how fast does the earth move?

where are you?

Earth
Sun

since you've clicked the button, you travelled:

Statement

At the equator (0 latitude) the earth has a circumference of 40075.017 kilometres.
At the poles (90/-90 latitude) it's just a point.
So if you spend one day at the equator, you are travelling 40075.017 kilometres at one day DUE TO THE EARTH'S ROTATION. At the poles you only spin once around your own axis.
That it is, why it is important to know on which latitude your are (approximately).

The mathematical formulas

To know whats the circumference at a specific latitude, you have to calculate this formula:

2 * PI * (cos(latitude) * (6378.137))

6378.137 is the half of the equator diameter.
At the 47. latitude the result would be about 2700 kilometres.
Now you have to divide it by 24 to get the km/h of earth's rotation.
Next you divide it by 3.6 to get the m/s.
Finaly you divide it by 1000 to get the km/s.
That's all.
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To get the speed of earth's orbit, you need the average of the distance of her to the sun.
The nearest point (the Perihel) is about 147100000 kilometres.
The farthest Point (the Aphel) is about 152100000 kilometres.
So the average is about 149600000 kilometres.
If we accept that the earth's orbit is an perfect circle (it's an ellipse, but very slightly), we can use PI to calculate the circumference of the earth's orbit.

2 * PI * 149600000

The Result (939964521.954 kilometres) is the circumference of the earth's orbit.
To get the route of one day, you have to divide it by 365.25 (because the real year is a littlebit more than the calendaric year).
The Result (2573482.60631) you have to divide by 24 to get the km/h.
Now you have to divide it by 3.6 to get the m/s.
To get the km/s you have to divide it by 1000.
So we know, the earth's speed around the sun is about 29.7856783138 km/s.
Thats all.
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To know the speed of the sun around the galaxys center, i've just researched and taken the average.
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The numbers

1.000 means 1.
1000.000 means thousand.
the point is used as a comma.
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The author of the earth's orbit animation is Julian Garnier.
Julian Garnier on Github