After a trans-Mars transfer, what is the direction of the rotation of the orbit around Mars?

Question

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?

Answer 1

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.