When Maths goes right

I found out I had been doing gravity wrong.

This is what I was getting:

image

There seemed to be gravity, but it was messy.

I had been using the good old (G*m1*m2)/(r^2) equation.   However, in an effort to be smart, I calculated the (x2-x1) * (y2-y1) to be the (r^2) value..

WHICH IS TRUE.

And when you apply that force to an object of mass m1, the m1 disappears (F=ma; a=F/m) and you get the acceleration, the pull of gravity.

But, the kicker is, I then have to scale the normal vector out by that.   And the normal vector is…  just the x component .. is .. (x2-x1)/r. 

When you do the whole thing, the acceleration felt is proportional to 1/r^3, not r^2.

So I did that.  And I pulled out the gravitational constant, G, to use elsewhere (turns out you can calculate orbital velocities and periods as well). 

The result:

image

No matter where you start, no matter your initial velocity and direction (within reason), you get a nice orbit.

What’s more, I could use the maths where “velocity at distance r” can be calculated, as well as “radians per unit time” can be calculated, for a circular orbit.

This means, I could write an autopilot to get you in a circular orbit around a star or planet at a particular distance pretty easily.  I think.

However, I also found out that due to gravitational effects of planets,  it was very easy to get swept into the sun.. and then gravitationally flung out of the solar system.

So, I changed it when you get within the radius of a planet, gravity is about constant – like it would be at the surface.  “Airbrakes”, as it were.  

THIS HAS PROMISE!  I spent probably an half hour flying around in this simulation, gravity made it so interesting. 

source: https://github.com/sunnywiz/dotnetmud2015/blob/e5db82581382e43a721f0abc4a5c45710ed7fee4/canvasTest/solarSystemFlight.html

it needs one image from the same directory.  Otherwise, just run that file.

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