Question in description

Question

Assume the orbit of the earth is a circle having radius 93 million miles.

The radius from the sun to the earth sweeps out how many radians in one day? How about in one week?

How far does the earth travel in one day? How about in one week?

Answer 1

A circle has 360 degrees. Similarly, if the earth does one complete orbit around the sun, it is said to have gone 360 degrees. One complete orbit around the sun is what we call a year. Therefore, 1 year = 360 degrees. So, (1 year / 365 days) * ( 360 degrees / 1 year) --> 0.986 degrees per day

To go from degrees to radians, we use the formula, 180 degrees = pi radians. So in order to convert our 0.986 degrees to radians, we simply multiply --> (0.986 degrees) * (pi radians/ 180 degrees) = 0.0172 radians

Simply multiply the above answer by 7 to get the answer for one week --> 0.1204 radians

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Assuming the orbit is circular, the geometric formulas for a circle apply:

Area = pi*radius²

and

Circumference = 2*pi*radius

What we call a "year" is when earth completes one full orbit around the sun. Therefore, a day is equal to 1/365 of that since there are 365 days in a year. In other words, the distance earth travels in one day is approximately equal to 1/365 of a complete orbit around the sun. So the distance traveled in one year (or one full orbit) can be calculated as the circumference --> (2)*(pi)*(93 million miles).

The distance traveled in one day is therefore equal to [(2)*(pi)*(93 million miles)] / [365].

The distance traveled in one week is the above calculation multiplied by seven --> [(7)*(2)*(pi)*(93 million miles)] / [365].