Question

Observing the solar system model of concentric circles with center being the sun. The Earth is 1 AU from the sun. 1 AU is equal to about 150 million kilometers (93 million miles). Using a scale factor of 10¹⁰​ meters per astronomical unit (AU); let say that the Earth is 15 meters away from the sun. And let say, Earth takes on an average 365 days to complete a full cycle around the sun.

How far Earth travels in its orbit in one day?   What would be its speed?

​

Answer 1

Solution -

According to question,

We have to assumed that

the distance sun and earth = radius of the circular orbit = R = 15 meters.

Earth completes one revolution in t= 365 days.

Now, circumference of the circlular orbit in which earth rotates is

= 2×π× Radius of circular orbit

= 2×π × 15

=30π

Now, since in one revolution Earth travels = 30π meters

So, we can say in 365 days earth travels = 30π meters.

So, in 1 day earth travels =30π/365 = 0.258213095 meters.

Hence, Earth travels 0.258213095 meters in one day where 15 meters is equivalent to meters per AU.

(b)

Speed of the earth is same as calculated above . It means speed of the Earth is 0.258213095 meters per day.

Hence, speed of the earth is 0.258213095 meters per day, where 15 meters is equivalent to meters per AU.