Remember how in the last BAN issue I noted that 756 is the sum of six consecutive primes numbers? Well, guess what? Today’s issue number, 757, is the sum of seven consecutive prime numbers! 97 + 101 + 103 + 107 + 109 + 113 + 127 = 757. How about that? By the way, the first such number is 58, and again there are an infinite number of such numbers. Math is cool, but sometimes it’s kinda weird.

As I mentioned in the News Roundup section of BAN 742, NASA plans on de-orbiting the International Space Station (ISS) sometime on or after 2030. The station is old, upkeep is expensive, and NASA is hoping that commercial companies will step in to build their own stations around that timeframe. I think that’s…aspirational, but OK.

Journalist and science communicator Swapna Krishna has an in-depth article about the whys and hows of all this. Read that to get tons more info.

Still, I got a question from a BAN reader recently, asking why we don’t attach a rocket to it and send it out into deep space like the Voyager probes.

There are several answers to that. One is that there’s no reason to send it out into the solar system at large; it’s not designed to do that sort of exploration. We’d need to keep astronauts on it alive for years, and there’s no way to easily automate it to do the kind of science we’d want for a mission like that. There’s no equipment on board to do that anyway! So it makes more sense to send small probes to explore the solar system like we do now.

The other problem is physically getting it out of Earth orbit. Let’s look into that a bit.

Right now ISS is about 415 kilometers over Earth’s surface. At that height the atmosphere is almost a vacuum, but not quite. There’s enough air up there to cause drag on the station. This steals orbital energy from it, which lowers the orbit. Judging by the orbital height graph on the site Heavens Above, it drops roughly 3 km every month (though that changes all the time, depending on things like solar activity which heats the upper atmosphere, causing it to expand and cause more drag).

Those sharp jumps you see are when rockets (Russian Progress spacecraft or Northrup Grumman Cygnus cargo ships docked to the station) push it up to a higher orbit. The average boost looks to be roughly 3 km, and they’re done every few weeks.

It’s not like the rocket just pushes it straight up, though. What they actually do is give it more velocity, essentially adding energy to the orbit, which then raises the orbital height. Orbital mechanics is weird; something at a higher orbit will orbit more slowly. But you have to give it more velocity to get up there. It takes getting used to thinking that way. I tend to think of it in terms of energy; a higher orbit takes more energy to get to, so you add it to an object in the form of velocity. That’s a big oversimplification, but it makes the logic process easier for me to grok.

The orbital speed of an object depends on three things: the mass of the object it’s orbiting (in this case, Earth), the orbital height (really, for the math to work out you use the distance to Earth’s center), and the universal constant of gravity. (I’m assuming a circular orbit here; elliptical orbits are more complicated and we don’t need to look into them for this analysis). Doing the math, the velocity of ISS at 415 km up is 7679.5 meters per second, and at 418 km that slows to 7677.8 m/s, a change of 1.7 m/s. That’s about walking speed! Not a big change.

But the ISS is huge. It’s 100 meters long, and has a mass of over 400,000 kilograms! Moving something that massive even by 1.7 m/s takes a lot of energy.

Now the important bit: To escape from Earth you need a velocity of about 11 kilometers per second (fun fact: the way the math works out, no matter where you are in a circular orbit that winds up being the square root of 2 (about 1.4) times your orbital speed). For ISS that means a change in velocity of roughly 3 km/s. That is a big change, nearly 2,000 times the change it takes to boost it a few km.

Obviously, that would take a big rocket.

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