Astronomy & Celestial Mechanics
the sky, computed
Concept

Dynamic pressure — where it appears

The pressure a flowing gas exerts by its motion, its density times the square of its speed. For the solar wind it sets how hard the wind pushes on a planet's magnetosphere or ionosphere, and it rises several times during a storm.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

Where the missing kilometres a second go. The two losses along a gravity-turn ascent, against the vehicle's thrust-to-weight ratio at lift-off, from an integration of the trajectory rather than from a table. Every run spends the same 9400 m/s of ideal Δv and every one is flown as the same manoeuvre: one pitch kick, solved by bisection so that the vehicle is horizontal at burnout, and thereafter zero angle of attack so that gravity alone turns it — which makes the steering loss identically zero and the comparison a fair one. What differs is how much of the Δv survives as speed. The gravity loss is ∫g sin γ dt, the part of the thrust spent holding the vehicle up rather than accelerating it, and it falls as the thrust rises because a vehicle that leaves quickly spends less time doing it: 1263 m/s at T/W = 1.15 against 381 at 2.2. The drag loss is ∫(D/m) dt and it rises, because the same haste means reaching high speed lower down where the air is: 119 m/s against 1874. The sum is least at T/W ≈ 1.5, at 1198 m/s, and the minimum is shallow — which is why real vehicles cluster between 1.2 and 1.5 and none of them is there because of this curve. At the marked 1.5 the 9400 m/s of ideal Δv leaves the vehicle at 8202 m/s and 42 km, against a circular speed of 7884 m/s there, so the 1198 m/s of loss is the whole of the answer to why orbit costs about 9.4 km/s when orbital speed is under 7.9.

Orbit costs 7.8 and a launch buys 9.4

The gap between orbital speed and the velocity change a launcher spends is not overhead. It is three integrals along the ascent, only one of which can be reduced by flying better, and the two that can be traded move in opposite directions.

spaceflight · Rocket equation Two exponents a solar cycle cannot pull apart. The exponents of a fit of an unmagnetised planet's ion loss to the ultraviolet (horizontal) and to the solar wind's pressure (vertical), shown as the region each fit allows at two standard deviations around a true pair of (0.5, 0.5), from 200 independent samples with a scatter of 0.2 decades, over a cycle in which the ultraviolet varies by 0.12 decades and the pressure by 0.25, for correlations of 0.3, 0.7, 0.9 between the two. The marked corners are the two pure limits: a loss set by the ions the ultraviolet makes, (1, 0), and one set by the wind's power, (0, 1). With weak correlation the two exponents are each known to ±0.25 and ±0.12; at a correlation of 0.9 the ultraviolet's is uncertain by ±0.54, and the ellipse stretches along the line on which raising one exponent and lowering the other leaves the fit unchanged.

Two exponents a solar cycle cannot pull apart

Whether a magnetic field protected the early Earth's air depends on what limits the escape of ions from a planet without one — the ultraviolet that makes them or the solar wind that carries them off. Measured at Mars through a solar cycle, the two causes rise and fall together, and the fit that tries to separate them leaves each exponent uncertain by half its value. Remarkably, the young Sun's loss is predicted well anyway. What spoils the prediction is not the confusion but a switch between the two limits that the present-day data cannot see coming.

sky · Magnetosphere

Named alongside it

The objects these essays reach for when they reach for this one.

Atmospheric escapeBallistic coefficientΔvDrag lossExtreme-ultravioletFlight-path angleGravity lossGravity turnMagnetosphereOrbital velocityScale heightSolar cycle

All concepts