# Gravity on a trip to the moon

Hi all,

This isn't a homework question, its just something I'm personally wondering about.

I understand why an astronaut in orbit around the Earth feels weightless, because he is in a constant state of freefall, travelling towards the Earth just as fast as the Earth is dropping away underneath him.

However, when travelling towards the moon, the astronaut is no longer in freefall around the Earth. The bulk of the Earth would be underneath him and he would be travelling effectively vertically upwards from the Earth towards the Moon. I liken this to being in an elevator travelling upwards away from the Earth. In an elevator travelling upwards the person still feels the gravity of the Earth and still stands on the surface (floor of the elevator) closest to the Earth.

So why in a journey to the Moon were the astronauts still weightless?

Thanks
Dan

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At every stage in the journey where the engines were not in use they are not accelerating.
They only experience 'weight', or 'g force' while accelerating away from Earth.
When not accelerating, the capsule and the people inside it are traveling at the same speed.
They are not weightless in the sense of having no mass, they just don't have any momentum relative to the capsule.

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Chestermiller
Mentor
Once they stop circling the earth, they regain gravity. However, as they get further from the earth, because of Newton's inverse law of gravitation, the amount of gravitational force acting on them by the earth decreases. When they are 4000 miles away, the gravitational force is only 1/4 of the value at the surface. By 8000 miles, it is only g/16. At some point between the earth and the moon, the gravitational force of the moon cancels the gravitational force of the earth, and they achieve exactly 0 g. However, beyond this point, they start picking up the gravitational force of the moon more than the gravitational force of the earth, and they start regaining gravity again (from the moon). When they arrive at the moon, before going into orbit, they are essentially experiencing the gravitational attraction of the moon at close to its surface value (which is somewhat lower than on the surface of the earth).

Chet

russ_watters
Mentor
At every stage in the journey where the engines were not in use they are not accelerating.
They only experience 'weight', or 'g force' while accelerating away from Earth.
When not accelerating, the capsule and the people inside it are traveling at the same speed.
They are not weightless in the sense of having no mass, they just don't have any momentum relative to the capsule.
That's not quite right: At every stage in the journey where the engines were not in use, they were accelerating, in free fall, at a rate and in a direction dictated by their distance from the Earth and Moon.

It's complicated because you have to calculate the acceleration applied by each body and add them together. What it means is that for most of the journey the craft is decelerating (accelerating toward earth, while flying away from earth) and at some point switches to accelerating toward the moon.

Chestermiller
Mentor
That's not quite right: At every stage in the journey where the engines were not in use, they were accelerating, in free fall, at a rate and in a direction dictated by their distance from the Earth and Moon.

It's complicated because you have to calculate the acceleration applied by each body and add them together. What it means is that for most of the journey the craft is decelerating (accelerating toward earth, while flying away from earth) and at some point switches to accelerating toward the moon.
Yikes. You're right. What could I have been thinking? As long as the engines are off, the craft is in free fall. As long as the craft is in free fall, they experience zero gravity. Duh.

Chet

YES, both the capsule and the occupants do experience acceleration due to the gravity of Earth and Moon, but the acceleration experienced by the crew is is equal to the acceleration of the capsule , so they don't experience any 'weight' - ie they float freely inside the capsule instead of finding themselves pushed toward one end or side of the capsule.

sophiecentaur
Gold Member
You experience 'weight' when there is a force between you and the (local) floor. If the rocket is accelerating, then your acceleration will be because the floor is pushing at you and you will be aware of a force on your feet and interpret it as 'weight'. Once the forces in your body, boots and carpet have reached equilibrium,m you will be accelerating at the same rate as the ship. This force will stop when the motor is turned off and you are in 'free fall' (there is always some gravitational force on you, of course - even if it is just due to the Sun or the rest of the Galaxy)

Microgravity is another issue and it can be detected when a ship is in orbit. The CM of the ship and contents is in an equilibrium condition, with the centripetal force and gravitational attraction being equal. However. parts of the ship are further out and parts are nearer to the Earth (by a few metres). they would take up different orbits if not constrained by the structure of the ship because there would be small forces acting (away from the line of the CM's orbit) . This microgravity effect will be less and less, as the orbit gets bigger and, on the journey between Earth and Moon, it would not be detectable, I think. So there would be a difference in the on board experience during the journey.

