Launch-site Δv lab

Due East

The rotation you actually get, the inclination you cannot dodge, and the 82 m/s story — not 500.

Equator · 465.10 m/sNorth pole
Cape Canaveral · 408.7 m/sCanso · 327.1 m/s

Looking down on the pole. East is counterclockwise. Parallel radius is R cos φ — the only lever arm Earth gives you. Tangential speed is ω R cos φ.

Latitude increment, same heading

81.6m/s

183 mph. That is the rotation story. Not 500.

Pad A east speed

408.7 m/s

Pad B east speed

327.1 m/s

vrot(φ) = veq cos φ

Pad A

Cape Canaveral

Florida

imin = 28.5°
28.50°
cos φ
0.8788
v_rot due east
408.7 m/s

Pad B

Canso

Nova Scotia

imin = 45.3°
45.30°
cos φ
0.7034
v_rot due east
327.1 m/s

Mission

200 km

Losses 1.70 km/s combined

1.35 km/s
0.20 km/s
0.15 km/s

Falcon-class sea-level east LEO: gravity ~1.2–1.5, drag ~0.1–0.3, steering ~0.05–0.15. Same losses at both pads unless the trajectory is wind-loaded.

What the rocket must supply

Δvveh = v + Δvg + Δvd + Δvs − vrot

Pad A9076 m/s

burn 9076 · Earth gives 409 · inertial target 9484

Pad B9157 m/s

burn 9157 · Earth gives 327 · inertial target 9484

v insert
7784 m/s
Losses
1700 m/s
Δv_veh A
9076 m/s
Δv_veh B
9157 m/s

Vehicle Δv difference: 81.6 m/s — equal to Δv_lat when both pads fly due east with the same losses.

Inclination — the equation that actually hurts

imin = |φ| · Δvpc = 2 v sin(Δi / 2)

A short east burn from latitude φ yields i = φ. Canso’s proper product is i ≥ 45.3° (including polar and SSO). Then Δv_pc = 0 and you only pay the rotation term.

Pad A

i = 28.5° · A = 90°

cos i = cos φ sin A. Useful rotation 409 m/s.

Pad B

i = 45.3° · A = 90°

cos i = cos φ sin A. Useful rotation 327 m/s.

Payload sensitivity

mf/m0 = e−Δv / v_ev_e = I_sp g_0

320 s
50%

Stack sized for pad A. Dry mass held fixed. Extra Δv at pad B is taken out of payload. v_e = 3138 m/s.

Leftover A
5.55%
Leftover B
5.40%
Payload A / GLOW
2.77%
Payload B / GLOW
2.63%

95%

Pad B payload relative to a pad-A-sized stack.

Rotation vs latitude

v_rot = 465.10 cos φ · due east

|φA| = 28.5° → 408.7 m/s (914 mph). |φB| = 45.3° → 327.1 m/s (732 mph).

Constants and boxed equations

1. Constants

μ = 3.986004418×1014 m³ s⁻² · R_E = 6.378137×106 m · ω = 7.2921150×10⁻⁵ rad s⁻¹

v_eq = ω R_E = 465.10 m/s

2. Rotation you actually get (due east)

v_rot(φ) = v_eq cos φ

3. Speed you must reach in orbit

v_circ = √(μ / (R_E + h))

vis-viva: v = √(μ (2/r − 1/a)) · a = (r_p + r_a)/2

4. What the rocket must supply

Δv_veh = v_circ + Δv_g + Δv_d + Δv_s − v_rot(φ)

5. Inclination

i_min = φ · Δv_pc = 2 v sin(Δi / 2) · cos i = cos φ sin A

6. Payload

m_f / m_0 = e−Δv / v_e · v_e = I_sp g_0