A spaceship approaches the Moon along a parabolic trajectory which is almost tangent to the Moon's surface. At the moment of the maximum approach the brake rocket was fired for a short time interval, and the spaceship was transferred into a circular orbit of a Moon satellic. Find how the spaceship velocity modulus increased in the process of braking.

Explanation

In a parabolic orbit, `E=0`
So `1/2mv_i^2-(gammaMm)/(R)=0` or, `v_i=sqrt2sqrt((gammaM)/(R) )`
where M=mass of the Moon, R=its radius. (This is just the escape velocity).
On the other hand in orbit
`mv_f^2R=(gammaMm)/(R^2)` or `v_f=sqrt((gammaM)/(R))`
Thus `Deltav(1-sqrt2)sqrt((gammaM)/(R))=-0*70km//s`.