Core Mnemonics

Mnemonic 1: "Escape is Root-Two Times Orbit" v_e = √2 × v_{0}

If you remember v_{0} ≈ 8 km/s (near surface), then v_e ≈ 8 × 1.414 ≈ 11.3 km/s

Mnemonic 2: "One Positive, Two Negative, One Negative" (Energy Ratio) KE : PE : E = +1 : −2 : −1 KE = +GMm/2r (one positive) PE = −GMm/r (two negative: twice KE in magnitude) E = −GMm/2r (one negative: equals KE in magnitude but negative)

Mnemonic 3: "Altitude Drops by Square, Depth Drops by Line"

• Altitude: g' = g/(1 + h/R)^{2} — "drops by square"
• Depth: g' = g(1 − d/R) — "drops by line" (linear)

Mnemonic 4: Kepler's Laws — "Ellipse, Areas, Cubes"

• 1st: Ellipse (orbit shape)
• 2nd: Equal Areas (angular momentum conservation)
• 3rd: $T^{2}$ ∝ $r^{3}$ (Cubes)

Mnemonic 5: "PE-TE-KE" Triple

• PE is always = 2 × (TE) in magnitude; PE = 2E (with sign, PE = −2|E|)
• TE is always = −(KE): total energy = −kinetic energy
• KE is always = |TE|: same magnitude, opposite sign

Quick numerical values to memorize:

• G = $6.674 \times 10^{-11}$ N $m^{2}$ $kg^{-2}$
• R_Earth = $6.4 \times 10^{6}$ m (or 6400 km)
• g = 9.8 ≈ 10 m/$s^{2}$ (use 10 in calculations)
• v_{0} ≈ 7.9 km/s (near surface)
• v_e ≈ 11.2 km/s
• Geostationary height: 35,786 km ≈ 36,000 km
• Near-surface period: ≈ 84.6 min ≈ 1.4 h