The Orbit consists of the trajectory that an object in the solar system has around another, such as, for example, all the planets around the Sun. In the following article we will learn more about what the orbits consist of. Solar System Orbits and more.
In the field of physics, the definition of an orbit is the path that a physical object follows around another while it is under the influence of a powerful central force, such as gravity. Knowing these orbits is essential to understanding various characteristics of the planets of the Solar System.
History
It begins with the great mathematical contribution of Johannes Kepler, who was to be the person who formulated the great results of the 3 laws of Planetary Motion made by himself, which are:
- Kleper's 1st Law of Planetary Motion: It is where he pointed out that the orbits of all the planets within the solar system become elliptical and that they are not circular or, failing that, epicycles, as was previously thought and that the Sun was at one of its foci and not as everyone thinks that It is in the center of the orbits of the planets.
- Kleper's 2nd Law of Planetary Motion: It is where he describes that the orbital speed of each of the planets is not frequent, as was also believed, but that the speed of the planet would depend on the kind of path between the planet and the Sun.
- Kleper's 3st Law of Planetary Motion: It is where Kepler came to find a kind of correlation in a universal way between what are the orbital properties of each of the planets that are orbiting around the Sun. For each of the planets, the path between it and the Sol cubed (Distance 3), is usually measured in astronomical units, this is in the same way as in the case of the period of the planet squared (Period of the Planet 2), which is measured in Earth years.
The renowned Isaac Newton was the person who demonstrated that the laws of the great Johannes Kepler came from Newton's theory of gravity and that, in general, the orbits of each of the bodies that usually responded to the force of gravity were conic sections. In addition, his work has been fundamental to understanding the planets of the solar system.
So Isaac Newton himself also pointed out that 2 bodies continue in their orbits of dimensions that are usually inversely proportional to their respective masses about what is their usual center of mass. When one body becomes much larger and of greater mass than in the case of the other, a kind of convention is made whereby the center of each of the masses is taken to be the central point of the body with a mass that is much larger. bigger or bigger.
Through knowledge of orbits we can learn, for example, about the Earth movements, that's why it's important to know What is an orbit? and everything related to it.
Planetary Orbits
Within what is a planetary system that is composed of:
- The planets
- The Dwarf Planets
- Asteroids
- the comets
- Space Junk
All of them orbit around the largest main star in our Solar System, that is, the Sun. For example, the case of a comet that is in an orbit called parabolic or also known as hyperbolic around the main or central star which would be the Sun, does not have a gravitational link with said star and therefore it will not be considered as part of this planetary system of the main star.
Comets with clearly hyperbolic orbits have not been visualized within the Solar System. The bodies that gravitationally have a link with each of the planets of the planetary system, whether they are artificial or natural, are the ones that execute the so-called elliptical orbits around the planet.
Due to bilateral gravitational perturbations, the eccentricities of each of the planetary orbits tend to differ over the years. The Planet Mercury, which is the smallest planet in the entire Solar System, has a much more eccentric orbit unlike the rest. The next is Mars the Red planet, while the other planets with less eccentricity become:
- the planet venus
- the planet neptune
When two objects come into orbit around each other, periastron is the initial point at which both objects will be closest to each other, and apoastron is the point at which both objects are as far away from each other as possible. For more information, you can read about the activity of bodies in the solar system.
In the case of an elliptical orbit, the center point of the masses of the system between the object being orbited and the object being the orbiter is located at 1 of the foci of either orbit, with nothing else in between. another focus.
At the moment when one of the planets approaches the so-called periastron, then the planet increases its speed. The opposite, that when the planet approaches its apoastro, then it lowers the intensity of its speed.
Intuitive Explanation
There are several ways to explain what the functioning of an orbit is, some of them are the following:
- When an object (Planet, asteroid, comet, satellite, among others) moves obliquely, it falls towards another orbited object. However, it moves so quickly that the curvature of said orbited object will fall below it at all times.
- A powerful force, such as gravity, is responsible for pulling an object a curved distance while trying to keep it going in a straight line.
- When an object comes to fall, it moves from one side so quickly since it has the necessary tangential speed to be able to avoid the orbited object.
One of the most commonly used examples to illustrate an orbit around a planet is Newton's Canyon. For this example we are going to imagine a cannon that is located at the top of a mountain that is going to shoot cannon balls that have a horizontal shape.
It is going to be required that the mountain does not have a very high altitude in order to avoid what is the terrestrial atmosphere and in the same way to be able to ignore the effects caused by the friction on the cannon ball.
