The Final Days of Mir

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Glossary

apogee
The point on a satellite's elliptical orbit farthest from the earth. The apogee altitude ha of a satellite's orbit is equal to the distance from the center of the earth to apogee, ra, minus the mean equatorial radius of the earth, RE= 3443.92 nmi= 6378.145 km. Further, it should be noted that the sum of the apogee and perigee distances of an orbit are equal to twice its semi-major axis a. That is,
ra + rp = 2a.

argument of perigee (w)
One of the six classical orbital elements. For a typical satellite's orbit, the argument of perigee w is measured from the ascending side of the line of nodes to the perigee direction of the orbit. The perigee direction/vector is directed from the earth's center to the perigee point of the orbit. The argument of perigee w is shown in this figure of the classical orbital elements.

center of mass (cm)
The average position of a collection of fragments, weighted by their masses. For example, the center of mass rcm of two fragments with masses m1 and m2 and positions r1 and r2, respectively, is given by
rcm= (m1r1+m 2r2)/(m1 + m2).

classical orbital elements
Six independent quantities that are used to specify a satellite's position as a function of time t. The six classical orbit elements for an Earth orbiting satellite include

  1. semi-major axis (a)
  2. eccentricity (e)
  3. inclination (i)
  4. right angle of the ascending node (RAAN)
  5. argument of perigee (w)
  6. true anomaly at time t (v)

The semi-major axis a and eccentricity e define the size and shape of the orbit, respectively. The inclination i, right angle of the ascending node RAAN, and argument of perigee w, are angles that define the orientation of the orbit with respect to the Earth-Centered-Inertial (ECI) coordinate frame. The final element, the true anomaly v, gives the satellite's position in its orbit at time t. The six classical orbital elements are shown in this figure.

eccentricity (e)
One of the six classical orbital elements. For a particular satellite's orbit, the eccentricity e is a constant that defines the orbit's shape. For a circular orbit, e= 0. The overwhelming majority of satellite orbits, however, are elliptical in shape with 0 < e < 1.

ground track
The path traced out along the earth's surface by a satellite's subpoint, the point on the surface where the satellite is directly overhead at a given time. The ground track of a Low-Earth-Orbit (LEO) satellite appears sinusoidal on flat earth maps and is confined between latitudes equal to -i and +i, where i is the inclination of the satellite's orbit. Satellite ground tracks drift westward over the earth's surface due to the earth's rotation. For LEO satellites, the westward drift rate is approximately 20 degrees of longitude with each orbit.

This Mir animation shows the generation and drift of Mir's ground track (yellow curve) as the station travels along its orbit (green curve) and the earth rotates. The viewpoint for this animation is fixed in the Earth-Centered-Inertial (ECI) frame. Thus, while the earth rotates and Mir moves along its orbit, the earth's center and the orbit remain fixed.

This ground track figure shows the ground track of a LEO satellite with i=51.65 degrees, the same as Mir's, on a flat earth map. The ground track is plotted for successive orbits of the satellite, showing its westward drift due to the earth's rotation.

inclination (i)
One of the six classical orbital elements. For a particular satellite's orbit, the inclination i is a constant angle defining the tilt of the orbit's plane with respect to the earth's equatorial plane. It is shown in this figure of the classical orbital elements.

line of nodes
The line of nodes connects the two points where a typical satellite's orbit crosses the earth's equatorial plane. At the ascending node, the satellite traverses the equatorial plane from south to north. At the descending node, it crosses the plane from north to south. The line of nodes is shown in this figure of the classical orbital elements.

perigee
The point on a satellite's elliptical orbit closest to the earth. The perigee altitude hp of a satellite's orbit is equal to the distance from the center of the earth to perigee, rp, minus the mean equatorial radius of the earth, RE= 3443.92 nmi= 6378.145 km. Further, it should be noted that the sum of the apogee and perigee distances of an orbit are equal to twice its semi-major axis a. That is,
ra + rp = 2a.

Progress M
This automated spacecraft transports food, water, and propellant to Mir and typically provides the station with reboost when its orbit becomes too low. The Progress M spacecraft is launched to Mir aboard a 3-stage Soyuz rocket. It usually docks at Mir's Kvant 1 module. When its fuel is nearly exhausted, the spacecraft, carrying garbage, undocks and is eventually deorbited into the Pacific Ocean.

Currently, the Progress M1-5 spacecraft is docked to the vacant Mir. Instead of carrying food, water, and other equipment for visiting cosmonauts, this modified Progress spacecraft carries additional fuel, 2.5 times more than a Progress M. Progress M1-5 will provide the three burns for Mir's controlled reentry/deorbit.

Further information on the Progress M spacecraft is provided by

right angle of the ascending node (RAAN)
One of the six classical orbital elements. For a typical satellite orbit, RAAN is the angle measured in the earth's equatorial plane from the XECI-axis of the Earth-Centered-Inertial (ECI) frame to the ascending side of the line of nodes of the satellite's orbit. In this figure of the classical orbital elements, RAAN is designated by the capital Greek letter Omega.

semi-major axis (a)
One of the six classical orbital elements. For a particular satellite's orbit, the semi-major axis a is a constant that defines the orbit's size. For an Earth orbit, it is half the distance between apogee and perigee. It is shown in this figure of the classical orbital elements.

Soyuz SL-4 launch vehicle
The 3-stage Soyuz SL-4 launch vehicle is used to launch both Soyuz and Progress spacecraft to Mir and the ISS. With over 1500 successful launches, it is regarded as the most reliable launch vehicle in the world. More information on the SL-4 is provided by Mark Wade's Encyclopedia Astronautica.

Soyuz TM spacecraft
The Soyuz TM spacecraft is used to transport cosmonauts to Mir and the International Space Station (ISS). Soyuz carries 2 or 3 cosmonauts, depending on the mission. It docks to Mir at the axial docking port of the Mir Core module's multiple docking adapter.

When it is time for the cosmonauts to return to earth, the Soyuz TM undocks from Mir (or the ISS) and executes deorbiting maneuvers. The spacecraft's reentry capsule carrying the returning cosmonauts reenters Earth's atmosphere and lands in Russia using parachutes and solid rockets to cushion the capsule's impact.

Further information on the Soyuz TM spacecraft is provided by




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