonder they have thruster pushing Philae down, harpoons, drills and screws…..
Good luck Philae!
And the moral of the story: If you want to lose weight, move to a comet!
ADDENDUM: Philae landed and ‘bounced’…….
Some more quick physics:
Take your paperclip and give it enough speed to go a foot in the air on its own. You gave it about 5mph of speed. A brisk human walk.
Now, if we gave the same initial speed to Philae, it’d go 20km before stopping and take 21 hours to come back down! Quite a bounce!