Scientists calculated that the asteroid, traveling at 46,000 miles an
hour, is on an elliptical path that orbits the Sun once a year and regularly brings it back toward Earth.
(A) hour, is on an elliptical path that orbits the Sun once a year and regularly brings it -> "it" refers back to "Sun" or "the asteroid". Pronoun error. Incorrect.
(B) hour, is orbiting the Sun once a year on an elliptical path that regularly brings it -> Now, "it" refers back to "the asteroid" which makes sense. Further, Orbiting is taking about "the asteroid". Meaning wise, progressive tense makes sense too. Let's keep it. If we get a better one, we can drop the option.
(C) hour, once a year orbits the Sun, regularly bringing it on an elliptical path -> again we have "it" refers back to "sun". Incorrect.
(D) hour and orbiting the Sun once a year on an elliptical path, regularly bringing it -> we don't have verb here. Incorrect.
(E) hour, orbits the Sun on an elliptical path once a year and that regularly brings it -> It is the closest to correct option. There is a small issue, "and" conjunction is not required. Incorrect.
So, I think B.