Bandersnatch
However, when travelling towards the moon, the astronaut is no longer in freefall around the Earth.
This is the source of the confusion. The spaceship on a transfer orbit - on any orbit - is in free fall. This is NOT a situation analogous to an elevator travelling upwards. This is analogous to how parents play with their kids by throwing them up in the air and then catching them. The kid is in free fall (disregarding minor air resistance influences) throughout the journey, and only during the throw and the catch any non-gravitational acceleration is applied.

In other words, to launch a rocket to the Moon you give it a good 'kick' right at the start, and let it follow an elongated orbit for the rest of the journey, with another period of deceleration at the destination.

ulianjay
Chestermiller
Mentor
This is the source of the confusion. The spaceship on a transfer orbit - on any orbit - is in free fall. This is NOT a situation analogous to an elevator travelling upwards.
Yes. This is like when you're in an elevator and someone cuts the cord.

Chet

DaveC426913
Gold Member
One way to intuit this is to ask yourself what would happen if, at a given point in the journey, the astronaut stepped outside the spaceship and floated next to it. Now you have two bodies on the same trajectory toward the Moon (or in Earth orbit, or in lunar orbit).

Is there any reason to think they would start to move relative to each other? No. So there is no reason to think they would move relative to each other when the astronaut is inside either. i.e. he would not experience the craft pushing up on his feet.

The only time the floating astronaut's trajectory would differ from the craft is if the craft fired up its engines.

A.T.
I understand why an astronaut in orbit around the Earth feels weightless, because he is in a constant state of freefall, travelling towards the Earth ...
In a circular orbit he isn't "travelling towards the Earth", just accelerating towards it.

However, when travelling towards the moon, the astronaut is no longer in freefall around the Earth.
With engines off, the rocket is in free fall. The "around the Earth" part is irrelevant here.

The bulk of the Earth would be underneath him and he would be travelling effectively vertically upwards from the Earth towards the Moon. I liken this to being in an elevator travelling upwards away from the Earth. In an elevator travelling upwards the person still feels the gravity of the Earth and still stands on the surface (floor of the elevator) closest to the Earth.
Not if the elevator was shot vertically from a cannon.

sophiecentaur
Gold Member
Elevators are poor models to take for some thought experiments because there are more forces at work than people consider. An elevator travels so slowly (relatively) that its trajectory under 'free fall' would be very short - just enough to bring your heart up into your mouth at the end of a ride.

Chestermiller
Mentor
Elevators are poor models to take for some thought experiments because there are more forces at work than people consider. An elevator travels so slowly (relatively) that its trajectory under 'free fall' would be very short - just enough to bring your heart up into your mouth at the end of a ride.
Not if someone cut the cable. (Where is Lt. Columbo when you need him?)

Chet

sophiecentaur
Gold Member
Not if someone cut the cable. (Where is Lt. Columbo when you need him?)

Chet
But the Otis system (in all modern lifts (??)) would lock the lift onto the sides of the shaft. (My Wife watches all of your shows.)

diogenesNY and Chestermiller
Thanks for the replies everyone.

If I may continue. I understand now that an astronaut travelling towards the moon is under the influence of gravity but he can't actually 'feel' the gravity because him and the rocket are travelling at the same velocity. And I can see now that it would be the same situation if an elevator was fired upwards from a canon as one poster suggested.

Would the astronaut 'feel' the effect of gravity if he tried to move an object in the rocket? For example on Earth, if you try and move an object away from the Earth you must overcome the gravity and you 'feel' that of course as a force you must overcome to lift the object. When in the rocket, would trying to move an object further away from the direction of the Earth mean you 'feel' any force to overcome?

