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I'm not quite familiar with space exploration vocabulary.

For the Apollo missions, the trajectory was figure-8-shaped. Thus, the direction of rotation of the Earth orbit was opposite to the one around the Moon.

When speaking about a mission to Mars, I imagine the spacecraft first describes a few Earth orbits, then performs trans-Mars trajectory injection, and then describes a few Mars orbits before beginning its mission.

  • for the initial orbits around earth, finding the direction of the orbit is quite easy as rockets are usually launched toward the East.
  • for the Mars orbit, if the orbit goes in the same direction, the trans-Mars trajectory put the spacecraft slightly further; if the direction is the opposite, the trans-Mars trajectory looks like the Apollo trans-lunar trajectory.

When launching a spacecraft to Mars, what is the direction of the Mars orbit?

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Either prograde or retrograde entry is easy to achieve; the choice of trans-Mars trajectory can put the spacecraft slightly ahead of Mars' position at arrival (yielding retrograde orbit) or slightly behind (prograde). A midcourse correction maneuver of about 1 m/s ∆v can make the difference.

For Apollo, the retrograde entry was, I think, needed for the free return option. Prograde approach would have sped the spacecraft up on flyby and made for a very long trip home.

However, unlike the moon, Mars has significant rotation speed. Beginning descent from a prograde orbit makes the relative surface speed for landing slightly lower, and if a returning Mars lander is to rendezvous in orbit like Apollo did, taking advantage of the free horizontal speed provided by Mars' rotation likewise calls for eastward ascent toward a mothership's prograde orbit.

As @MarkAdler notes, Viking 1 and 2 each consisted of an orbiter which released a lander after achieving orbit. Viking 1's orbit was prograde, but inclined at 39.3˚ (inclination of 0˚ means west-to-east, equatorial, prograde; inclination of 180˚ means east-to-west, equatorial, retrograde). Viking 2's orbit was more steeply inclined, at 55˚, and after the departure of the lander, it was moved into progressively more inclined orbits, 75˚ and 80˚, that is, orbiting almost north-south.

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