The Force with which the Sun Repels Planet Earth

The Pressure of Light

Did you know that the Sun pushes the earth out of its orbit? Of course, we're overreacting with language, but there is a force due to radiation pressure.

§ What is Radiation Pressure?

Electromagnetic waves, when they fall on a object, transmit impulse and quantity of movement, given their particle qualities that they present at that moment.

Before approaching the radiation pressure theory, it is important to know the historical chronology of the theories that gave it scientific basis.

◪ In 1666, Isaac Newton separated the colors of the rainbow by means of a crystal cousin, showing that the colors were due to the light itself and not produced in the crystal. And so he discovered the visible light spectrum.

◪ In 1690, Huygens published a theory in which he proposed the wave nature of light.

◪ In 1873, while investigating infrared radiation and the element thallium, Sir William Crookes developed a special kind of radiometer, an instrument for measuring radiant energy of heat and light.

◪ In 1800, William Herschel discovered the infrared region of the light spectrum.

◪ Johann Ritter, in 1801, discovered the ultraviolet radiation of light.

◪ In 1820, Oersted noticed that, in the presence of an electric current, the magnet needle of a magnetic compass suffered deflections.

◪ In 1827, André-Marie Ampère presents the mathematical deductions based on Oersted’s observations. Ampere’s law appears.

◪ Faraday’s Law of Induction: Michael Faraday in 1831 discovered how to generate an electric current in a coil of copper wire by varying a magnetic field through it.

◪ James Maxwell , in 1865, published work that meant the unification of the theories and mathematical equations of the physics of electricity and magnetism. These equations include: Gauss’s law for Electricity, Gauss’s law for Magnetism, Faraday’s law of induction and Ampère’s law modified by Maxwell. Due to the symmetry of the equations, both in the concept of physics and in the algebraic aspect, including reciprocity between the magnetic and electrical nature, Maxwell predicted the existence of electromagnetic waves in the form of radiation, whose speed could be determined solely by electrical and electrical magnitudes. magnetic. This speed was deduced by him and embodied in the formula:

where μ₀ and ε₀ correspond to the magnetic and electrical quantities respectively. Because the electromagnetic understanding proposed by him was shown to be wavelike in nature, he suggested that light also has an electromagnetic wave nature. In addition, he also predicted that one could count on the possibility of the electromagnetic wave transporting energy and linear momentum, which he idealized as a radiation pressure.

◪ In 1884, Poynting analytically described the energy transport of an electromagnetic wave, and introduced the Poynting vector:

where the wedge-shaped symbol represents a non-elementary algebraic multiplication operation between the electric field vector E and the magnetic field vector B. The intensity, or magnitude, of the vector S is expressed in units of mechanical power (watts) per measure of area (square meters).

◪ Hertzian waves: Heinrich Rudolf Hertz in 1888 discovered radio waves and consequently the transmission of electromagnetic waves in the air predicted by James Maxwell.

◪ In 1895, Roentgen, seeking to detect the high-frequency electromagnetic radiation predicted by Hertz, repeated Thompson’s experiment in his laboratory at the University of Wurzburg, Germany, and eventually discovered X-ray radiation.

◪ Marconi in 1896 developed wireless telegraphy.

◪ In 1901, P.N. Lebedev performed experimental measurement of the radiation pressure of light.

◪ In 1903, Nichols and Hull confirmed Lebedev’s results.

◪ In 1933, M. Bell and S. E. Green published experimental measurements correcting the results of Nichols and Hull.

What can be observed in this sequence presented here is the existence of two scientific strands, one focused its attention on radiation as a source of energy and heat and the other sought to describe the phenomena of electricity that showed promise in terms of technology. It seems that, following paths based on logic, sooner or later, the results converge. But specifically in this case there was a sui generis chain of events that intertwined very well historically.

§ Analytical formula

Once we consider the transposition of the behavior of the electromagnetic wave to the behavior of a beam of light, regarding the primary effect of transporting energy and momentum due to an undulatory behavior, and, if we represented such energy by U, then the amount of motion p transmitted to a body struck by a beam of light would be

in the case of total absorption of such energy, and on account of total reflection, since we are talking about waves we would have

In the case of an intermediate situation between total absorption and total reflection, the amount of movement imparted by the light beam would be between these two values ​​mentioned above.

§ Mathematical estimate

The calculations presented here are only for the purpose of knowing the order of magnitude. So it will be greatly simplified.

• As the body or object will be considered a flat circular region comprised by a meridian of the Earth, therefore, its radius will be equal to the radius of the planet Earth:

and the luminous beams of the Sun will be considered to be incident perpendicularly on this area as a part of the surface of the terrestrial sphere;

• The solar radiant power will be considered to produce an irradiance on the surface of the planet of:

• We will make the estimate such that it understands the effect of the supposed force in a time interval of 1s.
• The calculation of U in joules.

• The calculation of p in newtons times seconds.

where c corresponds to the speed of light in vacuum.

• Substituting the values, results:

that is, the force due to radiation pressure on the surface of the planet, would be in the order of:

which is considerable, comparable to the weight, for example, of an aircraft carrier type ship. However, this order of value, if compared to the order of value of the gravitational force of attraction that the Sun exerts on the planet, it would correspond to the percentage of: