Fallin' and missin'Orbit is not about goin' up. Up is the easy part and it does not stay bought. Orbit is about goin' sideways fast enough that the ground curves away as quick as you drop toward it.
Newton explained satellites in 1728, which is two hundred and twenty-nine years before there was one[22]. He drew a cannon on a mountain so tall it was above the weather and fired it level. Small charge: the ball arcs over and lands in the next county. Bigger charge: the next country. Big enough charge, and the ball falls toward the Earth at the same rate the Earth is curving out from under it, and it never lands at all. It comes around and hits you in the back of the head.
The number
Set the fall equal to the curve and the speed drops out of the arithmetic:
v = √(GM / r)
G is the constant of gravity[27], M is the mass of the Earth, r is how far you are from the middle of it — not from the ground, from the middle. At the height the space station flies, about 420 kilometres up, that comes to 7,661.31 m/s[14], which is 17,138 mph, which is Mach 22.34 if there were any air left to measure it against. One lap in 92.8 minutes. Sixteen sunrises a day.
Farther out is slower — a bigger r means a smaller v. The Moon is doin' about a kilometre a second and takes a month. A satellite parked over one spot on the equator sits at 35,786 km and takes exactly a day, which is the whole point of it.
Quittin' entirely
Go faster still and the loop opens up. Put in a factor of two under the root:
v = √(2GM / r) = 11,186.2 m/s at the ground
Throw somethin' that fast and it does not come back — no engine after the throw, no fuel, nothing. It coasts out forever, slowin' the whole way, never quite stopping. That is escape velocity[15], and notice what it is not: it is not a speed you have to hold. It is a speed you have to have, once, and then you are done paying.
Why nobody launches at escape velocity
Because of the air. Eleven kilometres a second at sea level would cook a rocket like a meteor — and meteors are exactly the demonstration. A rocket goes up slow through the thick part, where the cube law is brutal, then turns sideways and does its real accelerating up high where there is nothing left to shove. Going up is not the mission. Going up is just gettin' out of the way of the air so you can go sideways in peace.
The fastest thing we ever built did it by fallin'
The Parker Solar Probe touched 192,000 m/s — about 691,200 km/h — in December 2024[17]. No engine on Earth did that. The Sun did. The probe gave up speed at Venus seven times to drop its orbit closer in, and then it fell, the same way a rock falls off a barn, except the barn is the Sun and the drop is ninety million miles deep. Falling is free. Everything fast in the solar system is fast because it fell a long way, and the ones we call slow are the ones that stayed up.