Orbital Mechanics Part 1
So, you have launched an object above the atmosphere. It is free of Earth’s gravity, right?
Wrong.
Gravity still acts - if it did not, the Earth would not be bound to the sun and the moon would escape from the Earth.
So why do astronauts appear to be weightless in the space station?
The astronauts have not escaped gravity, the astronauts are falling, so is the space station. Outside of the Earth’s atmosphere, both they and the space station change their motion in the same fashion, and so the astronaut floats relative to the station. They feel weightless, but they are not free of gravity. If you could build a huge tower and climb up to watch the ISS go past, standing on the tower (in your spacesuit) you would feel very similar to standing on the ground, even though the astronauts would feel like they were weightless.
You can get a sense for this by looking at Felix Baumgartner’s jump from the edge of space (lofted via balloon). Even though he’s high enough to be on the ‘edge’ of the atmosphere, and requires a spacesuit, he still moves and falls as he would near the surface.
We can feel weightless without needing to go into space. When filming for the (fantastic) Apollo 13 film, Tom Hanks, Bill Paxton and Kevin Costner were not made to appear weightless by using wires and cgi, they built a set in a plane. That plane flew parabolic arcs, with just enough engine to counter air resistance. In this way everything in the plane could experience apparent weightlessness. The plane’s contents, shielded from drag by the body of the plane, moved only under the influence of gravity - the plane acts like a giant wind-break.
Planes that fly in this fashion are lovingly given the name: ‘vomit comet’ (aside: I’d love to do this!)
So, if the space station has not escaped gravity, why does it not fall to the surface? The station is falling, but it is also going sideways - and so its rate of falling causes its path to curve. The sideways speed is just enough to make the curvature of the path match the planet, and we have an orbit.
In the diagram below, the red arrow would be the path without gravity, the blue arrow would be the path if the sideways speed is just right so the path curvature matches the planetary radius, and the green arrow is ‘sub orbital’, i.e. the sideways velocity is too low.
Note that, in general, orbits will be elliptical rather than circular (circles are a special case). (Circles, parabolas and ellipses are all part of the same family of curves called conic sections).
Orbital Mechanics. Credit: Me
If you’re above the atmosphere, then maintaining an orbit doesn’t require fuel - as there is no drag to slow you down. In practice, in low Earth orbit, the vacuum is not perfect, and there is a tiny amount of drag. This causes the space station to slow, and left unchecked it would come back to Earth. As a result, the space station needs to be periodically reboosted.
Part 2: I will look at how we can look how the orbital properties vary with distance for circular orbits.
Links
Bill Paxton and Kevin Bacon on the vomit comet (note at the end, they throw the ball whilst on the floor, at this point they are experiencing greater than one g as the plane is at the bottom of the parabolic arc and its trajectory is curving upward)
Dianna Cowern aka The Physics Girl on the the ESA Vomit Comet.
Felix Baumgartner’s jump from the edge of space.
More Space
More Physics
Extension
Not all spacecraft orbit, if given enough energy they can move away from the planet and escape. That is exactly what the rocket for the Perseverance Mars rover was designed to do. However, it is also true that once the craft is moving only under the influence of gravity it experiences apparent weightlessness.
