A suborbital tourism hop (Blue Origin New Shepard, Virgin Galactic SpaceShipTwo) is a near-vertical ballistic flight: a short powered boost, then an unpowered coast up past the Kármán line (100 km, the internationally recognised edge of space) and back down under gravity alone, followed by atmospheric-drag deceleration on the way in.
The model integrates 1-D vertical motion with altitude-dependent gravity and an exponential atmosphere:
g(h) = g0 · (Re / (Re+h))²
ρ(h) = ρ0 · e^(−h / H) H ≈ 8500 m (scale height)
a_drag = ½ · ρ(h) · v² / BC BC = m / (Cd·A) (ballistic coefficient)
During the boost the engine adds a constant acceleration set by the thrust-to-weight ratio; once it cuts off the vehicle coasts on momentum alone. What passengers actually feel is not gravity — free-fall never feels like anything — it's every non-gravitational force divided by mass:
apparent g = (a_thrust − a_drag·sign(v)) / g0
- Boost: engine thrust dominates → several g pressed into the seat.
- Coast (weightless): above the thick atmosphere, thrust = 0 and drag ≈ 0 → apparent g ≈ 0, true weightlessness, exactly as flown.
- Re-entry: falling back into thicker air, drag opposes the (downward) velocity → felt as g-force again, peaking low in the atmosphere where density is highest.
Higher thrust-to-weight or longer burns push the apogee higher and lengthen the weightless window; a lower ballistic coefficient (more drag per kg) brakes the vehicle earlier and gentler, while a high one lets it fall faster into denser air before decelerating hard.