The pin back button measures 7/8'' wide. It is in excellent condition as pictured. Most of the tiny spots on it in the picture are only dust and fuzz. Below here, for reference, is some additional historic information on the Sputnik Satellite:
From Wikipedia, the free encyclopedia
Operator: Soviet Union
Major contractors: OKB-1, Soviet Ministry of Radiotechnical Industry
Mission type: Atmospheric studies
Satellite of: Earth
Launch date: 19:28:34, October 4, 1957 (UTC) (22:28:34 MSK)
Launch vehicle: Sputnik rocket
Mission duration: 3 months
Orbital decay: 4 January 1958
Apoapsis: 7,310 km (4,540 mi) from centre, 939 km (583 mi) from surface
Periapsis: 6,586 km (4,092 mi) from centre, 215 km (134 mi) from surface
Orbital period: 96.2 minutes
Sputnik 1 was the first artificial satellite to be put into Earth's orbit. It was launched into an elliptical low Earth orbit by the Soviet Union on 4 October 1957. The unanticipated announcement of Sputnik 1's success precipitated the Sputnik crisis in the United States and ignited the Space Race, a part of the larger Cold War. The launch ushered in new political, military, technological, and scientific developments. While the Sputnik launch was a single event, it marked the start of the Space Age.
Apart from its value as a technological first, Sputnik also helped to identify the upper atmospheric layer's density, through measuring the satellite's orbital changes. It also provided data on radio signal distribution in the ionosphere. Pressurized nitrogen in the satellite's body provided the first opportunity for meteoroid detection. If a meteoroid penetrated the satellite's outer hull, it would be detected by the temperature data sent back to Earth.
Sputnik 1 was launched during the International Geophysical Year from Site No.1/5, at the 5th Tyuratam range, in Kazakh SSR (now at the Baikonur Cosmodrome). The satellite travelled at 29,000 kilometers (18,000 mi) per hour, taking 96.2 minutes to complete an orbit, and emitted radio signals at 20.005 and 40.002 MHz which were monitored by amateur radio operators throughout the world. The signals continued for 22 days until the transmitter batteries ran out on 26 October 1957. Sputnik 1 burned up on 4 January 1958, as it fell from orbit upon reentering Earth's atmosphere, after travelling about 60 million km (37 million miles) and spending 3 months in orbit.