Apollo 18: They KeY to the Next Mission to the Moon Jon Xia and Richard Zhu

Types of Transfer Orbits

Hohmann Transfer

Retrograde vs. Prograde Orbit

Models and Proof

Models and Proof

Models and Proof Circle Dynamics: Ellipse Dynamics: 𝑥 2 + 𝑦 2 = 𝑟 2 ∧𝑑 𝑥 2 +𝑑 𝑦 2 =1∧𝑣>0∧𝑟>0→ 𝑥 ′ =𝑟𝑣𝑑𝑥, 𝑦 ′ =𝑟𝑣𝑑𝑦,𝑑 𝑥 ′ =−𝑣𝑑𝑦,𝑑 𝑦 ′ =𝑣𝑑𝑥 ( 𝑥 2 + 𝑦 2 = 𝑟 2 ∧𝑑 𝑥 2 +𝑑 𝑦 2 =1) Ellipse Dynamics: 𝑣 𝑥 2 + 𝑣 𝑦 2 =𝐺𝑀 2 𝑑 − 1 𝑎 ∧𝑑>0∧𝑎>0→ [ 𝑥 ′ = 𝑣 𝑥 , 𝑦 ′ = 𝑣 𝑦 , 𝑣 𝑥 ′ =− 𝑑 𝑥 𝐺𝑀 𝑑 3 , 𝑣 𝑦 ′ =− 𝑑 𝑦 𝐺𝑀 𝑑 3 &𝑥≤𝑎] 𝑣 𝑥 2 + 𝑣 𝑦 2 =𝐺𝑀 2 𝑑 − 1 𝑎