Gravitation and Motion Equations

• Sobeita
In summary, the conversation discusses the standard equation for motion and how it can be expanded to include more axes and orders. It also mentions the need to convert gravitation into acceleration form in order to use it in the motion equation. The concept of using an iterative approach to approximate motion due to gravitation is also mentioned. The question of whether there is a unified equation that can calculate motion due to gravitation without iteration is posed.
Sobeita
The standard equation for motion is:

X= .5 * ax * t^2 + vx * t (+ cx)
Y= .5 * ay * t^2 + vy * t (+ cy)

...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.

Fg= G * mM / r^2;
F= m*a; Ag = Fg/m;
Ag= G * M / r^2.

But if you use substitution, using Ag, 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, Ag and motion, into a true unified equation?

Sobeita said:
The standard equation for motion is:

X= .5 * ax * t^2 + vx * t (+ cx)
Y= .5 * ay * t^2 + vy * t (+ cy)
These equations only apply to motion with constant acceleration; they are not true in general.

That was more or less the purpose of posting this question. Is there an equation that can calculate motion due to gravitation, without using some sort of sigma iteration approach?

1. What is the equation for gravitational force?

The equation for gravitational force is F = G * (m1*m2)/r^2, where F is the force of gravity, G is the universal gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between them.

2. How do I calculate the acceleration due to gravity?

The acceleration due to gravity can be calculated using the equation a = G * M/r^2, where a is the acceleration, G is the universal gravitational constant, M is the mass of the larger object, and r is the distance between the two objects.

3. What is the equation for centripetal force?

The equation for centripetal force is F = m*v^2/r, where F is the centripetal force, m is the mass of the object, v is the velocity, and r is the radius of the circular motion.

4. How do I find the velocity of an object in orbit?

The velocity of an object in orbit can be calculated using the equation v = sqrt(G*M/r), where v is the velocity, G is the universal gravitational constant, M is the mass of the larger object, and r is the distance between the two objects.

5. What is the equation for Newton's second law of motion?

The equation for Newton's second law of motion is F = m*a, where F is the net force acting on an object, m is the mass of the object, and a is the acceleration of the object.

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