Using these expressions we can easily derive the speed in orbit for the asteroid which we discussed in last weeks lecture. The general
approach is to use the Kepler's third law to derive the semi-major axis and then derive the total mechanical energy from
Eq. 4. The kinetic energy and hence the speed
is then readily derived from
Putting in numbers we get at 
We could use the same technique to derive the speed
for 
but it is actually easier to
use the fact that angular momentum is conserved in the motion of the
asteroid (or equivalently use Kepler's second law) to write
