Orbit

As orbit or orbit the trajectory is called, on which an object moves periodically to another ( mass richer, central ) object. This railway has idealized the shape of an ellipse. As ever, forces from outside on such a two- body system, the web form, however, can not be mathematically exact ellipse. The circulation is rarely referred to as a revolution.

Orbit as a two-body problem

Pairs of orbiting objects are mainly:

• The earth around the sun; see Earth's orbit the Earth around the Earth-Moon center of gravity

• The moon around the earth (more precisely, the Earth-Moon center of gravity); see lunar orbit
• Satellite, Space Shuttle or similar spacecraft; see satellite orbit

Any elliptical orbit has a characteristic round trip time (especially of the central body ) and the mean orbital radius is derived from the mass of the objects. The circulation takes place in a path approximated plane containing the center of gravity of the two bodies. The vector comprises the rotating object from the central object is called the radius vector.

However, all paths are not closed or stable over time. Cometary orbits can be elongated as hyperbolas, and multiple stars or asteroids can get on unstable orbits. The circulation of all the stars around the galactic center is like a spiral rotation with a period of 100 to 300 million years ago. Relativistic disorders cause a Keplerian orbit is an idealized case. In fact, all trajectories are unstable, even the earth.

Planet orbital elements, double stars

The most accurate way to know the orbits of the planets in our solar system. Beginning of the 17th century Johannes Kepler recognized in the analysis of the orbit of Mars, that these orbits are ellipses (see Kepler laws). The same applies to all celestial bodies that move around the sun and no other forces ( such as the solar wind ) are exposed.

From the Newtonian law of gravitation, one can deduce that in each two-body system, the orbits are conic sections - that is, circles, ellipses, parabolas or hyperbolas.

They can be - with moving point masses in a vacuum - exactly described by six orbital elements.

The true orbits soft but from these ideal Kepler ellipses, because they are subject in principle, the gravity of all the other bodies of the system. As long as the bodies are far enough away from each other, the differences from the idealized conic sections remain minimal. These perturbations can be determined by the perturbation theory of celestial mechanics, which goes back to Carl Friedrich Gauss, and some of his contemporaries. They modeled the individual forces, and calculates, as the current passes oskulierend Kepler ellipse in the next ellipse.

In addition, causes any uneven mass distribution - such as the flattening of the rotating planet - a slightly inhomogeneous gravitational field; It should be noted in particular to changes in the orbits of their moons. Also, the general theory of relativity describes effects that are changing the orbits slightly.

For example, the planet Mercury is a small but quite measurable deviation from an elliptical path. It comes after a round no longer exactly on the starting point, but followed by a rotation of the line of apses rechtläufigen a rosette orbit. This may explain the perihelion Newtonian theory of gravitation, but not completely. To this end, the sun would have a slightly flattened shape. A sufficient explanation for the overall size of the perihelion of all affected planet provides the general theory of relativity.

Also follow binaries approached the kepler 's laws, if you understand their movement as two ellipses around the common center of gravity. Only in case of multiple systems or very tight star pairs specific methods of perturbation theory are required.

Even greater instability have the orbits of two closely orbiting each other neutron stars. Due to the effects of space-time relativity arises gravitational radiation, and neutron stars plunge ( after a long time ) with each other. Numerous X-ray sources in the sky can be explained in this way.

When physicists began around the turn of the century, to calculate the orbits of the electrons in the atom, they thought of a planetary system in miniature. The first models were Keplerian orbits of the electrons around the nucleus.

However, we soon realized that electrons orbiting around the nucleus, according to the Maxwell equations emit electromagnetic waves and fall into the nucleus because of the way the energy radiated in fractions of a second would have. This was one of the problems that eventually led to the development of quantum mechanics.

Descriptive explanation based on the conic section orbits

The mechanics of an orbit is often demonstrated by an illustrative thought experiment: It is believed to stand on a high tower or mountain and shoots a projectile from horizontal. The air resistance is allowed to simplify away for now. Even clearer is the thought experiment, if it is not organized on the earth, but on a small planet or moon, in the manner of the famous cover picture of the book The Little Prince or on the Martian moon Phobos (see also below).

• At low firing velocity the projectile flies along a parabolic trajectory and, after a short flight on the ground (lane A in the adjacent diagram).
• With greater launch speed is an elliptical arc from the parabola, and the projectile strikes again only on the earth's surface after it has flown over an appreciable part of the earth's circumference ( path B ).
• Achieved the launch velocity the first cosmic velocity is calculated from the elliptical arc is a full circle, one orbit. The projectile is therefore too fast to fall off again; they say that it'll be " around the Earth falls " (lane C ).
• If the launch speed further increased, from among an elliptical orbit, the launch point is the erdnächste point and remains (lane D).
• Exceeds the launch velocity, the second cosmic velocity, the ellipse opens to the hyperbola. It comes about not orbit the projectile leaves the sphere of influence of the Earth (lane E).

Near-surface orbits

As long as the track diameter approximately equal (more precisely, only slightly larger) than the diameter of the central body is assumed to be exactly spherical, it is called shallow or low orbits. When the web is also assumed to be circular, is obtained with equation of the weight force of the centrifugal force results for circulating speed (the first space velocity) and rotation time.

Newton's law of gravitation:

With weight = force = gravitational constant, = mass of the satellite, = mass of the central body, = radius of the central body

The weight of the satellite is obtained by using the average density of the central body ( instead of the ground) so that, as follows:

By equating the expression for the gravitational force results from the centripetal acceleration (in the case of the earth the acceleration of gravity ):

The gravitational force and the centrifugal force at web speed should () be in equilibrium:

Solving for by shortening of:

The circulation time is based on, so circumference / speed:

Apart from physical constants so the turnaround time depends only on the density of the central body, but not of its radius.

Specific values ​​for orbits around the Earth:

The value of about 90 minutes is known from low satellite orbits and of most manned orbiting space ships as a rule of thumb.

For comparison, the Mars moon Phobos:

Thus, although Phobos having a diameter of only about 25 km, the round trip time for a near-surface orbit with him is very similar to that of the earth (and even higher ). The web speed in this orbit, however, is only about 33 miles an hour. An astronaut on the surface of Phobos could therefore throw a ball loose from his hand into orbit.

The fact that the turnaround time for a near-surface orbit is independent of the radius of the central body, can thus be generalized: If a central body has a similar mean density as the Earth, so it is roughly speaking " stony " structured, then there is the orbital period as the Earth in the order of 90 minutes to see if this is an asteroid or an exo- planets around a completely different planet.

Earth orbits

In orbit, the gravitational force of the earth and the centrifugal lift in the local co-moving coordinate system to another. Therefore there is on board a spacecraft that is in orbit, gravity (see also microgravity ). Most space flights are housed in low orbits (some 100 km) around the Earth instead (eg space shuttle missions). Physically applies requires that the line speed according to the distance to the earth is increasing or decreasing. Of particular importance is the geostationary orbit - in around 35,800 km altitude and without orbital inclination to the equatorial plane. Satellites in orbit are such a relatively quiet surface of the earth, what for communication satellites and weather satellites is necessary in particular.