GravField

Sorry you have to have java turned on..

ok how to use this:

1. type in some number for the mass. the bigger the better.
2. click anywhere to create a new point mass at the mouse location (with whatever the field is set to)
3. as you click the gravity field will be redrawn

Please note that:

1. the gravity field is calculated as the net grativational force vector (upon a hypothetical 1-mass unit body) at each point taking into consideration the mass and location of all other masses that you've clicked into existance.
2. Darker means less force (smaller magnitude), white means more.
3. the force vectors will be drawn every so often, they have green bodies for the line and a blue head. (so you can see the direction).
   They are in the negativedirection of rhat, so they show the direction of the force towards the clicked masses.
4. Warning, if you put one of your masses too close to one of the sample vectors it's size will be off the map! Hit reload/refresh on your browser and try again.
5. for purposes of demonstration, big-G is set to the value 1
6. The calculations run something like this:
   • Given: point masses m₀...m_n with locations r_n = r_{n x} j + r_{n y} k,
     and given that for any i, the displacement vector r is
     r_i(x,y) = [ (x-r_{i x})i + (y-r_{i y})j ]

     and of course:

     r_i(x,y) = |r_i(x,y)| = Sqrt [ (x-r_{n x})² + (y-r_{n y})² ]

     also the unit vector rhat is simply:

     rhat_i(x,y) = r_i(x,y) / r_i(x,y)

     then the gravity field's force vector (?) for each point g_x,y where m_p=1 [mass of the body being affected is set to 1 ] is given by:
     

     g_x,y = Sum [i=0...i=n]
     
     of: [ ( G * m_p * m_i) / r_i(x,y)² ] * rhat_i(x,y)
   • Whew.
   • the shades of gray are directly proportional to ln(|g_x,y|) and the arrows of course are showing rhat_i(x,y)
7. Source is here
8. Be sure to visit the De Anza Physics Department which is where I learned about this.

(c) 1999 steven r. loomis