The first sign of failure during Tuesday’s doomed launch of an Orbital Sciences Corp. Antares rocket from Virginia came from the booster’s first stage about 15 seconds after liftoff, according to engineers studying what triggered a fiery mishap that destroyed a commercial cargo craft heading to the International Space Station. The rocket’s 13-foot-diameter first stage, containing tanks with more than 50,000 gallons of kerosene and liquid oxygen propellants, is made in Ukraine and powered by Soviet-era engines built in the 1970s for Russia’s moon program. “Evidence suggests the failure initiated in the first stage after which the vehicle lost its...