Why can't Earth orbit be parabolic?

Nautical Lexicon - Astronomy for Tides

A more detailed excursion into astronomy is required to understand the tides. To answer the question Why Stars circling each other and not just flying past each other, and how the stars orbit one another (namely in general Not on circular orbits), we have to examine the underlying physics more closely. Only then can we take a closer look at the astronomical constellation of the three stars that are essential for the tides (earth, sun and moon). In the case of the moon, we also look at everything to do with the phases of the moon, because these determine the main clock for the tides.

For an explanation of all the terms related to astronomy and tides, there is a glossarywhich can be kept open on a separate page for repeated reference.

Gravitation and centrifugal force

estirne run around each other permanently, because Gravity and Centrifugal force (the Key forces in astronomy) "work together" in a certain way. This is the only way to ensure a constant path. We look at it earth and moon.
  • The Gravitational force, also called mass attraction, is a force that generally occurs between two bodies. It increases as the distance decreases, and the greater the larger the masses involved, the greater it is.
    An important property is that there is gravitational force between two spherical Bodies "don't care" how big these balls are. The balls always attract each other as if their entire mass were in theirs Focus focused, regardless of their size and distance. The moon does not "see" whether it is orbiting an extensive earth or a tiny, but highly compressed mass point.
  • The Centrifugal force belongs to the so-called inertial forces. Every body in space "would like" to stay in a straight, uniform movement, i.e. to fly straight ahead. Is z. For example, the moon is forced into an orbit by the mass attraction of the earth, then it seems to want to fly away from this orbit into space with all its might. This outwardly directed apparent force is called centrifugal force. It is an apparent force because it only exists from the point of view of the earth. From the point of view of the moon, it is not driven by any force outwards, on the contrary, the attractive force keeps pulling it towards the earth and prevents its constant straight flight.
    The centrifugal force increases when the speed of the rotating body increases, it decreases when the distance increases, and is also greater, the greater the mass of the rotating body.

Since the stars have been patiently orbiting each other for a long time, the two forces must be in equilibrium, at least in the middle. What is decisive is what the orbit of the orbiting star looks like:

  • Exact circular path: gravity and centrifugal force are always exactly the same, the distance between the stars does not change. This would require a very specific orbital speed of the moon and a path exactly parallel to the earth's surface.
    Exact circular orbits are practically never available in space, they are a theoretical borderline case.
  • Elliptical orbit: The moon does not have the combination of orbital speed and orbit required for a circular path. This results in an elliptical orbit for the moon (and in most other cases) (more on ellipses below).
    Elliptical orbits are in the universe of Usually for circulating railways.
  • Parabolic and hyperbolic orbits: If the speed of a body in the gravitational field of another reaches or exceeds a certain amount (so-called escape speed), the ellipse becomes "infinitely long" and becomes a parabola or hyperbola, i. H. there is no more orbit, but only one after the other approaching from infinity, flying past each other with a path deflection and moving away into infinity (whereby the parabola is again a theoretical limit case for an exact speed value, the general case is that of the Hyperbole).

Orbits are created by the interaction of the body's own momentum (Centrifugal force) and those acting on him Gravity. Due to the centrifugal force, the circulating body would continue to move in a straight line from every point on its path due to its inertia (arrowsa). However, at the same time it is accelerated by gravity in the direction of the central body (b). The actual trajectory movement (red) results from both variables according to the parallelogram of forces.

Most celestial bodies describe elliptical orbits, but mostly with little eccentricity. B1 and B2 are the foci of the ellipse, B1 is also the place of the common center of gravity of the two celestial bodies. 1 denotes the point of greatest distance from the central body ("apo point"), 2 the point of closest distance ("peripoint"). On the descending Half of the path, the resulting path speed increases with the approach to the central body up to the peripoint, from then on it falls on the ascending Half of the track back to the apo point.

Celestial mechanics in principle possible Orbits of a body in the gravitational field of another with a relatively very large mass (central body):

  1. Circular path around the central body B1. Requires the lowest possible rotational speed.
  2. Elliptical orbit at a higher mean rotational speed than required for a circular path. The central body is in one focal point B1, the second focal point B2 the ellipse is empty.
  3. Parabolic orbit when the so-called escape speed is reached, which is necessary to escape from the gravitational field of the central body.
  4. Hyperbolic orbit if the escape speed is exceeded.

Elliptical orbits

It was the famous astronomer Kepler who showed that the general case of the orbit of the stars is not a circular orbit at all, but one elliptical orbit (the circle is only the special case of an ellipse with an eccentricity of zero). And it is even more precise that one star does not run around another, but rather both walk (on different ellipses) around the common focus. There is no reason to mentally prefer one star to the other, they are both equal. From the point of view of every star it is itself in one of the two so-called "focal points" of the ellipse, the other runs around the outside. The second focus is "empty". The ellipses shown above have a very strong so-called "eccentricity". This term describes the deviation of the ellipse from the circular shape; the greater the eccentricity, the more elongated the ellipse. With an eccentricity of zero you have a circle, and in fact most of the stars run around each other on very circular orbits (eccentricity close to zero). At the other end of the elliptical scale are z. B. the comets that run on extremely stretched orbits (high eccentricity) and yet always "find their way back" to earth (or just past it ...).

