The Hwasong-12 is an intermediate-range ballistic missile that the North says is designed to carry a large nuclear warhead. After the launch on Tuesday, the Japanese government sent a text alert to its people, advising them to take protective cover in case the test went wrong.

Japan said it did not try to shoot the missile down because it did not detect a threat to its territory. But analysts said the test nevertheless underlined some uncomfortable questions about the possibility of defending against such missiles.

The allies could do little more than track the missile Tuesday as it arched over Hokkaido and splashed into the northern Pacific. Analysts said Japan could have tried to shoot it down if its Aegis destroyers, which are armed with SM3 Block I interceptor missiles, happened to be in waters between North Korea and Japan. But because the SM3 is slower than the Hwasong-12, they would have had to make the attempt before the missile passed over the ships.

And one analyst noted that Japan could have been caught off guard entirely had the destroyers been elsewhere — for example, if Japan had ordered them south in response to North Korea’s threat to fire missiles into the waters around Guam.

“After distracting attention toward Guam, North Korea fired the missile over Japan,” said Shin Jong-woo, a defense analyst at Korea Defense Forum, a Seoul-based network of military experts. “By doing so, it reduced the chance of its missile being shot down, and at the same time demonstrated its ability to hit a target as far away as Guam without actually launching the missile in its direction.”