Landing at a specific location on the moon requires orbiting around the moon over that spot. One of our landing options is the South pole, which would necessitate a polar orbit. The first step in acquiring a desired orbit is to determine the lander’s current orbit.

Orbits are defined by six parameters, which can be determined by taking pictures of the lunar surface. In fact, only three images of the lunar surface taken from the lander need to be analyzed. The application of Kepler’s laws with the time and position data is enough to determine the lander’s current orbit.

The key insight into determining orbits from known points is Kepler’s second law: An object in orbit sweeps over the same amount of area per unit time.

As the lander travels from the Earth to the Moon (also known as cruise stage), the gravitational effects of both the Moon and the Earth affect the motion of the lander. To determine the lander’s orbit and location during cruise stage a series of osculating or reference orbits are calculated assuming only two bodies are involved. Because the true orbit is a three-body system, the true or perturbed orbit deviates from the osculating orbits. After a point, a new osculating orbit is calculated using new position and velocity estimates. This process repeats so that a series of orbits assuming only two bodies are present represent the single, three-body true orbit.

A series of approximate orbits are used to calculate the true orbit of the lander during cruise stage.