Taking another poster's comment however that travelling to the moon is actually just an englarged and elipitical orbit path, then freefall still applies, so in that case there would be no apparent gravitational force to overcome when moving the object? This appears to be what I see in practice when astronauts push pens around in space on the TV.

If a rocket was launched to the moon on a ballistic trajectory, i.e it did not start from an Earth orbit, then in that case would gravitational forces be felt by the astronauts on board?

Nugatory
Mentor
Taking another poster's comment however that travelling to the moon is actually just an englarged and elipitical orbit path, then freefall still applies, so in that case there would be no apparent gravitational force to overcome when moving the object? This appears to be what I see in practice when astronauts push pens around in space on the TV.
That's right.

If a rocket was launched to the moon on a ballistic trajectory, i.e it did not start from an Earth orbit, then in that case would gravitational forces be felt by the astronauts on board?
No. It would be the same as the previous situation.
A ballastic trajectory is actually just an elliptical orbit that happens to intersect the surface of the earth so the object smashes into the ground instead of orbiting around the center of the earth. If I, standing on the earth's surface, fire a cannon ball into the air it will rise and then fall back to earth on a curved path; the high point of that path is the apogee of an elliptical orbit with its perigee very close to the center of the earth.

(Most textbooks describe the path of the cannonball as a parabola - that is a very very good approximation that you get by assuming that the earth's gravity acts in the same direction ("down") along the entire path of the cannonball. But in fact, the earth's gravity always pulls towards the center of the the earth, and the direction to the center of the earth is changes very slightly as you move around on the surface.)

sophiecentaur
Gold Member
he can't actually 'feel' the gravity because him and the rocket are travelling at the same velocity.
As I have already mentioned, the astronaut will still be able to measure a 'micro gravitational' effect because the orbit (/trajectory) of the CM of the craft will be the only part of the craft that is in true fee-fall. Some parts would be travelling faster or slower than they would if they were not constrained by the structure of the craft.
Of course, on an orbit to the Moon, the curvature of the path will be large and the g field will be small and, over the dimensions of a real ship, the forces would be minuscule.
But, if you imagine a spacecraft of diameter 1km in low Earth orbit (100km), the natural period of two unconstrained objects one at the lowest point and one at the highest point would be significantly different; they would drift away from the CM of the craft. Their respective orbit radii would be 6,471.5 km and 6,470.5 km in a 100 km. The spacecraft would deforcing them to have the same orbital period, if attached. A small difference, but that's why it's referred to as microgravity.
An astronaut's pen will slowly move away from the place where he puts it.

A.T.
And I can see now that it would be the same situation if an elevator was fired upwards from a canon as one poster suggested.

If a rocket was launched to the moon on a ballistic trajectory, i.e it did not start from an Earth orbit, then in that case would gravitational forces be felt by the astronauts on board?
The elevator shot from a cannon is on a ballistic trajectory.

DaveC426913
Gold Member
If a rocket was launched to the moon on a ballistic trajectory, i.e it did not start from an Earth orbit, then in that case would gravitational forces be felt by the astronauts on board?
Not sure what you're asking here. Ballistic trajectory simply means 'unpowered'. It's path will be constrained by gravitational forces only. All the scenarios we've discussed - in which the rocket (or any other object) does not use some sort of the propulsion - are ballistic trajectories.

DaveC426913
Gold Member
Would the astronaut 'feel' the effect of gravity if he tried to move an object in the rocket? For example on Earth, if you try and move an object away from the Earth you must overcome the gravity and you 'feel' that of course as a force you must overcome to lift the object. When in the rocket, would trying to move an object further away from the direction of the Earth mean you 'feel' any force to overcome?
It is important that you understand that any object of mass - whether under a gravitational influence or not - will have inertia. i.e. when an astronaut approaches a pencil floating weightless in the cabin, even if gravitational forces are vanishingly small (say, he's in interstellar space), its inertia does not change, and the astronaut still needs to apply a force to the pencil to start it (or stop it) moving.

sophiecentaur