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Gravitational constanT G - HELP!

  1. Jun 6, 2004 #1
    gravitational constanT G -- HELP!

    :yuck:

    ok, right now I'm working on a physics project :) satelite motion around earth...I managed to create a program that simulates all that stuff...but I don't quite like my G constant!

    In my program I want to recreate moon and earth relationship!

    so scale looks this way:
    1pixel = 1829773.7957659496946338217168068 meters

    so now I want my G number to be written in pixels, I know it's m*m*m/kg * s * s

    so, I can't make up my mind, how to write that in pixels...:)

    any help appreciated :)
     
    Last edited: Jun 6, 2004
  2. jcsd
  3. Jun 6, 2004 #2
    You can do it by dimensional analysis. Just treat a pixel as just another unit of length, as if you were going to convert G from SI units to British units.

    First, let b = 1829773.7957659496946338217168068, where your conversion factor is "b meters per pixel." Additionally, I'm going to write G = 6.673*10^-11 m^3/(kg*s^2) here, but you should use a value to however many decimals you wish.

    So:

    [tex]
    \newcommand{\unit}[1]{\mathrel{\mathrm{#1}}}
    G = \frac{6.673\times 10^{-11}\unit{m^3}}{\unit{kg\cdot s^2}}\cdot
    \frac{\unit{pixel^3}}{(b\unit{m})^3}
    [/tex]

    Therefore, your new value of the gravitational constant is:

    [tex]
    \newcommand{\unit}[1]{\mathrel{\mathrm{#1}}}
    G = \frac{6.673\times 10^{-11}\unit{pixel^3}}{b^3\unit{kg\cdot s^2}}
    \approx \frac{1.089\times 10^{-29}\unit{pixel^3}}{\unit{kg\cdot s^2}}
    [/tex]

    To make a long story short, divide by 1829773.7957659496946338217168068^3.
     
    Last edited: Jun 6, 2004
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