Space Fundamentals

Draft

Everything else on this site reduces to the material in these eight pages. The first four are dynamics: what an orbit is, what it costs to leave one, how to find a position at a given time, and what happens when a third body is added. The last four are the physical and bookkeeping constraints: relativity where it has operational force, the environment hardware has to survive, ionising radiation, and the frames and time scales without which a state vector means nothing.

Reading order

The dynamics pages build on each other and are best read in sequence. The remaining four are independent and can be read in any order.

The four results everything else uses

If you take nothing else from this section, take these.

Vis-viva

v^2 = \mu\left(\frac{2}{r} - \frac{1}{a}\right)

Speed at any point on an orbit, from radius and semi-major axis alone. Every impulsive manoeuvre calculation is two applications of this and a subtraction.

Orbital period

T = 2\pi\sqrt{\frac{a^3}{\mu}}

Period depends on semi-major axis and nothing else. Eccentricity cancels, which is what makes phasing manoeuvres possible.

Escape speed

v_{\text{esc}} = \sqrt{\frac{2\mu}{r}} = \sqrt{2}\,v_{\text{circ}}

Escape is an energy condition, and from any circular orbit it costs a 41.4% speed increase.

Radiative equilibrium

T = \left(\frac{\alpha}{\varepsilon}\cdot\frac{S}{\sigma}\cdot\frac{A_{\text{abs}}}{A_{\text{rad}}}\right)^{1/4}

Radiation is the only path for heat to leave a spacecraft, and surface finish is the design lever.

Pages

01Gravitation and the two-body problem

Newton’s law, the reduction to a single equation of motion, the conserved quantities, spheres of influence, and a magnitude table for everything the model leaves out.

02Escape velocity and characteristic energy

The energy condition for escape, escape speeds across the solar system, the C3 used in launch vehicle performance curves, and the Oberth effect.

03Kepler's laws

The three laws derived from an inverse-square force, Kepler’s equation and the anomalies, a Newton solver in Rust, and where the laws stop working.

04Lagrange points

The circular restricted three-body problem, where the five points sit, why Coriolis stabilises two of them, the halo and NRHO families, and the missions at each point.

05Relativity for space systems

The GNSS clock correction worked in full, the altitude where the two effects cancel, Shapiro delay, frame dragging, and a table of what to include when.

06The space environment

Vacuum and outgassing, cold welding, atomic oxygen erosion, spacecraft charging, hypervelocity impact and Whipple shields, and the radiative thermal balance.

07Space radiation

Trapped belts, solar particle events and cosmic rays; total ionising dose, displacement damage and single-event effects; and why more shielding is sometimes worse.

08Reference frames and time systems

Inertial, Earth-fixed, topocentric and orbital frames, the transformation chain, the five time scales, and four frame mistakes that cost tens of kilometres.