Topic
Your first nights under the stars: what to look at first, how to let your eyes adapt, and which piece of equipment is genuinely worth buying before any other.
On 23 September Venus reaches magnitude -4.78, its brightest of the year, while only 22 % of it is lit. The paradox resolves into a multiplication: the crescent thins, but the disc grows faster, 42 arcseconds across at 59 million kilometres. The calculation, the observing window that is melting away, and what binoculars make of the crescent.
At 2.5 million light-years, M31 is the most distant thing the unaided eye catches without strain. It spans three degrees, six full Moons laid end to end, climbs to 82 degrees above Paris, and the moonless window runs from 5 to 17 September. The exact star-hop, and what your own sky will let through.
Tonight, shadows on the Moon are seven times as long as the relief that casts them. On 27 August they will be a tenth of it. A factor of seventy in seven nights, and it comes down to a single angle: the Sun's height above the lunar ground. Here is the arithmetic, evening by evening.
There is nothing to buy and nothing to set up: the International Space Station is visible to the naked eye, and often brighter than the brightest star. You just have to know when. The answer depends on three things at once, and it changes every day.