) min gR ( . ) Using the value of g and R E , numerically ( V i ) min ≈ . km/s. This is called the escape speed, sometimes loosely called the escape velocity.
Equation ( . ) applies equally well to an object thrown from the surface of the moon with g replaced by the acceleration due to Moon’s gravity on its surface and r E replaced by the radius of the moon. Both are smaller than their values on earth and the escape speed for the moon turns out to be . km/s, about five times smaller.
This is the reason that moon has no atmosphere. Gas molecules if formed on the surface of the moon having velocities larger than this will escape the gravitational pull of the moon. Example . Two uniform solid spheres of equal radii R , but mass M and M have a centre to centre separation R , as shown in Fig.
. . The two spheres are held fixed. A projectile of mass m is projected from the surface of the sphere of mass M directly towards the centre of the second sphere.
Obtain an expression for the minimum speed v of the projectile so that it reaches the surface of the second sphere. Fig. . Answer The projectile is acted upon by two mutually opposing gravitational forces of the two spheres.
The neutral point N (see Fig. . ) is defined as the position where the two forces cancel each other exactly. If ON = r , we have ) ( R – r ) = r R – r = ± r r = R or – R.
The neutral point r = – R does not concern us in this example. Thus ON = r = R . It is sufficient to project the particle with a speed which would enable it to reach N. Thereafter, the greater gravitational pull of M would suffice.
The mechanical energy at the surface of M is At the neutral point N, the