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Comment by fbonetti | Hacker News Reader

Before I played KSP I had a lot of hilarious misconceptions about the physics of rocketry and space travel.

On my first attempt to get into orbit, I loaded up my rocket with as many engines and boosters as I could strap on and fired the rocket straight up. The rocket breached the atmosphere but to my surprise the rocket came straight back down. I literally thought that launching rockets into orbit meant shooting them really high until they were "in space" haha. I then quickly learned that being in orbit means having a horizontal momentum that is balanced with the gravitational pull of a given body. This balance produces a curved elliptical trajectory.

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And you have to decelerate to catch up to the station in orbit. If you accelerate you will fall back.

That's because if you fire your rockets to accelerate you end up in a higher orbit, i.e. your circle is much bigger, and vice versa, to overtake/catch up you want to fall to a lower orbit. That's also not intuitive to someone with "earth-experience".

Yet objects in higher orbits like the moon are going way slower around the earth than low earth orbits.

What's the deal with that?

Without any assessment of the math, I'll point out that being in a higher orbit means two things:

(1) Your speed is higher; you cover the same distance in less time.

(2) The distance around the earth is larger than it would be if you were lower down.

Higher circular orbits are indeed slower than lower ones. The shuttle goes around the earth in 90 minutes, the moon takes 28 days. Geosynchronous orbit, where one orbit takes one day, is in between.

What's confusing about transfers is that elliptical orbits are orbits where your velocity varies based on where you are in the orbit. Your speed is highest at perigee and lowest at apogee. In fact, your speed at perigee will be higher than the speed of an object in a circular orbit at that altitude. The reverse is true at apogee; your speed will be slower than an object in a circular orbit at the same altitude.

So if you and your docking target are both in circular orbits, and you increase your speed in order to catch up, then you will simultaneously be raising the other side of your orbit, half a turn away. The difference at your current location will be minute, but will grow every continuously over that half a turn. If you're docking in the next few seconds it won't be a problem (the docking mechanism will handle a small offset, and it equalizes your speeds provided the difference isn't too much). If you're still several minutes away, however, you might find that the extra radial velocity means that you fly over the top of your target.

If you miss and continue to follow your new orbit you will indeed find that your overall time to orbit is now higher than your target's. It may be many orbits before you again have a close approach with your target, although if the difference in speeds is small then it may appear from your perspective that you are in fact orbiting your target.

This is exactly the point grandparent was attempting to explain.

The moon is going much, much faster than satellites in LEO. But it has so much farther a trip, it takes orders of magnitude longer to complete an orbit.

If you're behind a satellite in orbit and want to catch up, counterintuitively you have to decelerate. This slows you, but puts you in a smaller orbit. The effect of the smaller orbit greatly outweighs any loss in absolute velocity, so you catch up to your target.

This sounds like I'll have to start playing KSP after all. Lots of interesting space facts!

That's very interesting, but I don't completely understand.

> I literally thought that launching rockets into orbit meant shooting them really high until they were "in space"

It makes sense that having a high horizontal speed keeps you in orbit if orbit is your goal, but with enough firepower you should be able to make it to a point where you don't fall backwards anymore, right? Or at least where falling is negligible enough that you can stay in that spot for a while.

Yes, you will eventually reach an altitude where the gravitational pull of a given body is negligible. At that point you will have escaped it's orbit.

That is possible, yes. Just rarely useful - it all depends where you're trying to go. If you head straight up with enough velocity to leave Earth's sphere of influence, you end up in orbit around the Sun, not the Earth. And in that case, you inherit Earth's velocity relative to the Sun, so you don't just fall straight back down into the Sun. (because 'head straight up' was relative to the Earth, not the Sun).

From the point of view of the game, several of my little green men can attest that coming home from a solar orbit is rather difficult (energy-intensive, time-intensive, or both)

If the plan is to end up in Earth's orbit, you don't want to shoot so far as to leave our sphere of influence. Earth's gravity drawing you towards it is a key component of orbit. But the other component is having enough horizontal (relative to the surface) to keep missing it - and that's what was missing from the parent's "what goes up, must come down" flights.

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