Relative speeds

How can astronauts conduct EVAs without the ISS falling away and leaving them behind? Similarly; a spaceship returning to the Earth from the Moon, should it not undershoot the earth given Earth's relative speed?

The answer probably has to do with Earth's gravity, but I think it's an interesting issue: given everything's relative speed (earth, sun, galaxy) should it not be easy to be left behind? Or how difficult would it be to catch up with anything?

• One quirk of orbital mechanics, that is a mixed blessing: for given orbit (same speed, altitude, direction) mass of the orbiting body doesn't matter. So, no matter, ISS, astronaut, a box of tools, they all orbit Earth on exactly the same orbit (or so little off that a push with one's finger is enough to keep up). Downside: as you observe a planet without moons, you can't easily guess its mass; same if you observe a moon without anything orbiting it. But for a planet with a moon, you can calculate the planet mass, knowing the moon's orbital parameters.
– SF.
Commented Dec 4, 2017 at 7:56
• I just hope that ISS don't do orbital manoeuvres while some astronaut is doing an EVA and forgot to tether her- or himself :-) Commented Dec 4, 2017 at 10:17

Newton's first law of motion says that an object in motion remains in motion unless acted on by some force.

An astronaut leaving the hatchway of the ISS starts off moving at the same speed, in the same direction, as the ISS; both she and the space station continue to move at the same speed as she steps out of the hatch. Gravity acts on both of them to change their direction of motion, but it does so equally, so again they move together.

If the astronaut were to push away from the station slightly, she would drift away from it slowly, but astronauts are tethered to the station for safety.

This situation is different from what your intuition says about, say, a skydiver leaving the doorway of an airplane in flight. In that case, both the aircraft and the skydiver are moving rapidly relative to the air around them; the resistance of the air produces a very large force on both the skydiver and the aircraft which tends to slow them both down. The engines of the aircraft provide a force which counteracts the air drag force, so the aircraft continues on at the same speed; the skydiver has no engine, so is slowed down, and rapidly falls -- backward relative to the plane, but still moving forward for a while relative to the air.

• Unless someone decides to do an orbital manoeuvre during an EVA ;-) Commented Dec 4, 2017 at 10:15

It does and doesn't have anything to do with gravity.

Far out in intergalactic space are vast regions with almost no matter, not merely millimeters between atoms, or even meters, but kilometers or more. In the middle of these, anything larger than a diffuse cloud of cold gas may be many parsecs away. Even out there, though, a hypothetical astronaut leaving their hypothetical spacecraft for an EVA would simply hang around very near the craft unless they accelerated relative to it. There is nothing that would make the craft "fall away and leave them behind". Simple inertia is enough to keep them close together.

But in Earth orbit, of course, there are quite a few quite large masses quite nearby. However, in each case, the distance between the center of gravity of the large body (Earth, the Sun, the Moon, etc etc etc) and the CG of the spacecraft is almost exactly the same as the distance between that same CG and the CG of the astronaut. And likewise, the mass of the spacecraft or astronaut is effectively irrelevant when considering the acceleration. So in Earth orbit, the ISS does "fall away", but so does the astronaut, at almost exactly the same speed. That is in fact what an orbit is: continuously falling away from the straight-line course that would otherwise be taken, at such a high speed that the ballistic curve of the fall matches the curve of the planet. So here, inertia plus gravity keeps them together.

The gravitational environment in orbit is sometimes referred to as microgravity. This is more accurate than the other term, zero-g, but both are an approximation of the relative accelerations; because everything around you is in constant freefall at the same acceleration and velocity, there's no large force to make you move relative to your immediate surroundings if you let go of the wall or ceiling or floor. But because there are very small differences in distance and therefore gravity, "microgravity" is more accurate: an astronaut in the closest-to-Earth (or farthest-from-Earth) sections of the ISS could very slowly start drifting relative to the whole structure. But this is so slow that rather than taking a fraction of a second to fall a meter or a yard, it could very easily take many hours.

• So if I understand this right then our intergalaktic astronaut would stay by the vehicle because of inertia, but this doesent apply if the craft is accelerating? Commented Dec 4, 2017 at 20:25
• @user21901 If the spacecraft turns its engines on, it will leave the astronaut behind, yes. Commented Dec 4, 2017 at 20:28