91影视

The applied force equals the rate of change of momentum.

Step1:Explanation for why shining sail is more effective sail

(a)

A shining sail that reflects photons back toward the Sun would be more effective; the shiny sail absorbs the energy emitted by the Sun and reflects the photons back to the Sun's surface. In this instance, the change in photon momentum will be higher, and the net force will be bigger (the net force can be expressed as the rate of change of momentum).

(b)

If N photons per second strike a gleaming sail perpendicular to the sail, and each photon has energy E, the energy of each photon (a massless radiation, hence no rest mass) is:

$$\begin{gathered} E=pc \\ p=\frac{E}{c} \end{gathered}$$

On shiny sail photon is absorbed and re-emitted in the opposite direction, so the change in its momentum:

$\begin{array}{rcl}螖p& =& p_f-p_i\\ & =& -p-p\\ & =& -2p\\ & =& -2\frac{E}{c}\\ & & \end{array}$

The magnitude of change in momentum for N photons/second is

$\left|螖p_{N/s}\right|=2N\frac{E}{c}$

The net force for N photons/second is the rate of change of momentum:

$\begin{array}{rcl}F& =& \frac{螖p}{螖t}\\ & =& 2N\frac{E}{c}\\ & & \end{array}$

Thus, the force ()on the sail is$2N\frac{E}{c}$ .