Great question! You asked specifically if one of the Lagrange points could be a good place to hide a time capsule from the past. The answer is “no” because, you see, an orbit in a Lagrange point is inherently unstable and would eventually either fall to Earth or fall to the Sun.
According to space.com, “L1, L2 and L3 are all unstable points with precarious equilibrium. If a spacecraft at L3 drifted toward or away from Earth, it would fall irreversibly toward the sun or Earth, “like a barely balanced cart atop a steep hill,” according to astronomer Neil DeGrasse Tyson. Spacecraft must make slight adjustments to maintain their orbits.”
In any orbit, around any planet, you’re going to be in micro-gravity. You will “feel” weightless because essentially you are falling around the planet in an orbital trajectory.
Just like astronauts on the ISS float around their space station, an astronaut orbiting Jupiter would also float around his or her space craft. It matters not how far away from the surface the space craft is as long as it is orbiting above significant atmospheric drag.
In theory, by having a wheel shaped craft that spins slowly, just like in the movies, you could achieve 1G.
By looking at the illustration below, you would think so! Earth and Mars are so close, why not build an outpost between to make it easier to go there!
Unfortunately, this image only shows us the relative distances the planets have from the sun. Actually, Earth orbits the sun faster than Mars because Earth is closer to the sun. The closer to the sun, the faster the orbit. The further from the sun, the slower the orbit.
This means that sometimes the two planets are close together and other times they’re on opposite sides of the Sun.
If you could somehow position an outpost so it stayed midway between the two planets then as the planets move to opposite the sun from each other where would the outpost go? Into the sun!
You couldn’t have that! The best you could do is put an outpost in orbit around the sun, between Earth and Mars, but then the outpost would have the same problem for both Earth and Mars. Sometimes the outpost would be near one planet or the other and sometimes it would be on the opposite side of the sun. It would be very rare to find all three of them lined up in a row like stepping stones.
Now another idea might be to have an outpost orbiting Earth, way out in space halfway the distance to Mars. It could work, but it would take a long time to orbit Earth at that distance. It wouldn’t remain stationary. It would be in orbit, albeit a fairly slow one. Sometimes it will be on the opposite side of the Earth from Mars, being of no use. Such an orbit would be influenced by the orbit of Earth’s moon, and by Mars itself, throwing it off orbit, and would be inherently unstable.
So if somebody thinks we might one day build such an outpost to make going to the planet Mars easier, that idea wouldn’t work too well.