## The Photon Sail

The photon exerts a pressure on a surface. It is not a large pressure in the case of solar radiation, but is present as seen with the Nichols radiometer. This pressure P = 4.6 x 10~6 p for solar radiation on the Earth's surface requires large amounts of surface area for it to create a significant force. A solar sail with a radius R would then experience a force F = 2nR2P. For a solar sail of 100 km in radius the force on the sail would be about 3 x 105 N. For a sail material made of aluminum 16 nanometers thick the volume would be 1000 m3 or a billion cubic centimeters. Since the density of 2.7 g/cm3 this is 2.7 x 107 kg of material. Thus the acceleration would be g ~ .011 m/sec2. This estimate involves the absorption of the photon, where the reflection of photons would double this acceleration. The small acceleration will create a longer duration for the time of flight, but it is reasonable to consider a photon sail can reach low gammas. A version of the interstellar photon sail was studied by Robert Forward, with the proposed Starwisp craft [8.1].

The same relativistic analysis is employed to solve this problem. The energy the spacecraft before it starts to accelerate has the initial energy

The solar sail converts some of the photon energy to kinetic energy. For Eph the photons sent to the craft and Eref the photon energy reflected back and the final energy of the system is

Similarly, momentum is conserved. Before accelerating the total spatial momentum is zero in the Earth frame. Fig. 8.1. Schematic of momentum transfer from photons to a light sailing craft.

The final momentum is the momentum of the solar photons incident on the sail, which is equal to the momentum of the spacecraft plus that of the reflected photons is