Naked-Eye Mir Visibility Data From Selected Cities 9-15 March 2001


The OSF Orbital Visibility schedules at present cover 3,409 locations worldwide. To determine if your data for your city is available click on the "List of Cities Served" link below and scroll through the list (alphabetized by city name). If you do not find your city/location on the list, for the time being, we ask that you to select the nearest listed entry.



Please note that the times reported in the U.S. Cities tables are in the a.m./p.m. format familiar to most people in the United States. The times reported in the Non-U.S. Cities tables are in 24-hour format most commonly in use elsewhere.

U. S.
City Initials:
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Non-U.S.
City Initials:
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

List of Cities Served



Click on the appropriate line below if your browser is unable to display HTML3 Tables:

NOTES: Included are only major cities currently in the range of visibility, with maximum spacecraft elevations over the horizon larger than 10 degrees. The data are also valid for suburban regions around these cities, with slight changes in Direction of Movement and Max. Elevation.

 


Mir Altitude Update

There are two altitude charts provided below. The first chart shows the altitude history in 7-day increments for the most recent 525 days. The second chart displays the altitude history in 14-day increments and spans the entire time period beginning with Day 1.

 

Mir Altitude History -- 7-day Increments

Apogee -- Mean Altitude -- Perigee

 

Mir Altitude History -- 14-day Increments

Apogee -- Mean Altitude -- Perigee



Two-Line Keplerian Orbital Elements

Jesco von Puttkamer

The "Two-Line Elements" (or TLE) format generally used by PC-based satellite tracking programs contain all necessary numerical data describing the orbit (position, flightpath and motion) of a satellite such as Mir or the coming ISS, as well as its exact position along that orbit at a specific reference time (the "epoch"). This format dates back to the days when NORAD (North American Aerospace Defense Command, today US Space Command) still used IBM punched cards on its computers. Thus, because each card could only carry one line, today's Two-Line Elements were "Two-Card Elements" back then. TLE files are always in ASCII format, and when they are copied or moved around with "Clip and Paste" commands, non-proportional fonts (like Courier) must be used to preserve the exact positions of the digits and their spacings.

To completely describe not only the size and shape of an orbit but also its orientation around its central body (for Mir, that would be the Earth, of course), only five independent quantities called "orbital elements" are required. The object in question can be anywhere on that closed path as long as its position at a specified time is not given. Thus, a sixth element is required to pinpoint the satellite's position. From this position, the satellite tracking program then calculates "forward", in effect predicting the object's locations at any desired future time. The real world is not ideal, however, and therefore all orbits are influenced by various disturbances called "orbital perturbations"; in the case of Mir and the Space Shuttle, such "perturbations" might include applications of thrust from the craftsí maneuvering jets as well as naturally-occurring conditions.

To fully include these perturbations in the predictions would be impractical for PC-based calculation routines. Thus, with time, their influences pile up, causing increasingly noticeable deviations of the real orbital path from the predicted one. To take care of that, predictions need to be "refreshed" periodically with up-to-date TLEs based on the most recent radar tracking measurements of the responsible organizations such as US Space Command.

The element data used by our TLE's to describe the orbit size and shape are: the Mean Motion (2nd line position 53-63) and the Eccentricity (2nd line pos. 27-33). Mean Motion is used because, according to Kepler, an object in an elliptical orbit moves at periodically varying speed, depending on its distance from the mass center at its focal point. From the Mean Motion (in degrees per second) we can calculate the orbital period and, with the Earth's gravitational constant, the semi-major axis of the elliptic orbit (which could, in rare cases, reduce to a perfect circular orbit). With the Eccentricity, the apogee (farthest point) and perigee (closest point) of the ellipse can be determined and, with the known Earth's radius, their altitudes above Earth and also the mean altitude. (When not referring specifically to Earth, we are using "apoapsis" and "periapsis", or "apofocus" and "perifocus" for these characteristic points of an elliptic orbit).

For determining the orientation of the orbit about the Earth, the TLE also contains the Inclination (2nd line pos. 09-16) of the orbit plane in degrees measured from the Earth's equatorial plane, the Right Ascension of the Ascending Node (RAAN, 2nd line pos.18-25), and the Argument of Perigee (2nd line pos. 35-42). The ascending node is the point where Mir crosses the Earth's equatorial plane in the northerly direction. (The opposite point is the descending node, and the line connecting both points is called the Line of Nodes). RAAN, measured in degrees, is the angular distance of the ascending node from the line pointing to the Vernal Equinox on the ecliptic (the point where the Sun crosses the celestial equator in spring around March 21). Argument of Perigee defines the orientation of the elliptical orbit's semi-major axis: measured in Mir's orbit plane in the direction of motion, it is the angle between its ascending node and its perigee.

The sixth element is the Mean Anomaly (2nd line pos. 44-51), which is used for calculating the satellite's exact position at a particular time ("epoch") from perigee.

The first line of the TLE file, under the name, contains the US Space Command-assigned Catalog Number of the object (often called the "NORAD Number"), the Epoch Year and Epoch Date (pos. 19-32) and other identifiers of interest. In line 2, pos. 64-86 are reserved for the number of revolutions accumulated at epoch.

The two-line elements are not the only factors necessary to predict the orbit of the Mir Space Station for the purposes of these visibility tables. Many additional factors must be taken into account to ensure the reasonable precision of these predictions over the dates covered by the tables.

Following are the Two-Line Elements and Translated Orbital Data for the Mir Space Station as of 3/8/01 9:17am EST:

MIR
1 16609U 86017A   01067.59524234  .00333173  63704-4  40049-3 0  6577
2 16609  51.6404 329.1783 0009514 105.4217 254.7773 16.07629756860947


Name...................................MIR
NORAD ID#..............................16609
Epoch Year.............................1
Epoch Day..............................67.59525   3/8/01  9:17am EST
Mean Altitude (km).....................253.306
Period (min)...........................89.57
Apogee (km)............................259.615
Perigee (km)...........................246.997
Inclination (degrees)..................51.6404
Right Ascension of Ascending
  Node (RAAN, degrees).................329.1783
Eccentricity...........................0.0009514
Argument of Perigee (degrees)..........105.4217
Mean Anomaly (degrees).................254.7773
Mean Motion (revs. per day)............16.0763
Decay Rate.............................0.00333173
Epoch Revolution.......................86094
Element Set#...........................657
Visible up to Latitude (degrees).......67.5


                                                  3/8/01 11:46 AM EST



NOTES: Included are only major cities currently in the range of visibility, with maximum spacecraft elevations over the horizon larger than 10 degrees. The data are also valid for suburban regions around these cities, with slight changes in Direction of Movement and Max. Elevation.

Pickup Time: The local time of day that the spacecraft becomes visible on the horizon.

Direction of Movement: The spacecraft will appear in the first direction and travel across the sky, rising to the "Maximum Elevation" and disappearing at the horizon in the second direction shown. These compass directions are understood to embrace an angular field of 22.5 degrees each, with their symbols defined as follows:

N:  North    NW:  Northwest    NNW:  North-Northwest    SSE:  South-Southeast
E:  East     SW:  Southwest    WNW:  West-Northwest     ESE:  East-Southeast
S:  South    NE:  Northeast    WSW:  West-Southwest     ENE:  East-Northeast
W:  West     SE:  Southeast    SSW:  South-Southwest    NNE:  North-Northeast

Responsible NASA Official:
Jesco von Puttkamer
Curator:
SAIC Information Services

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