I'm making a game in which the goal is to get as many planets as possible to orbit around a star. The user launches planets at any distance away from the sun (as long as it's on-screen), and in any direction (possibly even directly at the sun, though their game won't last very long).

This means orbits can be circular, elliptical, or--more than likely--irregular, something like this:

(Image originally from here)

The rules for my game that the player may launch planets as frequently as s/he likes...but they will only score a point for their first revolution (so spamming planets isn't likely to score very much).

Right now, the gravitational force is just F = ma (i.e. a constant force towards the sun). I'm trying to figure out when a planet in arbitrary orbit has completed a full revolution. This is how I'm doing it currently...

// If this planet is active... Vector2 a = _body.position.normalized; Vector2 b = (a + _body.velocity).normalized; float angle = Vector2.Angle (a, b); this._total_angle += angle * Time.deltaTime; if (this._total_angle >= 360) { // If this planet has made a revolution... ++this._revolutions; this._total_angle = 0; this.OnRevolution.Invoke (this); } 

However, this is incorrect for anything besides circular orbits. No good.

Given all of this (and my near-total unfamiliarity with orbital mechanics), how can I tell when a planet in an arbitrary orbit has completed one full revolution?

EDIT: No, the planets will not affect each other's orbits (though they can collide into one another, but they'll just explode).

I'm making a game in which the goal is to get as many planets as possible to orbit around a star. The user launches planets at any distance away from the sun (as long as it's on-screen), and in any direction (possibly even directly at the sun, though their game won't last very long).

This means orbits can be circular, elliptical, or--more than likely--irregular, something like this:

(Image originally from here)

The rules for my game that the player may launch planets as frequently as s/he likes...but they will only score a point for their first revolution (so spamming planets isn't likely to score very much).

Right now, the gravitational force is just F = ma (i.e. a constant force towards the sun). I'm trying to figure out when a planet in arbitrary orbit has completed a full revolution. This is how I'm doing it currently...

// If this planet is active... Vector2 a = _body.position.normalized; Vector2 b = (a + _body.velocity).normalized; float angle = Vector2.Angle (a, b); this._total_angle += angle * Time.deltaTime; if (this._total_angle >= 360) { // If this planet has made a revolution... ++this._revolutions; this._total_angle = 0; this.OnRevolution.Invoke (this); } 

However, this is incorrect for anything besides circular orbits. No good.

Given all of this (and my near-total unfamiliarity with orbital mechanics), how can I tell when a planet in an arbitrary orbit has completed one full revolution?

EDIT: No, the planets will not affect each other's orbits (though they can collide into one another, but they'll just explode).

I'm making a game in which the goal is to get as many planets as possible to orbit around a star. The user launches planets at any distance away from the sun (as long as it's on-screen), and in any direction (possibly even directly at the sun, though their game won't last very long).

This means orbits can be circular, elliptical, or--more than likely--irregular, something like this:

(Image originally from here)

The rules for my game that the player may launch planets as frequently as s/he likes...but they will only score a point for their first revolution (so spamming planets isn't likely to score very much).

Right now, the gravitational force is just F = ma (i.e. a constant force towards the sun). I'm trying to figure out when a planet in arbitrary orbit has completed a full revolution. This is how I'm doing it currently...

// If this planet is active... Vector2 a = _body.position.normalized; Vector2 b = (a + _body.velocity).normalized; float angle = Vector2.Angle (a, b); this._total_angle += angle * Time.deltaTime; if (this._total_angle >= 360) { // If this planet has made a revolution... ++this._revolutions; this._total_angle = 0; this.OnRevolution.Invoke (this); } 

However, this is incorrect for anything besides circular orbits. No good.

Given all of this (and my near-total unfamiliarity with orbital mechanics), how can I tell when a planet in an arbitrary orbit has completed one full revolution?

I'm making a game in which the goal is to get as many planets as possible to orbit around a star. The user launches planets at any distance away from the sun (as long as it's on-screen), and in any direction (possibly even directly at the sun, though their game won't last very long).

This means orbits can be circular, elliptical, or--more than likely--irregular, something like this:

(Image originally from here)

The rules for my game that the player may launch planets as frequently as s/he likes...but they will only score a point for their first revolution (so spamming planets isn't likely to score very much).

Right now, the gravitational force is just F = ma (i.e. a constant force towards the sun). I'm trying to figure out when a planet in arbitrary orbit has completed a full revolution. This is how I'm doing it currently...

// If this planet is active... Vector2 a = _body.position.normalized; Vector2 b = (a + _body.velocity).normalized; float angle = Vector2.Angle (a, b); this._total_angle += angle * Time.deltaTime; if (this._total_angle >= 360) { // If this planet has made a revolution... ++this._revolutions; this._total_angle = 0; this.OnRevolution.Invoke (this); } 

However, this is incorrect for anything besides circular orbits. No good.

Given all of this (and my near-total unfamiliarity with orbital mechanics), how can I tell when a planet in an arbitrary orbit has completed one full revolution?

EDIT: No, the planets will not affect each other's orbits (though they can collide into one another, but they'll just explode).