The picture opposite shows such a reciprocal orbit of two stars, one heavy, the other light. If the masses are so very different - as is the case with the earth-moon or sun-earth systems - then one speaks again in simplified terms of heavy resting central star and the light orbiting star, because the common center of gravity is then usually deep inside the heavier star, which only makes a very small orbit. But that's only an approximation, the common focus is never right in the center of the central star, and it never really rests. For many parts of the tidal discussion, however, the simplified picture is sufficient, only in special cases one does not get any further and has to discuss more precisely (with "real double circulation").

Another important result of Mr. Kepler's astronomical work was the realization that the orbiting star always gets faster when it approaches the central star on its ellipse. Because when you get closer, gravitational energy is released, which is converted into kinetic energy (there is no external energy available, everything stays in the system). When you remove it, it slows down again.

The constellation of earth, sun and moon

on the earth will the Sun within 365.24 days on an elliptical orbit (Ecliptic, almost circular, eccentricity only 1/30) at a mean distance of approx. 150 million km in the so-called ecliptical plane. The axis of rotation of the earth is inclined at 23 ° 30 'to the ecliptic, which gives us the change of the seasons. At the beginning of January the earth will reach its closest point to the sun, that Perihelion, and at the beginning of July the point furthest from the sun, that Aphelion. In addition to moving on its orbit, the earth rotates around its own axis. This rotation takes place from west to east, i.e. in same direction of rotation like the movement on its orbit (counterclockwise when looking at the North Pole).

The earth, for its part, is dated moon within one month (see glossary for definition) on a somewhat more elliptical orbit (eccentricity 1/18) at an average distance of 384,000 km. The plane of the lunar orbit is always inclined at 5 ° 9 'to the ecliptic. The closest point to the lunar orbit is called perigee, the furthest from the earth than apogee. During one orbit of the earth, the moon rotates exactly once around its own axis and therefore always shows the earth the same side (bound rotation, but this is irrelevant for the tides).

The fluctuating distances are practically uninteresting for the seasons or the appearance of the sun and moon, but the tides notice these slight fluctuations (or the effects can be more easily objectified in the tide tables).

The movement of the moon around the earth is, however, a lot more complicated because there are several Idiosyncrasies to join the lunar orbit:

  • The line connecting the points of intersection of the lunar orbit with the ecliptic (so-called. Lunar knot) is known as Knot line (drawn in green in the picture), and this line (and with it the whole ellipse) rotates in the plane of the ecliptic in a retrograde fashion with a period of 18.6 years (19 ° per year). Simply put, one can also say: The moon ellipse stumbles in the room like a juggler 's plate on a juggling stick. The rapid rotation of the plate is the orbit of the moon. The actual tumbling (i.e. the inclined position of the plate in space) is the turning back of the knot line. Of course, the plate wobbles much more slowly than it rotates. In the picture above this means: Just as the lunar ellipse is now directed from the bottom left to the top right, it is directed from the top left to the top right after 18.6 / 2 = 9.3 years and again after a further 9.3 years like now.
  • The line connecting perigee and apogee is called Vestibule line, and this line (the longer semiaxis of the lunar ellipse) rotates with a period of 8.9 years in the orbital plane of the moon. This means that perigee and apogee can sometimes lie in the ecliptical plane.

All of these perennial periods can be found in the tide tables. By the way: If the lunar orbit were exactly in the plane of the ecliptic, there would be one lunar and one solar eclipse each month. But since the moon is so crooked, this is seldom the case.

The phases of the moon

Since the moon is very close to the earth and has a surface that reflects sunlight well, it is the second brightest celestial body in the earthly company after the sun. The different positions of the earth, moon and sun to each other lead to the so-called Light phases of the moon. When the moon is new, the moon is between the earth and the sun (conjunction), opposite the sun when the moon is full (opposition). Between the new moon and the full moon there is a waxing moon, then a waning moon, with a half moon in the middle (1st and last quarter). A complete expiration of all light phases becomes Lunation called.

The moon rises and sets daily 24 / 29.53 hours later (approx. 50 min.), Because the moon continues on its orbit and the earth has to turn this 50 min. Longer to get the same position with respect to the moon again to reach. This leads to the following picture:

  • At a new moon, the moon rises in the morning and sets in the evening, parallel to the sun. Only then you don't see him.
  • The waxing moon rises during the day and sets during the night.
  • Only around a full moon does the moon rise "decently" in the evening and set in the morning, as a counterpart to the sun, so to speak.
  • The waning moon rises during the night and sets during the day.

The light phase of the moon is therefore a direct indicator of its position to the sun, and the position to the sun is decisive for the joint work of the two on the tides (half-monthly change of spring and nipp). For the daily Up and down the sea level, however, the phase of the moon does not matter at first, the relatively slow orbit of the moon in combination with the relatively fast rotation of the earth is sufficient for this. If you divide the above mentioned 24 hours 50 minutes by 2 (there are two "tidal mountains" on earth), you get exactly the mean tidal rhythm of 12 hours 25 minutes.

The apparently larger diameter of the moon, when it is just above the horizon when it rises and sets, is by the way an optical illusion for which the brain is responsible, which - like any good optical illusion - looks deceptively real, so that many people do not like to believe. However, it can easily be demonstrated objectively using photographs, including simple sensory physiological experiments (stereo images).