We present a simplified dynamical model of the “ Bullet ” system of two colliding clusters .
The model constrains the masses of the system by requiring that the orbits of the main and sub components satisfy the cosmological initial conditions of vanishing physical separation a Hubble time ago .
This is also known as the timing argument .
The model considers a system embedded in an over-dense region .
We argue that a relative speed of 4500 km / s between the two components is consistent with cosmological conditions if the system is of a total mass of 2.8 \times 10 ^ { 15 } h ^ { -1 } M _ { \odot } is embedded in a region of a ( mild ) over-density of 10 times the cosmological background density .
Combining this with the lensing measurements of the projected mass , the model yields a ratio of 3:1 for the mass of the main relative to that of the subcomponent .
The effect of the background weakens as the relative speed between the two components is decreased .
For relative speeds lower than \sim 3700 km / s , the timing argument yields masses which are too low to be consistent with lensing .