During the fall of my sophomore year at Tufts, I participated in NASA's
L'SPACE
Mission Concept Academy. The academy is a 12 week experience which includes weekly lectures by figures across the space industry. Students work in teams to create solar system exploration mission design proposals at the Preliminary Design Review (PDR) level.
My team, roughly 10 students across the east coast, designed a rover mission to a large main-belt asteroid called Vesta. I was in charge of designing the descent and landing portion of the mission, including choosing the orbit, selecting appropriate rocket engines, calculating the amount of fuel we'd need to land, sizing fuel tanks, and designing the descent profile.
In selecting an orbit around Vesta, I decided to begin the descent from a "geosynchronous" orbit, meaning our orbiter would complete one trip around Vesta in the time it takes Vesta to spin 360 degrees (1 day). This means the crater we were landing in would frequently be within sight, and we could perform remote sensing analysis before landing.
Using Kepler's Third Law, I calculated the orbital radius which would cause the orbital period to be equal to 1 day on Vesta. Using this value and Newton's Law of Gravitation, I calculated the total change in velocity (delta v) our descent engines would need to impart on the spacecraft.
A CAD model I created of the engine.
Since our entire spacecraft was only 15kg, I calculated it would only weigh about 3.3 Newtons on the surface of Vesta, meaning we could safely land with about 7 Newtons of thrust. After choosing a few potential rocket engine candidates, I was able to use their design specifications and the Rocket Equation to estimate how much fuel each engine would require to land the spacecraft. Ultimately I decided to use four smaller engines which would provide the necessary thrust, only required 2.7 kg of fuel, and could provide pitch and yaw control by throttling. I chose a fuel tank that would hold enough fuel and weighed about 1kg.
Finally, I got to work designing how the engines would fire to ensure a safe landing. I wrote a simulation in Python that modeled the physics of the lander, first programming the kinematics such that the simulation produced accurate orbits based on an initial radius and velocity. Next, I added a feature to allow the rocket engines to impart thrust on the spacecraft. Starting from the orbital radius and velocity I had calculated earlier, I settled on a descent profile which would involve three separate engine burns and resulted in the lander reaching the surface with about 0.5 meters/sec of velocity. My simulation agreed closely with the pen and paper calculation I performed earlier, showing that the descent would require about 3 kg of fuel.
The layout of the four rocket engines on the base of the lander.
A plot from the simulation showing the descent profile. The orange arc is the surface of Vesta, while the blue line shows the path the lander would travel.