The most energy efficient way to send a spacecraft to the Moon is to boost its speed while it is in circular orbit about the Earth such that the new orbit is an ellipse. The boost point is the perigee of the ellipse, and the point of arrival at the Moon is the apogee.
1. Calculate the percentage increase in speed required to achieve such an orbit Assume that the spacecraft is initially in a low-lying circular orbit about Earth (you can neglect the spacecraft height above the surface of the Earth) and the Moon is approximately 60 RE, where RE is the radius of the Earth.
2. What is the period of the spacecraft in the low-lying circular orbit about the Earth?