Question

What is the circumference of the Earth’s orbit around the Sun?

Answer 1

As a very first step, one could consider the earth’s orbit around the sun to be circular. Now, recall the value of distance of earth from the sun which would be one astronomical unit in kms. Now, recall the formula for finding the circumference of a circle. Substituting the values, we will get the answer.

Formula used:
Circumference of a circle,
$C=2\pi r$

Complete step-by-step solution:
In the question we are asked to find the circumference of Earth’s orbit around the Sun. You may recall that the very distance of the earth from the sun is given by the term ‘astronomical unit’. It is given as,
1 AU = 92955807 in miles and 1AU= 149597870 in kilometers. Now, let us recall that the circumference of a circle is given by,
$C=2\pi r$
Where, we know that ‘r’ is the radius of the circle whose circumference we have to find. Now, we could take the distance between the earth and sun to be the radius of the orbit in which the earth is orbiting around the sun. So, we could substitute the value to get,
$C=2\times \pi \times 149597870$
$\therefore C=939950334km$
Therefore, we found the circumference of the Earth’s orbit to be 939950334kms. We could say that the circumference of earth’s orbit would approximately be 940million kilometers.

Note: You may note that this calculation is done by assuming the earth’s orbit to be circular. But in reality we know that the Earth’s orbit is elliptical with the sun placed at one of its focus. Current eccentricity is found to be 0.0167 which is close to zero. So, we could take the centre of the orbit to be close to the Sun’s centre.