Image: Screen shot from video footage of NASA's STS-75 Shuttle Mission. The mission number is: TSS-1R; USMP-3.

What you are seeing is the Tethered Satellite System (TSS-1R) with Columbia's Infra Red camera pointed at the satellite. The shuttle is approximately 70 nautical miles away from the satellite. The tether of the satellite is approximately 12.8 miles (20.6 kilometers) when fully extended with the satellite at the top of the rod in the image.

The object behind the tether, the circle object, is estimated at 2 to 5 nautical miles in diameter when factoring in the tethers length and distance the shuttle is away from it.

Sources: exoticworldart.com^{[dead link]}
Youtube. Contains footage from still images at source below.
Zoomed out still images of screen shots (NASA)^{[dead link]}.

Why From NASA? The YouTube video clearly states the Mission STS-75. Also later in the video you hear communication between the astronauts and Mission Control who clearly acknowledge to the astronauts and vice versa, that they are "Houston."

	This file is in the public domain in the United States because it was solely created by NASA. NASA copyright policy states that "NASA material is not protected by copyright unless noted". (See Template:PD-USGov, NASA copyright policy page or JPL Image Use Policy.)
	Warnings: Use of NASA logos, insignia and emblems is restricted per U.S. law 14 CFR 1221. The NASA website hosts a large number of images from the Soviet/Russian space agency, and other non-American space agencies. These are not necessarily in the public domain. Materials based on Hubble Space Telescope data may be copyrighted if they are not explicitly produced by the STScI.[1] See also {{PD-Hubble}} and {{Cc-Hubble}}. The SOHO (ESA & NASA) joint project implies that all materials created by its probe are copyrighted and require permission for commercial non-educational use. [2] Images featured on the Astronomy Picture of the Day (APOD) web site may be copyrighted. [3] The National Space Science Data Center (NSSDC) site has been known to host copyrighted content. Its photo gallery FAQ states that all of the images in the photo gallery are in the public domain "Unless otherwise noted."