Where are you?
Or drag the pin up and down on the globe.
Compared with
What is happening?
Earth turns all the way around once a day. Everything on it, you included, rides along. At the equator you travel the whole way around the middle of Earth, about 25,000 miles, every day. That is about 1,040 miles per hour, faster than the speed of sound.
Closer to the North or South Pole, your circle is smaller, so you go slower. At the very pole you just turn in place, like the center of a merry-go-round.
A point at latitude φ moves on a circle of radius R cos φ, so its speed is
v = (2πR / T) cos φ ≈ 465 m/s × cos φ
with R = 6,378 km (the equator) and T = 23 h 56 min 4 s, the time for one turn relative to the stars. That gives about 465 m/s = 1,674 km/h = 1,040 mph at the equator. (Dividing by 24 hours instead gives the often-quoted figure of about 1,670 km/h, roughly 1,037 mph; the 24-hour day is slightly longer because Earth also moves along its orbit.)
Kansas City (39.1° N): 465 × cos 39.1° ≈ 361 m/s ≈ 807 mph.
Race the motions
Each dot moves as far as that motion carries you in the same time, drawn to scale.
Why don’t we feel it?
Think of riding in a smooth car or airplane. If it goes straight at a steady speed, a cup of water sits still and you could play catch in the aisle. You only feel motion when it speeds up, slows down or turns.
Earth's motions are very smooth and steady, and the air, the oceans and you all move together. So it feels like we are standing still, even while we race around the Sun.
Newton's first law: a body keeps moving at constant velocity unless a net force acts on it. Steady motion cannot be felt from inside; only acceleration can.
Our motions do curve, so there is some acceleration, but it is tiny. Spin at the equator: a = v²/r = (465 m/s)² / 6.378×106 m ≈ 0.034 m/s², about 0.3% of gravity (it makes you weigh about 0.3% less there). Around the Sun: (29,780 m/s)² / 1.496×1011 m ≈ 0.006 m/s².
The speeds do not simply add: they point in different directions that change through the day and the year. Each is measured relative to something different (Earth's axis, the Sun, the galaxy's center).
The heavens declare
All this motion runs so steadily that we set clocks and calendars by it. Long before anyone measured these speeds, a psalm said: The heavens declare the glory of God; and the firmament sheweth his handywork.
(Psalm 19:1, KJV)
Plan a launch
What is happening?
To stay up in orbit, a spacecraft must go sideways about 17,500 mph, so fast that as it falls it keeps missing Earth. A rocket sitting on the launch pad is already moving east with the spinning Earth, so if it launches east it gets that speed for free: the spin bonus.
Launch sites near the equator get the biggest bonus. Launching west means first undoing Earth's spin, which costs extra fuel. Rockets also launch over the ocean, so empty stages fall into the sea, far from homes.
To leave Earth for good and head to other worlds, a spacecraft needs about 25,000 mph: escape speed.
Spin bonus for a due-east launch from latitude φ:
Δvspin = 465 m/s × cos φ
Circular orbit speed v = √(GM/r) is about 7.8 km/s just above the atmosphere. Speed the rocket must add (ignoring losses): 7,800 − Δvspin going east, about 7,800 going polar, and 7,800 + Δvspin going west, a penalty of twice the bonus compared with east.
Escape speed vesc = √(2GM/R) = √2 × (orbital speed at the surface) ≈ 11.2 km/s.
A real rocket must also climb out of gravity and push through air: these losses add roughly 1.5 to 2 km/s, so about 9.3 to 10 km/s in all to reach low orbit.
A site at latitude φ launching due east lands in an orbit tilted φ to the equator; that is why satellites bound for the geostationary ring above the equator favor launch sites near the equator.
From history
- Apollo 11, July 16, 1969. The Saturn V rose from Launch Complex 39A at NASA's Kennedy Space Center, beside Cape Kennedy (renamed Cape Canaveral in 1973), and flew east-northeast over the Atlantic, borrowing roughly 400 m/s (about 900 mph) from Earth's spin.
- Polar orbits from Vandenberg. Since 1959 rockets from Vandenberg, on California's coast, have flown south over the Pacific to put weather and Earth-mapping satellites in polar orbits, which pass over the whole planet as it turns beneath them. Going polar gets no spin bonus, but there is open ocean to the south.
- Kourou, French Guiana. Just 5° north of the equator, Europe's launch site gets almost the full 465 m/s and has the Atlantic to the east.
- Baikonur, Kazakhstan. Sputnik 1 (1957) and Yuri Gagarin, the first person in orbit (1961), launched from here. At 46° N its bonus is about 324 m/s, and spent stages fall on empty steppe instead of the sea.
Try it (high school)
- How much bigger is the spin bonus at Kourou (5.2° N) than at Cape Canaveral (28.5° N)?
Show the answer
465 × cos 5.2° ≈ 463 m/s; 465 × cos 28.5° ≈ 409 m/s. Kourou gets about 54 m/s (about 120 mph) more.
- From Cape Canaveral, how much more speed does a rocket need going west instead of east?
Show the answer
East: 7,800 − 409 = 7,391 m/s. West: 7,800 + 409 = 8,209 m/s. The difference is twice the bonus, about 817 m/s (2 × 408.7).
- How far does Kansas City (39.1° N) travel in one turn of Earth? The equator is 40,075 km long.
Show the answer
40,075 × cos 39.1° ≈ 31,100 km (about 19,300 miles).
- Escape speed is √2 times the orbital speed at the same height. If orbital speed at the surface were 7.9 km/s, what is escape speed?
Show the answer
1.414 × 7.9 ≈ 11.2 km/s.