# Inverse-square law gravitational field ( free-fall time for two point objects on a radial path)

## Description

Two objects in space orbiting each other in the absence of other forces are in free fall around each other. The motion of two objects moving radially towards each other with no angular momentum can be considered a special case of an elliptical orbit of eccentricity e = 1 (radial elliptic trajectory). This allows us to compute the free-fall time (as a function of separation) for two point objects on a radial path.

Related formulas## Variables

t_{y} | The time after the start of the fall (s) |

y | The distance between the centers of the bodies (m) |

G | Newtonian constant of gravitation |

m_{1} | The mass of one of the objects (kg) |

m_{2} | The mass of other object (kg) |

y_{0} | The initial value of the distance between the centers of the bodies (m) |