# Orbits - Orbits follow kepler's laws, with the sun at one focus - We have to launch for Mars at specific times - Fuel is expensive - want the smallest spacecraft ## Hohmann Transfer Orbit - Most fuel efficient way - Accelerate, making your orbit more and more eccentric - Perihelion (nearest point to sun) in Earth's orbit - Aphelion (farthest from the sun) we enter Mars' orbit  - You can find that the semimajor axis of this orbit is halfway between Earth's semimajor axis and Mars' - Using this, you can find that the period is 18 months for the collision with Mars (9 months) - When pushing in to a faster orbit, we are accelerating - firing cannon ball faster and faster - accelerate our rocket to go into the orbit towards Mars - We want to match the speed between Earth and Mars (accelerate when nearing Mars) - We accelerate twice to end up going slower (Kepler's second law) - Transferred kinetic energy to potential energy # References 1. https://youtu.be/TpCAR1k2BOk # Footnotes