TeamIndus spacecraft lunar orbits explained

Designing lunar orbits to efficiently land on the Moon

The TeamIndus spacecraft will soft-land on the Moon in 2020. The landing site for this first mission (Z-01) is near Annegrit crater, in the vast lava plains of Mare Imbrium.

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

The location of the landing site poses multiple constraints on how the spacecraft orbits are designed, including the launch/landing time and everything in between. Let’s take a look at the constraints imposed by the landing site first, followed by the nature of the lunar orbits.

Part A: Constraints on lunar orbits

1. Sun illumination

A lunar day is equivalent to 14 Earth days (between 70 N/S) and we want to maximize the surface operations time post-landing. Landing at local dawn would thus be ideal. However, at least two of the three solar panels need to be illuminated by sunlight for surface operations to begin. It also needs to be ensured that the Sun is at a high enough angle to be not blocked by local obstructions.

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

For these reasons, landing time is selected to be post-dawn for maximizing surface operations time while ensuring power availability. The landing time is thus frozen.

2. Time spent in lunar orbit

The lunar orbits are designed such that landing time can be met regardless of the lunar phase at the time of spacecraft’s lunar orbital capture. The landing time being fixed, the lunar orbits thus need to be worked out backwards from that point. The time difference between the ‘lunar phase at the time of orbital capture’ and ‘dawn at the landing site’ gives the the time to be spent in lunar orbit i.e. ‘stay time’.

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

The lunar orbits and landing time thus ensure ability to target the longitude of the selected landing site.

3. Inclination and time of launch

Given the time of orbital capture and landing time, the final constraint comes from the latitude of the landing site. The spacecraft lunar orbits need to have an orbital inclination such that the required landing site latitude can be targeted, while meeting the post-dawn landing time constraint.

Post-launch, the spacecraft uses its propulsion system to alter the orbital inclination such that the desired latitude can be targeted.

With these landing site constraints in mind, let’s see how the spacecraft will get captured in lunar orbit and how the orbital maneuvers are planned to achieve mission goals.

Part B: Evolution of lunar orbits

1. Approaching the Moon

The spacecraft will approach the Moon in a Lunar Transfer Trajectory (LTT) which is a minimum energy transfer orbit and takes 4–5 days for the spacecraft to reach the Moon. When at its farthest point from the Earth (called the apoapsis), the spacecraft is well within the Moon’s sphere of gravitational influence.

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

At the apoapsis of the LTT, the Moon’s gravitational pull will be highest and is where the lunar orbital capture is attempted.

2. Getting captured in lunar orbit

When nearing the LTT apoapsis, the spacecraft thrusters fire to orient the spacecraft in the opposite direction of the trajectory. Firing the main engine about this point decrease the velocity of the spacecraft, while consuming minimal fuel. This will be referred to as a velocity-decreasing engine burn from here onward.

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. 

At the end of the engine burn, if the spacecraft velocity at the LTT apoapsis is larger than the Moon’s escape velocity at that point (from the lunar surface), the spacecraft will escape the Moon’s gravitational influence. Getting captured into lunar orbit will thus not be possible. The main engine needs to fire for a long enough duration and decrease the velocity to a lower value than the Moon’s escape velocity. A successful engine burn and the spacecraft is now orbiting the Moon! :D

Getting captured in lunar orbit using the Oberth effect

The resulting orbit is what we call the S1 orbit. Note that the apoapsis of the LTT is now the periapsis (closest point) of the lunar orbit. The way orbital mechanics works is quite elegant in its apparent simplicity.

3. Stabilizing the orbit

With S1, the spacecraft will now be in an elliptical orbit around the Moon. The periapsis of S1 orbit (100 km) is chosen such that it meets the velocity requirements for lunar descent.

You see, the nature of the orbit (periapsis and apoapsis) determines the velocity at any given point and changes proportionally to the orbit size. As such, lunar descent needs to start at a precise velocity, altitude and longitude to land at the selected location. Maintaining the periapsis of S1 orbit to ~100 km is crucial.

Due to orbital perturbations, the S1 orbit periapsis can deviate from 100 km significantly. If the periapsis is altered beyond a tolerable value, more fuel will be needed to prevent an uncontrolled altitude loss and subsequent crashing on the Moon. Gravity can be mean at times.

At the S1 periapsis, another engine burn is performed to reduce the spacecraft’s velocity and lower the orbit’s apoapsis to 1500 km.

Acquiring S2 orbit

4. Moving to a circular orbit

The spacecraft then performs another velocity-decreasing engine burn near S2 periapsis to lower its orbit size further. This time around the apoapsis of S2 is lowered to 100 km, making the new orbit a circular one.

Circular S3 orbit

Why a circular orbit though?

The answer to why a circular orbit is desired lies in the S4 orbit! The lowest point of the S4 orbit is dictated by the lunar descent’s altitude requirements (which is 12 km for optimal, fuel-efficient targeting). The descent also needs to start when the spacecraft is ~900 km away from the landing site, to target the said site.

Considering these requirements, another velocity-decreasing engine burn is performed at a point in S3 orbit, lowering the periapsis to the desired altitude of 12 km.

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

At the S4 periapsis, the descent can begin and it is the point where the physics advantage of the circular orbit comes in.

Had S3 been an elliptical orbit like S2, the closest point for starting the descent would lie only on the S2 periapsis (see S2 orbit diagram above). This would constrain the longitude for landing, leaving no flexibility in targeting various landing sites.

Instead, a circular orbit allows the engine burn to be executed anywhere in the circular S3 orbit and accordingly choose the lowest descent point in the S4 orbit. Circularizing the orbit thus allows flexibility in targeting various landing sites while requiring the least amount of energy expenditure.

The spacecraft now waits until lunar dawn occurs on the landing site before beginning the lunar descent.

Conclusion

That wraps up a look at the TeamIndus spacecraft lunar orbits. Efficient orbit design allows us to optimize the spacecraft’s mass for maximum payload delivery to the lunar surface, while maximizing the surface operations duration.

Check out the rest of our tech blog for more such deep dives into space technologies and our mission engineering.