A polar orbit passes over or near both poles, so as Earth turns underneath, the satellite eventually flies over almost every part of the planet.
A polar orbit runs from pole to pole. Its inclination — the angle between the orbit and the equator — is 90°, or close to it. ESA counts orbits within about 10° of the poles as polar, and most such satellites fly between 200 and 1,000 km up.
The orbit's plane stays fixed in space while Earth spins inside it. So each time the satellite comes round, a new strip of ground has turned under its path. Over days, it can see almost every point on Earth.
That is why mapping satellites such as India's Cartosat series use near-polar orbits. India's workhorse rocket for them is even named for it: the Polar Satellite Launch Vehicle, PSLV, can carry up to 1,750 kg to a sun-synchronous polar orbit 600 km high. Cartosat-3 flies at a mean altitude of 509 km with an inclination of 97.5°.
Cartosat-3 takes 94.78 minutes per orbit. In that time Earth turns 360° × 94.78 / 1,436 ≈ 23.8°. At the equator that is about 2,645 km. So every pass crosses the equator about 2,645 km west of the last one, and the satellite makes about 15 laps a day.
Passes on the following days fall in between those lines. Over several days the gaps fill in, and the satellite can image almost any point on Earth. How long that takes depends on how wide a strip its camera sees.
Earth spins eastward, so a rocket launched east gets a free push from the ground's own speed. A polar launch heads north or south and gets almost none of that push, so the rocket must supply more of the speed itself. NASA notes that polar orbits need more energy, and so more propellant, for that reason.
The idea works at other planets too. NASA's Magellan spacecraft used a nearly polar orbit around Venus and mapped one strip of the planet's full circle of longitude for each turn of Venus beneath it.
Cartosat-3's orbit path runs almost north–south, passing close to both poles, and each new lap crosses the equator farther west. Track Cartosat-3
Earth's surface speed due to rotation is v_rot = 2πR / T_sidereal × cos φ, where φ is the latitude. At the equator, v_rot = 2π × 6,378 km / 86,164 s = 0.465 km/s. Braeunig gives a check: at Cape Canaveral (28.5°N), a due-east launch gains 1,471 km/h, and 0.465 × cos 28.5° × 3,600 = 1,471 km/h.
A rocket's final speed relative to space is the vector sum of the speed it adds and the ground's eastward speed. For a due-east launch they simply add. For a polar launch the ground's speed is at right angles to the path, so it does not help. For a retrograde orbit (inclination above 90°, like Cartosat-3's 97.5°) the satellite moves slightly westward, so the rocket must also cancel part of the eastward speed.
The westward shift per lap is simply Earth's rotation during one period: Δλ = 360° × T_orbit / T_sidereal. For Cartosat-3, 360° × 94.78 / 1,436.07 = 23.76°, or 2πR × 23.76/360 ≈ 2,645 km at the equator. In one sidereal day it makes 1,436.07 / 94.78 ≈ 15.15 laps.
An exactly 90° orbit has one more property: Earth's equatorial bulge, which slowly swings most orbit planes around, has no turning effect on it, because the swing rate is proportional to cos i. That is why sun-synchronous orbits are tilted a few degrees past 90° instead — see orbital precession.
Its orbit plane stays fixed in space while Earth rotates underneath, so each pass covers a new strip of ground further west.
An eastward launch gains the speed of Earth's rotation for free. A polar launch travels at right angles to that motion and gets almost none of it, so the rocket must provide more speed.
Earth turns about 360° × 95/1,436 ≈ 24° in that time, which is about 2,600 km at the equator.