Astronomy & Celestial Mechanics
the sky, computed
Concept

Hyperbolic orbits — where it appears

Open orbits of bodies with more than escape speed, which pass a central mass once and leave. Their speed far from the mass is fixed, and a flyby turns it without changing its size, so only an encounter with a third body can make such an orbit bound.

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

A corridor 0.2 km wide, and a density known to a factor of 2. The apoapsis a vehicle is left on after a single atmospheric pass, against the periapsis altitude it aimed at, for ballistic coefficients of 60, 130, 300 kg/m² arriving at 3 km/s. The energy removed is the density at periapsis times an effective path length of √(2πrₚH), divided by the ballistic coefficient — so it falls exponentially with altitude and the curve is steep. Hitting a 1000 km apoapsis to ±10 per cent requires a periapsis inside 0.2 kilometres. Getting the atmosphere wrong by a factor of 2 moves the aim point by 7.6 kilometres, which is 30.7 times the corridor's own width — so a ballistic vehicle aiming at a planet whose density is known to a factor of two misses by more than the tolerance allows, and the manoeuvre has to be flown rather than aimed.

A manoeuvre that has never been flown once

Arrive on a hyperbola, dip once through the atmosphere, leave on a bound orbit having spent no propellant. The saving is a kilometre a second or more, the physics is the same as an entry corridor, and nobody has done it — because the corridor is a tenth of a kilometre wide and the density is known to a factor of two.

spaceflight · Atmospheric drag Captures counted over the Sun's life, cluster and field together. The cumulative number of ʻOumuamua-sized bodies Jupiter has captured since the Sun formed, against time, for birth clusters of 300, 1000, 3000 stars per cubic parsec whose bodies were captured at 4.3 a year per unit density for 3·10⁷ years, followed by today's visitors at 7.2 × 10⁻⁴ a year (dotted). The cluster's 3·10⁷ years supply 99.5%, 99.9%, 100.0% of all the captures the Sun has made: 7.2·10⁸, 2.4·10⁹, 7.2·10⁹ bodies, against 3.3·10⁶ from four and a half billion years of fast strangers. Almost everything Jupiter has ever captured, it captured from its siblings.

What Jupiter kept of the Sun's siblings

The Sun was born among a few thousand other stars, and while their planets formed they flung out small bodies at a few kilometres a second — exactly the speeds at which Jupiter can capture a passing body. Counted honestly, the birth cluster supplied almost every capture Jupiter has ever made: billions of bodies in thirty million years, against a few million in the four and a half billion since. And billions is still a hundred-thousandth of the Sun's own comets. Whatever the siblings gave the Sun, Jupiter was not how it arrived.

orbits · Hyperbolic orbits

Named alongside it

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

AerobrakingAerocaptureBallistic coefficientBirth clusterEntry corridorGravitational focusingGravity assistGuidanceInterstellar objectLift modulationOort cloudPropellant budget

All concepts