Space Shuttle mission STS-132 is currently orbiting over our heads. It’s scheduled to land a week from now. After that, there’s two more launches and that will be that for the program. At that point the US will officially be out of the business of launching people into orbit, and there’s not a lot of prospect of getting back into that business in the near future. I don’t really regret the end of the shuttle program as such – it was never a really good human spaceflight strategy – but it’s a real shame we have nothing to replace it.

Oh well. To commemorate STS-132, how about a quick physics problem? First, take a look at STS-1, the first shuttle launch:

Notice anything different in this photograph compared to most shuttle launches? The most obvious difference is the color of the external tank. Here it’s painted white. Now it’s not painted at all, and is left its normal dull orange. The reason for this is that the paint required to cover the whole external tank weighed about 600 pounds. That’s not much compared to the weight of the entire shuttle, which weighs more than four and a half million pounds. Still every bit makes a difference. Let’s estimate how much.

We’ll do this Fermi-problem style and use approximations. To a first estimate, the gravitational acceleration at the shuttle’s orbital altitude is about the same as it is on the ground. The apparent zero-g that the astronauts experience is a result of free fall, not a result of being very far away from the gravitational field of the earth. The potential energy gained by moving 600 pounds to orbit is:

Where U is potential energy, m is the mass (in kilograms), g is the acceleration due to gravity, and h is the orbital altitude. Using the 206km insertion altitude, I get a figure of about 600 million joules. For the kinetic energy by virtue of orbital velocity, we can use the kinetic energy equation:

Shuttle orbital velocity is about 7.6 km/s, so that’s about 8 billion joules of energy. Adding, and we get about 8.6 billion joules or so of energy that would have to be used to get that paint into orbit. Compared to the total energy of the whole shuttle, that’s not much. But in absolute terms it’s quite a bit. 600 extra pounds of payload is nothing to sneeze at.