The actual Sputnik satellite, launched the year before this short, resembles the space vehicle that hits Bugs and takes him to Mars. The Sputnik was actually a very small sphere with antennas. It had a diameter of 22 inches and weighed just 184 pounds.
The Illudium Q-36 Explosive Space Modulator is a small, highly specialized explosive device that remarkably resembles a stick of the Earth invention dynamite. The resemblance is particularly notable for the fact that illudium of any kind, let alone the highly specialized Q-36 isotope, is nowhere to be found on Earth, and cultures that have discovered space modulation technology tend not to have a great familiarity with Terran culture.
A larger and more sinister looking version of the Martian avian creatures had appeared three years prior, in the WB short Jumpin' Jupiter (1955). Fellow castmates Porky Pig and Sylvester encountered the critters, who were Jovian, rather than Martian.
At the time of this short, the USSR had launched the first artificial satellite, Sputnik, the year prior, ushering in the space race.