# Forces experienced during transfer orbit

As I understand it, astronauts are weightless because they are in constant free fall around the earth. To get from earth to the moon or earth to mars, spaceships execute a transfer orbit, where they accelerate at just the right time to start "spiraling out" and get captured by the target body's gravity.

During the impulse, I imagine the astronauts would feel the forces of acceleration (just like a car accelerating), but that only lasts for a small time.

What happens to the feeling of weightlessness during this time? Are astronauts in constant freefall around the Earth AND the Moon during this maneuver? What would a free body diagram look like at different points in the transfer orbit?

During a transfer, the only force acting on us is gravity.

This gravity can indeed come from multiple sources, like the Earth, the Moon, the Sun, etc, all at the same time. In fact, there's never a time where these gravitational forces do not act on us, as the range of gravity is infinite.

So yes, astronauts are in freefall around both the Earth and the Moon. Freefall just means "the only force acting on us is gravity", so it's not relative to anything. You can't be in freefall around one object but not around another.

Feeling weightlessness can indeed happen even if there's a force acting on us (freefall is not equal to no gravity). We can actually not feel force! What we can feel is if there's a difference in the forces acting on different parts of our body.

• When standing on the ground, we can't feel the gravity, because it's acting equally on all parts of our body. What we do feel is that the ground is acting on our feet but not the rest of the body.

• When the rocket engine is burning, the engine is acting on our ship and not us. Therefore, there will be a difference in acceleration, and we will be pressed against the floor until this acceleration is equal. We feel the floor acting on a part of our body.

• When in transfer, gravity affects our body and the ship equally, so there's no difference in acceleration, so we are not pressed against the floor, and are therefore feeling weightlessness.

Astronauts inside a spacecraft feel weightless because they are falling at exactly the same rate as the spacecraft. The spacecraft is pulled towards the Earth, Moon, Mars, Sun, and in fact every body in the universe. The astronauts on board feel exactly the same pull (specifically, same acceleration of gravity) since they are in the same place relative to the other objects in the universe. Because they are moving together, the spacecraft doesn't have to exert any force on the astronaut to stay moving together, so the astronaut feels weightless.

The only reason you feel any weight sitting in your chair is that you are being pulled towards the Earth (and every other object in the Universe, but the Earth far outpulls the entire rest of the Universe) but your chair is not falling, and so is exerting force up on you. You would feel the same force if instead of a chair, or the floor, ground, etc was holding you up, you were sitting on top of a rocket that is hovering.

(You can't actually ever feel gravity directly, just the contact force between you and whatever is keeping you from falling closer to the center of the Earth, be it a chair, the floor, the ground, etc. Ultimately that force is electromagnetic repulsion between the atoms in you and the atoms in whatever is holding you up. The only one of the four fundamental forces you can feel is electromagnetism)

During the impulse, I imagine the astronauts would feel the forces of acceleration (just like a car accelerating), but that only lasts for a small time.

What happens to the feeling of weightlessness during this time?

They don't have a feeling of weightlessness during this time. When the ship accelerates during a propulsive maneuver they would drift to the "bottom" of the spacecraft where the engine is located and then experience a small force. If they land feet first, it will feel like they are standing on an extremely low gravity body. If they are seated, they'll feel like they are sitting on one.

When the burn ends, they will regain their sensation of weightlessness.

You can see what a very low acceleration looks like for astronauts on the ISS during an altitude raising burn. The Apollo astronauts likely would have felt a larger acceleration than this.

above: liked in Can the ISS boost maneuver engine be heard by the astronauts on board? (another version);

Here's an answer which tries to explain this from the point of view of General Relativity, which is the best theory of gravity we have.

'Free fall' is what you experience when there are no forces acting on you. In this case, Newton's first law tells us what happens:

Every body perseveres in its state of being at rest or moving uniformly straight forward except insofar as it is compelled to change its state by forces impressed [Principia, translated by I. Bernard Cohen and Anne Whitman].

In particular it follows from this that if you are in a spacecraft and neither you nor the spacecraft are experiencing any force, and you start off moving in the same direction at the same speed, then you'll both keep moving uniformly straight forward in the same direction: you will just float inside the spacecraft. This is free fall.

But wait, this isn't right, is it? Both you and the spacecraft are experiencing forces: you're both subject to some complicated force of gravitational attraction from all the massive objects around you.

Well, in fact no: there are no forces on either you or the spacecraft.

