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The sign which accompanied the Sputnik 1 replica and the Explorer 1 backup.

It read

SPUTNIK 1 (replica) and EXPLORER 1 (backup)
First Artificial Satellites

Hanging above are copies of the first artificial satellites to orbit the Earth. Sputnik 1 was launched by the Soviet Union on October 4, 1957, and Explorer 1 was launched by the United States on January 31, 1958.

Sputnik 1 operated for 22 days, providing information about internal and external temperatures and atmospheric and electron densities at high altitudes. Explorer 1 operated for 105 days, transmitting data on micrometeoroids, cosmic radiation, and internal and external temperatures. Data obtained from Explorer 1 and Explorer 3 (launched in March 1958) revealed the existence of the Van Allen radiation belts. This was the first major scientific discovery of the space age.

Sputnik 1 on loan from the Science in Russia Exhibition of National Achievement

Explorer 1 transferred from the Jet Propulsion Laboratory and the National Aeronautics and Space Administration

Explorer 1
Length (with rocket):	203 cm (80 in)
Diameter:	15 cm (6 in)
Weight:	13.9 kg (30.7 lb)
Launch vehicle:	Jupiter-C (Juno I)

Sputnik 1
Diameter:	58 cm (23 in)
Weight:	83.6 kg (184 lb)
Launch vehicle:	A 1 Sputnik

The Explorer 1 backup appears to be NASM catalog #A19620034000. The Sputnik 1 replica is on loan; it does not appear to have a NASM catalog number, but NASM does have a page about it.