Solar radiation pressure

In addition to the force of gravity generated by the mass of the Sun, the central force of solar radiation pressure may also affect the orbits of interplanetary material. Its sense is opposite to that of gravity but is generally a very small effect certainly for objects such as planets. However, in the case of small dust particles, say those ejected from comets in forming a tail, for certain sizes of particle, it turns out that there can be an exact balance between solar gravitation and radiation pressure so that the resultant orbit of the ejected particle from the comet is a ‘straight line’, so fulfilling Newton’s first law (see earlier). This circumstance is a beautiful example of astronomy offering a circumstance to verify a law which is very difficult to explore within the laboratory.
Consider the condition of this special case, evaluating the forces on a small spherical grain of radius, a, mass, ma, and with density, ρ, at a distance, r , from the Sun. The force of gravity may be expressed as

Now the Sun has a luminosity (total energy output) of L_Θ (= 3·8 × 10²⁶ W) and the flux intercepted by the particle is given by 

The photons in the radiation carry momentum and hence give rise to a force acting along the direction of the received light. The force of radiation pressure, F_RP, is simply the flux received divided by the speed of light and, therefore, may be written as

For an exact balance, F_G = F_RP and, therefore,

and, hence,

Substituting for the various values and constants and by assuming a typical density of 3000 kg m⁻³, the balance of forces is achieved for a particle with radius

Thus, for such tiny dust particles emanating from a comet, no matter the distance from the Sun, they would continue to travel with their velocity at ejection and travel in a straight line without a force acting on them. Measurement of the movement of some parts of the cometary dust tail verifies this. The main body of the comet continues in its orbit about the Sun.
There are proposals and design studies for utilizing radiation pressure as a means of propulsion within the solar system. By making very large ‘sails’ of light-weight material with high area-to-mass ratio, it is feasible to propel light-weight space vehicles using solar radiation as the ‘fuel’. By altering the attack of the sail at any time, the orbit of the vehicle can be readily modified at any time. The principles behind the manoeuvres are referred to as solar sailing.