Before 1916 (and really it was clear well before then that this model didn't work) the way people thought about this was that both you and the spacecraft did indeed experience a force due to the various gravitational influences on you, but the force on you was always exactly proportional to your mass and the force on the spacecraft was always exactly proportional to its mass. Newton's second law, summarised as $$\vec{F} = m\vec{a}$$, then can be used to conclude that $$\vec{a}$$ is always identical for both you and the spacecraft (assuming that both you and the spacecraft are rather small). And thus, again, if you started moving along with the spacecraft, you always would continue to do so and you would be in free fall again.

But that turns out to be wrong. Einstein worked out that in fact there is no force of gravity, and both you and the spacecraft just trundle along straight lines according to Newton's first law. But there's a subtlety: gravity isn't a force, instead it is curvature: the spacetime you are trundling along through is not flat, and it's not flat because of gravity. And now you need to sort out what it means for a line to be 'straight' in a spacetime which is not flat. There are two definitions: a straight line is the extremum of distance along curves connecting two points, or a straight line is a line which, if you parallel-transport its tangent vector along the line, it remains the tangent vector of the line. In General Relativity those definitions are the same (as they are in Euclidean geometry), and the curves which are straight lines under these definitions are called 'geodesics'.

So the modern view is that, if you are moving under the influence of gravity alone, then you will move along 'straight lines' – geodesics – through a spacetime curved by gravity. And Newton's first law then tells you that you will just float inside the spacecraft, because you are both moving along the same geodesic.

A bit of a nitpick:

Astronauts aren't weightless because they're in free fall/orbit/space.

They're weightless because they're not experiencing thrust.

A famous thought experiment has a person in an elevator car in deep space. They can't see outside to judge their position, but they have all of their senses otherwise.

When that elevator is pulled "up" at a constant acceleration of 9.8m/s/s (that is, every second it's going 9.8m/s faster than it was before), this is completely indistinguishable from sitting still on the surface of Earth.

If whatever force was moving the elevator were to stop working -- that is, the elevator car is left to drift through deep space at whatever speed it wants to -- the person inside is traveling at the same speed as the elevator car.

If three skydivers were falling from an airplane, holding hands, and one lets go of the others, that one doesn't suddenly plummet to the ground any faster than the other two. They aren't "dropped," relative to the rest of their party, because gravity is working on everyone equally.

Since our skydivers are going the same speed as each other, they can push off and float around each other. The same for our passenger in our thought experiment elevator -- The elevator is drifting through space at great speeds relative to something out there, but since the passenger is going the same speed as the elevator, they're able to push off and float around, as if there were no gravity affecting them. Any gravity outside, such as from passing near a moon, goes completely unnoticed by the passenger, since the gravity affects the elevator the same as the passenger.

So, orbiting in the ISS, streaking through the rarest stretches of the upper atmosphere at a blindingly fast speed of 27,600km/h (17,100mph), feeling 90% of the same gravity that people on the surface feel -- they experience weightlessness because they're traveling at the same speed as their ship.

When the ISS uses engines to boost its orbit (because in Low Earth Orbit, there's enough drag to slow the craft down and bring it dangerously close to thicker parts of the atmosphere), the astronauts do experience some weight once again. As soon as the engines are off, they're back to being weightless.

Rounding back to your question, of astronauts traveling between different bodies such as entering orbit around the moon or Mars: No, passengers will not feel a difference in gravity, because any shift in gravity affects the ship and passengers in the exact same way.

If the ship fired its thrusters, or entered an atmosphere and aerobraked, the passengers would feel that as gravity -- but just going to different gravitational gradients does not change weightlessness.

• All correct, but I don't see any distinction at all between "not experiencing thrust" and "freefall". – Nuclear Hoagie Oct 1 '19 at 13:33
• @NuclearWang: That's the point. There is no distinction. It is slightly more pedantically correct to say there is no thrust, as freefall can have more meanings, including skydivers in an atmosphere who are experiencing a thrust from wind resistance. People commonly say they're in freefall despite the thrust from the atmosphere. -- but for conversations about space, there is no distinction. – Ghedipunk Oct 1 '19 at 15:28
• Right, I'm nitpicking the nitpick - astronauts are weightless because they are in free fall (in a vacuum). Not experiencing thrust is pretty much the definition of free fall, so I don't know why you attribute weightlessness to one and not the other. – Nuclear Hoagie Oct 1 '19 at 15:42