If this cannon were to fire a ball with a low initial speed class, the path of the ball would curve and collide with the earth's surface (A). Increasing the initial velocity, the cannon ball will collide with the earth's surface but this time at a much further distance from the cannon (B), because the tail is meanwhile descending, the earth's surface it will also bend.
These movements are technically defined as orbits, because they describe a kind of elliptical direction around a center of gravity, however, which is interrupted at the moment of colliding with planet earth. If the cannon ball were to be fired at a high speed, the ground would curve enough as the ball fell, in such a way that the ball would never collide with the earth's surface.
It must be said that it is executing an orbit without any kind of interruption or without any crossing. So we can highlight that there is a certain speed that will produce a circular orbit (C) for each of the heights above what is the central point of gravity.
If the speed of the detonation increases much beyond that speed, then elliptical orbits (D) will be produced. At a much higher speed, it is called Escape velocity, which again will depend on the height class from where the ball is detonated, for which an infinite orbit (E) is caused, firstly, of the parabolic class and much faster than the hyperbolic class.
In the case of the 2 classes of infinite orbits, as a result, the object manages to escape from what is the planet's gravity and goes towards outer space without any direction.
Orbital Motion Analysis
We are going to carry out an analysis regarding what the orbital movement of the solar system is, starting with the well-known classical theory of Isaac Newton, then we move on to Einstein's Relativistic Theory and later we proceed to the analysis of the orbits in the Newtonian case and the Orbits in the relativistic case.
Isaac Newton's Classical Theory of the Orbit
For a type of system of only about 2 bodies that influence each other only by gravity, the orbits can be calculated by means of the well-known laws of Newton and in the same way by Einstein's law of universal gravitation which is: The sum of all the forces would be equal to what is the mass times the velocity. This law can help us understand the gravity of other planets.
Gravity tends to be proportional to the product of each one of the masses and inversely it is proportional to the square of the path (this type of calculation is the one that ignores all the minimum effects such as the shape and also the dimensions of each one of the bodies, which are not usually relevant, if these bodies orbit at a much greater distance compared to their own dimensions and in this way it is possible to ignore the relativistic effects that are also very small in the general circumstances of the Solar System) .
In order to perform each of the calculations, it is convenient to be able to describe what movement is in a type of coordinate system that is focused on what the center of gravity of the system is. If one of the bodies becomes much larger than the other, the center of gravity will usually coincide with the type of center of the body that is much heavier, so it can be deduced that the lightest body is the which orbits around the heaviest.
Isaac Newton's theory states that in a 2-body problem, the orbit of a 1-body becomes a kind of conic section. The orbit can even be open, if the object never returns, or it can become closed, if the object does return. Everything will depend on the total sum of the kinetic energy and also the potential of the system that exerts on the planetary object. This type of orbit can be related to the types of planets in the solar system.
Einstein's Relativistic Theory
It is well known that the relativistic theory is in great contradiction with what is the Newtonian theory of gravitation, since in the former the action of the instantaneous path takes place. This and many more reasons were what moved Einstein himself in search of a more general theory that came to be known as the Theory of General Relativity that usually incorporates a kind of correct relativistic representation of what the gravitational field is.
In this theory, the state of a mass that is in outer space will bend space-time in such a way that its geometry ceases to be Euclidean even though it continues to be more or less Euclidean if said masses and velocities of each one of the bodies come to take some values like those that are visualized within our solar system.
The so-called planetary orbits are not usually strictly conical sections, but rather are geodesic curves, that is, they are a kind of line of a small curvature, on what is the bent geometry of space and time. This theory does not become linear, it is usually a matter of doing calculations with it, for example, to be able to get the result of a problem of 2 bodies with identical masses.
Another thing we can learn is about the Jupiter satellites, what they are called, what their orbits are and much more about them.
However, in the case of planetary systems such as our Solar System, where the central star, which is the Sun, is usually much more massive than in the case of the remaining planets, so a curvature of space / time that is committed towards the Sun, this compared to that of the other planets and in such a way we can assume that all other objects are therefore less massive and that they move according to the geodesic geometry bent by the Sun itself.
For the case of the values present within our Solar System, the quantitative results of what Einstein's Theory is, are approximately very close numerically speaking to what Newton's Theory is, that is, the Newtonian Theory, so This causes that it is justified for the most practical purposes to use the Newtonian theory, which is usually much simpler computationally speaking.
However, the Newtonian theory has not yet been able to explain certain types of facts that have been resolved through Einstein's own relativistic theory, among them is what is the effect of the advance of the perihelion, especially of the planet Mercury, which it has managed to be explained with an excellent approximation by Albert Einstein's relativistic theory, however, it is not possible by Newton's theory.
