How to determine the reflectivity of an asteroid

How do you describe the path of a celestial body?

Celestial mechanics deals with the movement of celestial bodies (stars, planets, asteroids, comets, moons, ...). Of course, you need a coordinate system for this.

For example, if we look at objects in our solar system, then that would be heliocentric coordinates the easiest choice. One simply uses a “normal” three-dimensional Cartesian coordinate system with the sun at the origin. An object that moves around the sun then has 3 position coordinates (x, y, z) and three speed coordinates (vx, vy, vz) which indicate how fast the object is moving in a certain direction. The position of a celestial body is clearly determined by these 6 coordinates.

For certain applications, however, the heliocentric coordinates are somewhat impractical. What is often of interest in celestial mechanics is not the movement of an object per se, but that Change of course of the celestial body. According to Kepler's first law, planets and asteroids move in elliptical orbits around the sun. Since the sun not only exerts a gravitational force on the planets, but the planets also influence each other, these ellipses change over time!

The orbital ellipses of the planets usually get bigger and smaller, more elliptical and less elliptical, they rotate back and forth in space ... If the planets (or asteroids, comets, ...) are on stable orbits, then these fluctuations can only be found within certain limits take place. With objects on unstable / chaotic orbits, these fluctuations get bigger and bigger until the celestial body falls into the sun, flies out of the solar system or collides with another object. In order to find out whether objects are on stable or unstable orbits, celestial mechanics do not examine the changes in the heliocentric coordinates (x, y, z, vx, vy, vz) but the changes in Track elements.

These orbital elements are a coordinate system based on the properties of the orbit of a celestial body. They are made up of 6 different sizes:

  • The major semi-axis (a) the train. The path of an object around the sun is described by an ellipse. The shape of an ellipse is defined by the small semi-axis (green) and large semi-axis (red):
  • The Eccentricity (e) the orbit ellipse. The more eccentric an ellipse, the greater the deviation from the shape of a circle. The eccentricity is specified with a number between 0 and 1. A circle would have an eccentricity of e = 0; with increasing eccentricity the ellipse becomes more and more elongated until finally at e = 1 the ellipse becomes a line.

Large semi-axis and eccentricity define the shape of the ellipse. However, this orbit ellipse now also has a certain position in three-dimensional space. Therefore 3 more parameters are needed to define how the ellipse is oriented in space:

  • The Inclination (i) the train. The inclination or orbital inclination indicates how strong the orbit ellipse is compared to the Ecliptic is inclined. The ecliptic is the reference plane in the solar system and corresponds to the (middle) orbit plane of the earth. An orbit with e.g. an inclination of i = 5 ° is inclined by 5 ° in relation to the earth's orbit.
  • The Length of the ascending node (Ω). The point at which the orbit of a celestial body penetrates the ecliptic from north to south is called descending node(). The point at which the orbit crosses the ecliptic from south to north is called ascending node ()1. The angle between the connecting line Sun-Ascending Node and the connecting line Sun spring equinox is the Length of the ascending node. The spring equinox () is a fixed “zero point” that serves as a reference point for astronomical coordinates. It is the point in the sky where the sun is exactly at the beginning of astronomical spring).
  • The Argument of the perihelion (ω). The argument of the perihelion is the angle between the connecting line Sun perihelion (the closest point to the sun) and the connecting line Sun ascending knot.

These three parameters (i, Ω, ω) define the position of the ellipse in space. The orbital ellipse of the celestial body is now clearly defined by the major semi-axis, eccentricity, inclination, length of the ascending node and the argument of the perihelion. But there is still another parameter missing about the Position of the celestial body set on this path. There are several possibilities for that; the most common is

Celestial mechanics deals with the movement of celestial bodies (stars, planets, asteroids, comets, moons, ...). Of course, you need a coordinate system for this. For example, if we look at objects in our solar system, then ...