# Proximity Operation Maneuvers at Asteroidal Deep Space In-Situ Resource Utliization Stations

## Faculty Mentor Name

Davide Conte

## Format Preference

Poster

## Abstract

Given a transfer from Earth to an asteroid, the goal is to determine a probability distribution of rendezvous trajectories and the associated velocity changes required to correct them to a desired trajectory. Once an appropriate asteroid is selected, it is necessary to determine a trajectory from Earth to the asteroid. The transfer orbit was determined by solving Lambert’s Problem. Position vectors for Earth and an asteroid will be acquired using ephemeris data from NASA JPL’s Horizons System. A time of flight and associated departure and arrival dates will be determined. Using the transfer semi-major axis from the solution to Lambert’s Problem, departure and arrival velocities can be calculated. Velocities are required for the purpose of determining rendezvous maneuvers when arriving at the asteroid sphere of influence (SOI). The methods to be used to calculate the relative motion and rendezvous are those developed by G.W. Hill in the 1870s and Clohessy Wiltshire in the 1960s and involve linearizing the Newtonian equations of motion for the relative motion between two bodies. This simplification technique is part of Linear Orbit Theory and allows for analytical computation of relative motion. It also provides deeper insight into the nature of the motion. The resulting equations are referred to as the Hill-Clohessy-Wiltshire (HCW) equations. Determination of a trajectory probability distribution will be achieved using Body Plane (B-Plane) targeting methods and an associated error ellipse.

Proximity Operation Maneuvers at Asteroidal Deep Space In-Situ Resource Utliization Stations

Given a transfer from Earth to an asteroid, the goal is to determine a probability distribution of rendezvous trajectories and the associated velocity changes required to correct them to a desired trajectory. Once an appropriate asteroid is selected, it is necessary to determine a trajectory from Earth to the asteroid. The transfer orbit was determined by solving Lambert’s Problem. Position vectors for Earth and an asteroid will be acquired using ephemeris data from NASA JPL’s Horizons System. A time of flight and associated departure and arrival dates will be determined. Using the transfer semi-major axis from the solution to Lambert’s Problem, departure and arrival velocities can be calculated. Velocities are required for the purpose of determining rendezvous maneuvers when arriving at the asteroid sphere of influence (SOI). The methods to be used to calculate the relative motion and rendezvous are those developed by G.W. Hill in the 1870s and Clohessy Wiltshire in the 1960s and involve linearizing the Newtonian equations of motion for the relative motion between two bodies. This simplification technique is part of Linear Orbit Theory and allows for analytical computation of relative motion. It also provides deeper insight into the nature of the motion. The resulting equations are referred to as the Hill-Clohessy-Wiltshire (HCW) equations. Determination of a trajectory probability distribution will be achieved using Body Plane (B-Plane) targeting methods and an associated error ellipse.