Orbits in the Newtonian Case
In order to analyze what is the movement of a mass under the influence of a great force which at all times moves from a fixed starting point, the most beneficial thing to use are the coordinates of the poles of which its origins coincide with those of the center of force itself. In this coordinate system, the radial and transverse components are as follows:
Due to the fact that this force is completely radial and that the acceleration in turn is proportional to this force, it will imply that the transverse speed becomes equal to (0) zero.
Which results in: 
After the integration, the following will be obtained: 
,
which is a kind of theoretical proof of what Kepler's 2nd Law is. The Constant of integration I becomes the angular chance per unit of mass. Whereby,
Where an added variable of:
The radial force becomes f(r) times unity which is ar, after eliminating the time variable from the radial component of said equation, which is obtained,
In the case of gravity, the universal law of gravitation carried out by Isaac Newton is the one that states that the force becomes inversely adjusted to the square of the trajectory,
Where (G) becomes the constant of universal gravitation, (m) is the mass of the orbiting body and (M) consists of the mass of the central body. Substituting in the equation above, we get,
For the case of the gravitational force, the concept on the right of said equation will become a kind of constant and in turn the equation will come to resemble the harmonic equation. The equation made for the orbit that is described by the particle consists of the following:
Where p,e and θ0 become the constants of an integration,
If the parameter (e) becomes less than 1, then (e) becomes the eccentricity and (a) becomes the semi-major axis for a kind of ellipse. In general, it can be recognized as an equation of the conic section in the coordinates of the poles (r,θ).
Orbits in the Relativistic Case
Now, in the case of relativistic theory, the 2-body problem can even be solved using what is the Schwarzschild solution, for which is the gravitational field established by 1 body with a class of spherical symmetry. The planetary orbit in space-time becomes a geodesic of Schwarzschild's own metric.
The orbit that is obtained would have, from a kind of geodesic of what is the Schwarzschild metric of it, an equivalent to which the particle will notice a very effective radial speed given by the following:
Where it is broken down as follows:
- g c It is the constant of universal gravitation and also of the speed of light.
- r, becomes the Schwarzschild radial coordinate.
- l, is the orbital angular momentum of the planet per unit mass.
The constants of movement are linked to energy and angular momentum, which are:
The equation of motion makes the change of u = 1/r, as in the classic case, where it is as follows:
For each of the planets belonging to the Solar System, the relativistic correction that is given by the 3rd term of the 2nd member is usually minimal compared to the other terms. In order to demonstrate all this, it is convenient to place a type of dimensionless parameter that would be: ∈ = 2 (GM/cl)2 and making a new exchange rate of the variable ū = ul2 / GM with what is the equation of motion which can then be rewritten as follows:
Where:
For the case of the planet Mercury, the parameter ∈ consists of the maximum and the value that is reached from ∈ = 5,09. 10 -8.
However, the minimum of said term means that the relativistic corrections are the ones that produce only small corrections and for that same reason Newton's theory, which is called Newtonian, gives such good approximations for what the solar system is. Looking for each of the roots of the function ƒ (ū), where the minimum of said parameter is taken into account, which is the following:
In the case of planetary orbits, they can be established in ū1 < ū < ū2 the case u > ū3 which is excluded since this implies that the particle will fall on the Sun ū → ∞. The solution of the equation is given by the following:
This kind of integral can be reduced to an elliptic integral by changing the variable from v = ū1 + 1/t2, coming to be as:
where: to2 = 1/ (ū2 - or1), b2 = 1/ (ū3 - or1). Using one of the so-called elliptic Jacobi functions, the integral can be completed as: ∈ 1/2 θ = bns -1 (t/a) with a module that is given by k = √ b/a, using this type of result for the equation of the orbit that can be obtained:
Where:
K2 = 2 e∈ + XNUMX (e2), becomes the module of all elliptic Jacobi functions for an orbit. If ∈ = 0, this means that A = 1 – e, B = 2e, n = ½, k = 0 and in that case the orbit of the planet is completely reduced to the case of classical Newtonian theory:
That it is a kind of ellipse of eccentricity e. The relativistic orbit, however, is not usually periodic, but it is a quasi-ellipse that rotates smoothly around the Sun. This is known as a perihelion advance that is usually much more pronounced, especially for the Planet Mercury. .
From what is the solution of the previous equations, the perihelion occurs at θ = K/n and the next value for which is given becomes θ = 3 K/n where k is ¼ of the period, which is originated so it is the elliptic integral of the 1st total species, for which between the 2 perihelions the rotated angle does not become 2 π but a class of quantity that is slightly greater than:
For the case of the Planet Mercury with ∈ = 5, 09. 10-8 the progress of the indicated perihelion manages to be about 41.07” per century, generally its period is about 88 days, which is usually the experimental value of 42.98” per century. It was this type of agreement that established the original great success of the theory which came to give it wide general approval.
