DARMSTADT, Germany—In what promises to be a nail-biting event worthy of a Hollywood script, rocket scientists Wednesday will attempt the challenging task of trying to land a probe on the surface of a comet.

After a decadelong trek through the solar system, the European Space Agency’s spacecraft Rosetta made a historic rendezvous with a comet known as 67P/Churyumov-Gerasimenko in August. The craft is now in orbit just 6 miles above the comet’s surface. If all goes well, a small probe called Philae will descend from the mother...