The Final Days of Mir

Uncontrolled Reentry

Unless Mir is continually reboosted or TsUP (Russian Mission Control) executes a controlled reentry, an uncontrolled reentry of the station will occur. In contrast to a controlled reentry, for an uncontrolled reentry, the impact time and location of the station’s debris footprint will be unpredictable. Time of Reentry Objects reenter naturally/uncontrolled when their orbits decay under the influence of aerodynamic drag. The drag force in turn depends on the atmosphere’s density at high altitudes. The density varies due to variations in the near-earth space weather, including both variable solar activity and earth magnetic field intensity. Since the drag force on an object will vary as density varies, it is impossible to determine exactly when reentry will occur for an uncontrolled object. However, its reentry time can be estimated with suitable orbit propagation tools using current space tracking data and space weather forecasts. As a rule of thumb, the error in predicting the time of an object’s reentry is estimated to be approximately 10% of the time remaining to reentry, meaning that if reentry is predicted to occur in 10 hours, it could actually occur sometime between 9 and 11 hours. Uncontrolled reentry predictions for Mir have been made over the last year by CORDS. It is seen from the more recent predictions that if the station is not deorbited via a controlled reentry, it will reenter Earth’s atmosphere in late March/early April 2001. Footprint Location The uncertainty in the time of reentry translates directly to an uncertainty in the location of where an uncontrolled object’s reentry debris will impact the ground in a debris footprint. Since it takes a Low-Earth-Orbit (LEO) object approximately 90 minutes to orbit once around the earth, an uncertainty of plus or minus one hour in the time of reentry means that reentry could occur anywhere along a segment of the object’s ground track over 27,000 nmi (50,000 km) long. Further complicating matters, the ground track defining the possible reentry points and associated debris footprint locations will change with time due to the earth’s rotation. Since an object’s orbit is essentially fixed in space, the ground track of an orbiting object will move from east to west with respect to the rotating earth as seen in this animation for Mir's orbit. In the animation, Mir's orbit, which is fixed in the Earth-Centered-Inertial (ECI) coordinate frame, is green while the ground track it generates as it orbits around the rotating earth is yellow. The drift rate of the object’s ground track is given by the product of the earth’s rotation rate, 15.04 degrees/hour, and the object’s orbital period, the time it takes the object to complete one orbit. For a low altitude orbit (LEO), the drift rate of the object’s ground track is approximately 20 degrees per orbit. This westward ground track drift is shown in this ground track figure, which shows successive ground tracks of a LEO satellite with inclination i= 51.65 degrees, the same as Mir’s. From the ground track figure, it is apparent that the highest latitude the orbiting object reaches is equal to the inclination of its orbit, i= 51.65 degrees. Correspondingly, its lowest latitude is equal to -i= -51.65. To summarize, the ground track and hence, the possible reentry points and debris footprint locations of an uncontrolled, reentering object will be confined between latitudes -i and +i. Probability of Impact Taking the above into account, two things become clear: (1) the locations of an uncontrolled object’s reentry point and debris footprint can be anywhere between latitudes -i and +i and (2) they cannot be predicted with any certainty for times in excess of a few hours before reentry is predicted to occur. Although a good estimate of the location of the center-of-mass (cm) of an object’s debris footprint is impossible to make in the long term, the probability that it will be at a specific latitude and longitude can be calculated from orbital mechanics. The probability of impact for an uncontrolled reentry of Mir is shown in this probability figure. In the figure, the redder a point is on the world map, the greater the probability for impact of the cm of Mir's footprint at that latitude and longitude in the event of an uncontrolled reentry of the station from a circular orbit.

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