2D Planet Gravity

Question

I'm trying to make a simple game where a spaceship is launched and then its path is effected by the gravity of planets.

Similar to this game: http://sciencenetlinks.com/interactives/gravity.html

I wish to know how to replicate the effect the planets have on the spaceship in this game so a spaceship can 'loop' around a planet to change direction.

I have managed to achieve some bogus results where the spaceship loops in a huge ellipse around the planet or is only slightly affected by the gravity of a planet using Vectors.

Thanks in advance.

p.s I have plenty of coding experience just none to do with game dev.

Answer 1

In your case there is an spaceship, which moves affected by the gravity of all the planets. Each planet applies force equal to 'm1*m2/ r^2' in which m1 and m2 represent masses of spaceship and planet, and r is equal to euclidean distance of planet and space ship. you just have to calculate sum of all the forces applied to ship. from the rules of newton we know 'f = m*a' where f is total force applied to an object, m is it's mass and a is it's acceleration. from this point you can read this page to learn how to use acceleration to compute velocity and position over time.

Answer 2

Each planet should have gravitational field that pulls any object in its vicinity towards its center. In other words, you should apply a force from the spaceship's position to the planet's center each step of the simulation.

This force depends on the mass of both objects, but in this case, since the mass of the spaceship is probably insignificant compared to the planet's, you can just try out different constant depending on the size of the planet until you get the feel right.

Most importantly, this force grows weaker the larger the distance between both objects. You will do this by dividing by the squared distance between both. After a certain distance you might want to "manually" cutoff and stop applying the force.

Just translate this force into an acceleration, and the basic physic equations should take care of the rest.

In pseudocode

force=0
for each planet
    if distance < constant
        force += mass * (planet.xy - ship.xy) / distance^2
apply force to ship