Supplement 1.6: Radiation pressure      (1/2)

Comet tails

Comets show a tail near the sun, which consists of dust, ice crystals and molecules that are detached from the surface of the comet by the strong solar radiation. You might think that a comet drags the tail behind it on its trajectory. In fact, the tail is directed away from the sun and is curved. The curvature is clearly visible on the comet, which was observed by the crew of the International Space Station on 21 December 2011 - just in time for Christmas. There is also a video of this encounter (3 MB).

Zoom Sign
Comet Lovejoy, photographed by Commander Dan Burbank of the International Space Station ISS on 21 December 2011. Source: Gateway to Astronaut Photography of Earth, NASA

The orientation and curvature of the tail of comets was already observed by Johannes Kepler (1571-1630) in 1607 and described in his work entitled Von dem neulich im Monat September und Oktober des 1607. Jahrs erschienenen Haarstern oder Cometen und seinen Bedeutungen:

"Die Sonnenstraalen durchgehen das corpus des Cometens und nemen augenblicklich etwas von dessen Materi mit sich ihren Weg hinaus, von der Sonne entan, daher, halt ich, komme der Schwantz des Cometens, der sich allwegen von der Sonnen entan streckt."

Kepler's observation points to a repulsive force that the sunlight exerts on the tail and deflects it from its trajectory. Today, this effect is described as radiation pressure. However, the gravitational force emanating from the sun also has an attractive effect, particularly on larger particles in the tail. The two forces often lead to a double comet tail as shown in the section on photons.

The double tail is analysed in more detail in Worksheet 1.2: Comet tails.
Équations ↓

Visualisation of the radiation pressure in the photon image

Please note: the letters p and E are used several times, do not confuse them!
Without taking spectral properties into account, we assume a particle stream of ΔN photons that hit a wall with momentum p in the time Δt. The force acting on the wall is

F= ΔN Δt p ,

whereby we only consider perpendicular collisions and therefore do not have to take vector properties into account. For the momentum and energy of photons - see the section on photons - the relationships

p= h λ              E=hf=h c λ

with Planck's constant h, the wavelength λ, the frequency f and the speed of light c apply. This means that

F= ΔN Δt h λ = ΔN Δt E 1 c

The power of the photons transferred to the wall is

P= ΔN Δt E    →    F= P c

The photon pressure p rad results from the force acting on a surface A:

p rad = F A = P A⋅c

Now let E rad be the radiant power acting on a surface, i.e. the irradiance given in W/m². For solar radiation above the atmosphere and at sea level, it is discussed in Chapter 3. At the outer edge of the atmosphere it is 1361 W/m² this is called the solar constant. The following applies:

E rad =P/A   →   p rad = E rad /c

How exactly does the radiation pressure of photons affect small objects such as atoms, molecules or larger dust particles? The topic of light scattering on particles is not dealt with in depth here. However, a distinction can be made between reflecting and absorbing particles.

  • Absorbing particles completely absorb the momentum and energy of the photon: the photon momentum generates the momentum of the collided particles, the photon energy leads to their heating.
  • Reflection does not heat particles, but leads to twice the particle momentum, because the particles also absorb the momentum of the reflected photons in the opposite direction.

The reflectivity r of a particle, with 0≤r≤1, can be taken into account in the photon pressure equation. It hereby becomes:

p rad =( 1+r ) E rad /c