How Do I Convert the Gravitational Constant to Pixels?

[devil]

gravitational constanT G -- HELP!



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 :)

 

[TALewis]

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:

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

Therefore, your new value of the gravitational constant is:

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

To make a long story short, divide by 1829773.7957659496946338217168068^3.