# At what speed does the earth move around the sun?

Let's calculate that. First of all we know that in general, the time it takes to travel a distance is equal to the length of that distance, divided by the speed at which you travel that distance. If we reverse that, we get that the speed is equal to the distance traveled over the time taken.

We also know that the time it takes for the Earth to go once around the Sun is 1 year. So in order to know the speed we just have to figure out the distance traveled by the Earth when it goes once around the Sun. To do that we will assume that the orbit of the Earth is circular (which is not exactly right, it is more like an ellipse, but for our purpose it will do just fine). So the distance traveled in one year is just the circumference of the circle. (remember that the circumference of a circle is equal to 2*pi*Radius)

The average distance from the Earth to the Sun is 149,597,890 km. Therefore in one year the Earth travels a distance of 2*Pi*(149,597,890)km. This means that the velocity is about:

velocity=2*Pi*(149,597,890)km/1 year

and if we convert that to more meaningful units (knowing there is 365 days in a year, and 24 hours per day) we get:

velocity=107,300 km/h (or if you prefer 67,062 miles per hour)

So the Earth moves at about 100,000 km/h around the Sun (which is 1000 times faster than the speeds we go at on a highway!)

Thanks for your explanation, but I was hoping for an explanation a little more precise, since I already knew the one you gave.

In the case of your question about the speed of the Earth around the Sun, there isn't really a more 'precise' answer. The only approximation I did in the calculation I sent you is assuming that the orbit of the Earth is circular. This is in fact a very good approximation. One of Kepler's law describing the planetary motions states that all orbits are ellipses. This is the case for Earth's orbit. But not all ellipses come in the same shape. They are described by their 'eccentricity' (which tells us how flatten they are). The eccentricity is a number that varies between 0 and 1, 0 being a circle, and 1 being a very flattened ellipse. It turns out that the orbit of the Earth right now as an eccentricity of 0.016. This means it is almost a circle, making our approximation valid. The rest of the calculation is very exact, I used a very accurate number for the Earth-Sun distance. So under the one approximation made, the calculation couldn't really be more 'precise'.

Now if you want to calculate the speed of the Earth on its orbit without assuming it is a circle, it is another ball game! First of all, I cannot give you a precise answer, because the speed of the Earth changes all the time as the Earth moves around the Sun. This is because Kepler's law says that on its orbit, a planet will sweep equal areas in equal amounts of time. This means that when the Earth is closer to the Sun (which happens in early January, about 2 weeks after the winter solstice) it's moving faster than when it is farther away. Unless you specified a specific day of the year, this means I cannot give you a precise value for the speed of the Earth assuming its orbit is an ellipse. We are better off to stick with the first number we got.

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