Earth’s acceleration due to gravity is 9.81m/s^2, the moons is supposedly 1/6th of that so around 1.6m/s^2 but I don’t know the exact value.
Does the value of acceleration remain constant, or is there some maximum velocity that is reached where gravity no longer has an effect?
I have read the reason acceleration stops is because negative acceleration via air resistance in our atmosphere counteracts the force of gravity, if so does that mean people never stop accelerating on atmosphere free planets/satellites like the moon? What is the maximum velocity on earth due to our atmosphere if gravity stops working due to air resistance after a while?
What is the highest distance a person can fall off of on the moon and not get hurt. I’m guessing it’ll take a six second free fall for the force to be equal to what we have on earth, anything beyond that could cause damage so i’m assuming it is around an 8 second free fall, giving me 58.8 meters (9.81/6=1.635 = 1.635+1.635^2+1.635^3…1.635^8=58.8) but I don’t know if that math is right.
If there are creatures on another planet, how strong must their normal gravity be on their homeworld for them to be able to jump from any height on earth and not get hurt when they land?
Gravity is a force. When we say that gravity is six times stronger on the Earth than on the Moon, what we mean is that for any object, the force it experiences due to gravity is six times a strong on the Earth as on the Moon.
Objects accelerate according to Newton’s 2nd law, force = mass x acceleration. Thus, the acceleration that an object experiences depends only on how much force is being put on it. There is no maximum velocity under gravity due to the laws of physics.
An object on Earth eventually stops accelerating when the force due to air resistance, which pushes against the direction of motion (in other words upward for a falling option) cancels out the downward force from gravity. The force due to air resistance depends on the size and shape of the object. A given object’s terminal velocity is the maximum speed that it will reach on Earth when it’s falling. On the moon or any other airless body, there is no terminal velocity. Objects keep speeding up until they hit the ground.
I think my original calculations were wrong, and it is momentum that is important and not force when it comes to hurting yourself. Would someone striking the moon at 7 meters/second have the same result on their body and bones as striking the earth at 7 meters/second? If so then it is closer to 18 meters that a person can fall from on the moon without hurting themselves.
What is the highest distance a person can fall off of on the moon and not get hurt. I’m guessing it’ll take a six second free fall for the force to be equal to what we have on earth, anything beyond that could cause damage so i’m assuming it is around an 8 second free fall, giving me 58.8 meters (9.81/6=1.635 = 1.635+1.635^2+1.635^3…1.635^8=58.8) but I don’t know if that math is right.
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10’ is probably about has high as you would want to fall. Even that might cause some injury but let’s accept some injury.
Since the moon’s surface acceleration from gravity is 1/6 that of the earth you could fall 60’ on the moon for the same effect as 10’ on the earth.
If you fall from infinity, to the surface of an airless planet, your speed at the moment you hit will equal the gravitational escape velocity for the planet; 11.2 km/sec for Earth, 2.4 km/sec for the moon.
I think the energy is more important than the momentum in causing you damage (though you can’t separate the two in any physical experiment to test my statement).
The energy in joules would be your mass in kg times your height in meters times the local acceleration of gravity in meters per square second.
If you go someplace like the moon where the acceleration is 1/6 that on earth, you could increase your height by 6X, with the same damage. Like an earlier poster said.
The momentum would, however, tell you how much you changed the moon’s own velocity when you hit it - but of course that would be a very small and immeasureable change.
That is what I came up with when I redid the calculations, I had 3m for earth and ended up with 18m for the moon. I also ended up with about 88 m/s^2 as the normal gravity force on another planet that you’d need to be able to jump from any height on earth and not get hurt. This was assuming a person can jump from a 3 meter height on both planets w/o getting hurt and that a person’s freefall speed on earth is 150 mph.
Escape velocity is calculated from the surface of the body. For the purpose of calculation, you can treat the gravitational force as if it’s concentrated at the center of the body, but the surface is already at some distance from that center. That reduces the escape velocity in a way that depends on the mass, radius, and hence density of a body.
I think I get what you’re saying – the moon’s diameter is proportionally smaller than Earth’s, so you’re closer to the center of the mass, so you have further to go to escape the gravity well. Right?
If so, this implies that a body of, say, 3x Earth’s diameter with the same 1g attraction at sea level would have a lower escape velocity. Yes?
Something like that. You can think about escape velocity as a measure of the total amount of work you need to get away from a moon or planet. If you start out from a stationary position ten thousand miles above the surface, a big chunk of that work has already been done. If you start from 10,000,000 miles above the surface 99.999…% of the work is already done, so you only need to add a little velocity to head out to infinity.
With your larger size and same mass Earth, it is the same thing as erecting a giant scaffold and talking about the escape velocity from the top of that rather than the surface.
88 m/s^2 is an acceleration, not a force. The rest of this post doesn’t seem to make any sense. You also realize that the 9.81 m/s^2 is only for the surface, right? As you go higher up the value of g goes down.
Actually, no. A larger planet with the same surface gravity as Earth has a higher escape velocity. You’re starting three times as far from the center, true, but the planet is also nine times heavier than Earth; so you need an escape velocity sqrt(9/3) = sqrt(3) times as high as for Earth.