The ancient Greek Eratosthenes found that the Sun casts different lengths of shadow at different points on Earth. There were no shadows at midday in Aswan as the Sun was directly overhead. 800 kilometers north, in Alexandria, shadow lengths were found to show the Sun at 7.2 degrees from overhead at midday. Use these measurements to calculate the radius of Earth.

The  radius of the earth is

Explanation:

From the question we are told that

     The distance at  Alexandria is  

      The angle of the sun is  

So we want to first obtain the circumference of the earth

   So let assume that the earth is  circular ()

  Now from question we know that the sun made an angle of so with this we will obtain how many    are in

 i.e    

=>      

     With this  value we can evaluate the circumference as

Generally circumference is mathematically represented as

=>        

jupiter is the largest planet in our solar system, having a mass and radius that are respectively, 318 and 11.2 times that of earth. suppose that an object falls from rest near the surface of each planet and that the acceleration due to gravity remains constant during the fall. each object falls the same distance before striking the ground. determine the ratio of the time of fall on jupiter to that on earth.