There are many experts in the field who continue with a controversy about what is the Solar System Scientific Disclosure Article, where the orbit of the solar system and each of the objects that compose it are mainly established.
Orbital Period
The so-called orbital period consists of the duration that a space object or a planet takes to be able to completely execute its orbit (when we speak of an object, we refer to planets, moons, satellites, among others). There are different classes of orbital periods for these planets or objects that are around the Sun:
- The First: Sidereal Period
The first is the Sidereal Period, which consists of the time it takes for an object to completely give its orbit around the Sun, with respect to satellites or stars. This type of period is considered as a true one of the object.
- The Second: Synodic Period
The second consists of the Synodic Period, which is the time that an object will take again to present itself at an initial point in space, with respect to the main star that is the Sun, when it is viewed from the planet Earth. This type of period is the one that intuits the time between 2 continuous approaches and we can also say that it is the fictitious orbital period of said object. This period differs from the first because the earth also revolves around the Sun.
- The Third: Draconitic Period
The Draconitic Period consists of the time it will take for the same object to pass twice through what is its ascending node, which is the point of its orbit that crosses the ecliptic orbit from the part of the southern hemisphere to the north. . This type of period is distinguished from the First Sidereal Period because the line of nodules generally varies slowly.
- The Fourth: Anomalistic Period
The fourth is the Anomalistic Period, which consists of the time it will take for the same object to pass twice through the area of its perihelion, which is the closest point to the Sun. This fourth period differs of the first Period due to the fact that the larger nodules also come to vary slowly.
- The Fifth: Tropical Period
The 5th is about the Tropical Period which consists of the time it will take for the same object to pass twice through the area of the just ascension of zero (2). This is usually slightly shorter than in the case of the first Sidereal Period because of the precession of the so-called equinoxes.
Geometric Parameters of the Orbit
The parameters required to determine an orbit are the so-called orbital elements, using a type of 2-mass models that obey Isaac Newton's laws of motion. So there are about 6 types of essential basic parameters, they are also known as the Keplerian elements, which honor the famous physicist Kepler and consist of the following:
- The First Parameter: Ascending Node Length = ( Ω )
- El Segundo Parameter: Pitch = ( i )
- The third Parameter: Argument from Perihelion = ( ω )
- The Fourth Parameter: Semi Major Axis = ( a )
- The Fifth Parameter: Eccentricity = ( e )
- The Sixth Parameter: Average Anomaly of the Epoch = ( Mo )
On the other hand, other orbital elements that are used in addition to the above are:
- True Anomaly = (v)
- Semi Minor Axis = (b)
- Linear Eccentricity = (∈)
- Eccentric Anomaly = (E)
- True Length = (l)
- Orbital Period = (T)
Types of Orbits
We are going to observe what are the types of orbits that exist in the Solar system, which are classified into 2 main ones that are:
- For its characteristics.
- For its Central Body.
By Characteristics
In the case of the classification by its characteristic there are about 14 types that are:
- Circle Orbit
- Ecliptic Orbit
- Elliptical Orbit
- Very Elliptical Orbit or Very Eccentric Orbit
- Graveyard Orbit
- Hohmann Transfer Orbit
- hyperbolic trajectory
- Inclined Orbit
- parabolic trajectory
- Capture Orbit
- Escape Orbit
- Semi-synchronous orbit
- Subsynchronous Orbit
- Synchronous Orbit
By Central Body
In the case of the 2nd classification, this is distributed in 3 classes of orbits that are:
- Earth's Orbits
- The Martian Orbits
- Lunar Orbits
- Solar Orbits
Earth Orbits
In the case of terrestrial orbits there are about 12 classes of orbits that are:
- Geocentric Orbit
- Geosynchronous Orbit
- Geostationary Orbit
- Geostationary Transfer Orbit
- Low Earth Orbit
- Medium Earth Orbit
- Molniya orbit
- Near Equatorial Orbit
- moon orbit
- polar orbit
- Heliosynchronous Orbit
- Tundra Orbit
Martian orbits
In the case of Martian orbits there are only 2 classes of orbits that are:
- Areosynchronous Orbit
- Aerostationary Orbit
lunar orbit
In the case of the Lunar Orbit there is only 1 which is the following:
- lunar orbit
In case you don't know what the Moon movements, You can discover it so that you can learn what the lunar orbit is like and how it is established.
Solar Orbit
In the case of the solar orbit, in the same way as the lunar orbit, there is only 1, which is:
- Heliocentric Orbit
