msk2000 / 2D_Gravity_simulation

This is a simple 2-body simulation of bodies in space and how their gravitation impacts the trajectories of one another.

2D Gravity Simulation

This is a simple 2-body simulation of bodies in space and how their gravitation impacts the trajectories of one another.

Some of the numerical details

Change in distance calcualted from:

$$dx = x_2 - x_1 \ dy = y_2 - y_1$$

Distance between the two bodies calculated from:

$$r = \sqrt{(dx)^2 + (dy)^2}$$

Force between the two bodies calculated from:

$$F = \frac{GM_1M_2}{r^2}$$

Horizontal and Vertical components of Force calculated from:

$$F^{(x)} = F \cos(\theta)$$

$$F^{(y)} = F \sin(\theta)$$

Angle(theta) between the two bodies calcualted from:

$$\theta = \arctan\left(\frac{dx}{dy}\right)$$

Horizontal and Vertical Components of acceleration calculated from:

$$a^{(x)} = \frac{F^{(x)}}{M}$$

$$a^{(y)} = \frac{F^{(y)}}{M}$$

Initial and final velocities calculated from:

$$v^{(x)} = u^{(x)} + a^{(x)}dt$$

Change in position calculated from:

$$v^{(x)}dt - \frac{1}{2}a^{(x)} dt^2$$

Dependencies

Make sure you follow the instructions at matplotlibcpp to setup the matplotlib extension for C++. This is what is being used to produce the visual output.