L2: escuela
ASTROEl brillo aparente de una estrella no te permite deducir nada hasta que sabes a qué distancia se encuentra. Ese es el orden de estos cuatro, y el mismo que siguió la astronomía: cada peldaño medido respecto al inferior, desde el triángulo de un topógrafo hasta los confines del universo observable.
L3: universidad
ASTROUna órbita queda determinada por su tamaño y su forma, y casi todo lo demás se deduce de ahí. Estas cinco herramientas te llevan desde la elipse hasta el combustible: dónde se encuentra una nave, qué velocidad lleva en ese punto, cuánto tarda el viaje, qué trayecto resulta más económico y cuánto cuesta en propelente.
The Sun pulls the Moon twice as hard as the Earth does
The Earth pulls the Moon with 1.98 × 10²⁰ newtons. The Sun pulls it with 4.35 × 10²⁰. The Sun wins by more than two to one, the Moon stays with us anyway, and the reason is not the one most people reach for.
The night sky should be as bright as the Sun. Step outside and check.
If the universe were infinite and eternal, every direction you look would eventually hit a star, and the night sky would glare like the surface of one. It is dark instead, and the darkness is evidence about the age of everything.
Nobody has ever weighed the Sun. We timed something going round it instead.
There is one way to measure a mass you cannot touch: watch something orbit it, and time the orbit. The same equation weighs planets, stars and whole galaxies. Dark matter turned up where its answer stopped matching the sky.
A quasar at z = 3 is receding at 1.46 times the speed of light
Cosmological redshift is not a Doppler shift, and the difference stops being academic above z ≈ 1.5, where the recession speed exceeds c without anything moving through space or breaking relativity.
To catch the spacecraft ahead of you, slow down
Firing your engine towards a target in the same orbit sends you further behind it. The only way to catch up is to brake, drop into a lower and faster orbit, and come back up in front.
Most of a rocket is fuel, and better engineering will not change that
The rocket equation is logarithmic in the wrong direction: speed goes up like the logarithm of the mass you carry. Reaching orbit costs more than everything after it.
