This is a follow-up of question http://www.experts-exchange.com/Other/Math_Science/Q_26846773.html
The 4 bodies have equal mass and same initial speeds. Their initial position is in a square with their velocities shown here:
Vb^ / \
| / \
\ / |
\ / v Vd
In the previous question, we learned that the perfect speed |Vp| required so that the 4 bodies rotate in a circle that inscribes the square, is determined by the equation:
f = G (m²)/(2*r)² + 2*G*(m²/S²)*cos 45 = m |Vp|²/r
where r is the radius of the inscribed circle and S is the length of the side of the square.
Now, if the initial speed is greater than |Vp|, then it may be possible that the bodies escape from their orbit. How do you determine the escape speed, |Ve|? If it is not possible to get a formula for |Ve|, then what numerical algorithm can be used to determine the value?