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TeamIndus spacecraft lunar orbits explained

Designing lunar orbits to efficiently land on the Moon

TeamIndus Z-01 spacecraft landing site: Near Annegrit crater, in the vast lava plains of Mare Imbrium. Source: LROC Quickmap

Part A: Constraints on lunar orbits

1. Sun illumination

Landing phase of the mission i.e. ‘lunar descent’ begins after the dawn terminator has crossed the landing site. Moon image source: Wikipedia

2. Time spent in lunar orbit

The time difference between ‘lunar phase at orbital capture’ and ‘dawn at the landing site’ determines the stay time in lunar orbit.

3. Inclination and time of launch

Part B: Evolution of lunar orbits

1. Approaching the Moon

Lunar Transfer Trajectory (LTT) to the Moon. Sources for Earth & Moon images: Pixabay, Wikipedia.

2. Getting captured in lunar orbit

Note: Ideally, the engine should fire at the exact point where the apoapsis of the orbit lies and deliver the required delta-V within an instant. This is however only possible with an ideal engine.As such, in practice the engine burn starts a bit before the ideal point and ends a bit after it. This engine burn (tracing an arc) averages out about the ideal point. This is called a center-burn and all mentions of main engine burns below imply the same. 
Getting captured in lunar orbit using the Oberth effect

3. Stabilizing the orbit

Acquiring S2 orbit

4. Moving to a circular orbit

Circular S3 orbit

Why a circular orbit though?

S4 orbit, enabling lunar descent from an altitude of 12 km

Conclusion

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Jatan Mehta

Space and Moon exploration writer ~ Contributing Editor, The Planetary Society ~ Thinker | Website: https://jatan.space