L2: escola
ASTRONada se pode deduzir sobre uma estrela a partir do seu brilho aparente até sabermos a que distância se encontra. É esta a ordem seguida por estes quatro, e foi este o percurso da astronomia — cada degrau aferido pelo que lhe fica abaixo, desde o triângulo topográfico até aos limites do universo observável.
L3: universidade
ASTROUma órbita é definida pelo seu tamanho e forma, e quase tudo o resto deriva disso. Estas cinco ferramentas vão da elipse ao combustível: onde se encontra uma nave espacial, a que velocidade se desloca, quanto tempo demora a viagem, qual o trajeto mais económico e o respetivo custo em 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.
