ara created by fluff-kevlar
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Description

Textless version and alternate expression. ARA in space!

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    0mnm652

    Member

    Queen_Sectonia said:
    I wonder what the gravitational pull of her ass is.

    According to Google, the average American butt has a mass of 4 kg. Obviously, this butt is very much NOT average, but we can take that as an estimate. We will assume the viewer has a mass of 80 kg, the human average.
    From Newton's Universal Law of Gravitation, we know that
    F=GmAssmViewer/r2
    F=(6.67*10-11 m3/kg*s2) * 4 kg * 80 kg / r2 = (2.1*10-8 m3*kg/s2) / r2

    From a distance of 1 m, the force would be 20 billionths of a Newton, about one quarter of the force between the proton and the electron of a hydrogen atom. With no other forces acting upon you, you would accelerate towards her ass at 27 nm/s2. At that rate, it would take you almost exactly one day to travel that 1 m. However, as you approach the ass the force would increase. It would be possible to solve more precisely using differential equations, but I think the numbers above get the point across.

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    High Botanist Telarn

    Blocked

    0mnm652 said:
    According to Google, the average American butt has a mass of 4 kg. Obviously, this butt is very much NOT average, but we can take that as an estimate. We will assume the viewer has a mass of 80 kg, the human average.
    From Newton's Universal Law of Gravitation, we know that
    F=GmAssmViewer/r2
    F=(6.67*10-11 m3/kg*s2) * 4 kg * 80 kg / r2 = (2.1*10-8 m3*kg/s2) / r2

    From a distance of 1 m, the force would be 20 billionths of a Newton, about one quarter of the force between the proton and the electron of a hydrogen atom. With no other forces acting upon you, you would accelerate towards her ass at 27 nm/s2. At that rate, it would take you almost exactly one day to travel that 1 m. However, as you approach the ass the force would increase. It would be possible to solve more precisely using differential equations, but I think the numbers above get the point across.

    You deserve a cadbury creme egg for that post

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    Eldroxyl

    Member

    Xenowarrior said:
    or a sweetroll :D

    Nope somebody stole your sweetroll now guards will make fun of you for it.

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    AWKnight

    Member

    Typical cat. Here she's floating in a deadly, hostile environment and she's focused on playing with her toes.

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    user 377517

    Member

    0mnm652 said:
    According to Google, the average American butt has a mass of 4 kg. Obviously, this butt is very much NOT average, but we can take that as an estimate. We will assume the viewer has a mass of 80 kg, the human average.
    From Newton's Universal Law of Gravitation, we know that
    F=GmAssmViewer/r2
    F=(6.67*10-11 m3/kg*s2) * 4 kg * 80 kg / r2 = (2.1*10-8 m3*kg/s2) / r2

    From a distance of 1 m, the force would be 20 billionths of a Newton, about one quarter of the force between the proton and the electron of a hydrogen atom. With no other forces acting upon you, you would accelerate towards her ass at 27 nm/s2. At that rate, it would take you almost exactly one day to travel that 1 m. However, as you approach the ass the force would increase. It would be possible to solve more precisely using differential equations, but I think the numbers above get the point across.

    Ditto

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    Schlapor

    Member

    0mnm652 said:
    According to Google, the average American butt has a mass of 4 kg. Obviously, this butt is very much NOT average, but we can take that as an estimate. We will assume the viewer has a mass of 80 kg, the human average.
    From Newton's Universal Law of Gravitation, we know that
    F=GmAssmViewer/r2
    F=(6.67*10-11 m3/kg*s2) * 4 kg * 80 kg / r2 = (2.1*10-8 m3*kg/s2) / r2

    From a distance of 1 m, the force would be 20 billionths of a Newton, about one quarter of the force between the proton and the electron of a hydrogen atom. With no other forces acting upon you, you would accelerate towards her ass at 27 nm/s2. At that rate, it would take you almost exactly one day to travel that 1 m. However, as you approach the ass the force would increase. It would be possible to solve more precisely using differential equations, but I think the numbers above get the point across.

    Wonderfully done, but I had to try the differential equation approach. Using the same formula for gravitational force and a bit of algebra, you arrive at the 2nd order differential equation of:

    r^2*r''=4G AKA r''=4G/r^2

    This is somewhere between difficult and impossible to solve analytically, but luckily we can use a numerical approximation. I set up a spreadsheet with columns for r, the position in meters; r', the velocity in meters per second; r'', the acceleration in meters per second per second; and t the time passed in seconds. For each row, we solve for acceleration given the current distance, integrate acceleration with respect to time to get our change in velocity, and integrate our velocity with respect to time to get our change in position. We update those values and repeat the process an arbitrary number of times until we've reached 0.

    It is an approximation so the more often we calculate our new acceleration, velocity, and position, the more accurate our answer will be but the longer to set up and run. I started 1 meter away with 0 velocity and used 90 second intervals. I got that it took 759 of these steps to pass 0 meters, therefore colliding with the ass.

    Therefore, by my approximation, it will take 18.975 hours (18 hours, 58 minutes) to collide with the ass due to the force of gravity getting higher as you get closer.

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