The standard equation for motion is:(adsbygoogle = window.adsbygoogle || []).push({});

X= .5 * a_{x}* t^2 + v_{x}* t (+ c_{x})

Y= .5 * a_{y}* t^2 + v_{y}* t (+ c_{y})

...and of course, you can expand it to include more axes and more orders if you like.

Gravitation is a force, but to use it in the motion equation, you need it in acceleration form.

F_{g}= G * mM / r^2;

F= m*a; Ag = Fg/m;

A_{g}= G * M / r^2.

But if you use substitution, using A_{g}, the motion equation is still always parabolic, despite what we know about orbits. The cause is obviously the presence of the "r" variable, which is dependent on the position of the object (so that acceleration changes based on its position, and that position affects the acceleration, and both change continuously.)

With an iterative approach, I am able to approximate motion due to gravitation. The result is essentially a long string of parabolas.

Is there a way to combine these two equations, A_{g}and motion, into a true unified equation?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Gravitation and Motion Equations

**Physics Forums | Science Articles, Homework Help, Discussion**