This explanation is excerpted from Shuttle-Mir: The U.S. and Russia Share History's Highest Stage.
On June 25, 1997, Vasily Tsibliev took remote control of the Progress resupply vehicle and fired its rockets to propel the craft toward the Mir Space Station. In ways, the procedure was similar to playing a video arcade game. Tsibliev had to virtually "fly" the Progress from onboard Mir while he watched a video screen that showed an image from a camera onboard the Progress.
The Progress left its parking orbit and began moving rapidly toward Mir. But, on the video screen "it was difficult to make out the station," according to Tsibliev. The Mir complex "looked very similar to the clouds below it." Tsiblievs deficient perspective had a further limitation. According to Mike Foale, "What Vasily was seeing on his screen was an image that didnt change in size very fast. Thats the nature of using a TV screen to judge your speed and your distance. He couldnt determine accurately from the image that the speed was too high."
By the time Tsibliev could judge the speed, the Progress was already traveling too fast. He fired the braking rockets, but it was too late. Aleksandr Lazutkin finally espied the Progress, and he realized the danger. "Michael, get in the escape ship!" he told Foale. Lazutkin later described the onrushing Progress as looking "full of menace, like a shark." He said, "I watched this black body covered in spots sliding past below me. I looked closer, and at that point there was a great thump and the whole station shook."
The Progress collided with a solar array on the Spektr module. Then, the spacecraft hit Spektr itself, punched a hole in a solar panel, buckled a radiator, and breached the integrity of Spektrs hull.
The collision had knocked Mir into a spin; and the power outage had shut down the gyrodynes so that the spin now went uncontrolled. To stop the spin and face the arrays toward the Sun, the crew needed to know the spin rate of Mir. However, the computer and other instruments were out of operation. So, in the dark and in the silence, Foale went to the windows in the airlock and held his thumb up to the field of stars. Combining a sailors technique with a scientists knowledge of physics, Foale estimated the spin rate of the space station. Then, he and Lazutkin radioed the estimates down to the Moscow Control Center. The ground controllers fired Mirs engines, and that stopped the spincertainly not perfectly, and in no way permanently; but it showed that it could be done.
The following are computer generated animations of the collision and the spin that followed and are provided by Analytical Graphics, Inc.
Progress Collision with Mir - MPEG (13 M) (No Audio)
Mir/Progress