"Celestial mechanics," as the science of stars was called in the days of Isaac Newton, obeys the classical laws of motion of bodies. One of the important characteristics of this movement is the different periods of revolution of space objects in their orbits. The article will discuss sidereal and synodic periods of revolution of stars, planets and their natural satellites.
The concept of synodic and sidereal time periods
Almost every one of us knows that planets move in elliptical orbits around their stars. Stars, in turn, make orbital motions around each other or around the center of the galaxy. In other words, all massive objects of space have certain trajectories of motion, including comets and asteroids.
An important characteristic for any space object is the time it takes to complete one full revolution along its path. This time is called the period. Most often in astronomy when studying the solar system, two periods are used: synodic and sidereal.
The sidereal time period is the time it takes for an object to complete a complete revolution in its orbit around its star, while another distant star is taken as the reporting point. This period is also called real, since it is such a value of the time of revolution in orbit that will be received by a motionless observer who will follow the process of rotation of an object around its star.
The synodic period is the time after which the object appears at the same point in the sky, if you look at it from any planet. For example, if you take the Moon, the Earth and the Sun and ask how long the Moon will be at the point in the sky at which it is currently, the answer to it will be the value of the synodic period of the Moon. This period is also called apparent, since it differs from the real orbital period.
The main difference between sidereal and synodic periods
As already mentioned, sidereal is the real period of conversion, and synodic is apparent, but what is the main difference between these concepts?
The whole difference lies in the number of objects relative to which the time response is measured. The concept of sidereal period takes into account only one relative object, for example, Mars revolves around the Sun, that is, motion is considered only relative to one star. The synodic time period is a characteristic that takes into account the relative position of two or more objects, for example, two identical positions of Jupiter relative to the terrestrial observer. That is, it is necessary to take into account the position of Jupiter not only relative to the Sun, but also relative to the Earth, which also revolves around the Sun.
Sidereal Period Formula
To determine the real period of revolution of a planet around its star or a natural satellite around its planet, it is necessary to use Kepler’s third law, which establishes the relationship between the real orbital period of an object and the half-length of its major axis. In the general case, the shape of the orbit of any cosmic body is an ellipse.
The formula for determining the sidereal period is: T = 2 * pi * √ (a3 / (G * M)), where pi = 3.14 is the number of pi, a is the half-length of the major axis of the ellipse, G = 6.674 * 10-11 m3 / (kg * s2) is the universal gravitational constant, M is the mass of the object around which rotation is carried out.
Thus, knowing the parameters of the orbit of any object, as well as the mass of the star, one can easily calculate the value of the real period of revolution of this object in its orbit.
Calculation of the synodic time period
How to calculate? The synodic period of a planet or its natural satellite can be calculated if we know the value of its real period of revolution around the object in question and the real period of revolution of this object around its star.
The formula that allows such a calculation is: 1 / P = 1 / T ± 1 / S, here P is the real period of revolution of the object under consideration, T is the real period of revolution of the object with respect to which the movement is considered around its star, S - unknown synodic time period.
The sign "±" in the formula should be used as follows: if T> S, then the formula is used with the sign "+", if T <S, then you need to substitute the sign "-".
Using the formula on the example of the moon
To show how to use the above expression correctly, let us take as an example the rotation of the Moon around the Earth and calculate the synodic period of revolution of the Moon.
It is known that our planet has a real period of revolution in orbit around the Sun, equal to T = 365.256363 days. In turn, from observations it can be established that in the sky the Moon appears at the considered point every S = 29.530556 days, that is, this is its synodic period. Since S <T, then the formula connecting the different periods should be taken with the “+” sign, we get: 1 / P = 1 / 365,256363 + 1 / 29,530556 = 0.0366, whence P = 27.3216 days. As you can see, the Moon performs its revolution around the Earth 2 days faster than the Earth observer can again see it in a marked place in the sky.