The distance from the sun to the other focus

Question

The maximum and minimum distances of the earth from the sun respectively are 152 × 10⁶ km and 94.5 × 10⁶ km. The sun is at one focus of the elliptical orbit. Find the distance from the sun to the other focus.

Answer 1

we have an elliptical orbit and let maximum and minimum distance is A and A’ and let S be the sun on the orbit.

we have SA = 152 x 10⁶ km 

we have SA’ = 94.5 x 10⁶ km 

Another focus point is S’ 

The distance between S’ and S be C 

So SA = a + c = 152 x 10⁶ km .......(1)

focus a – c = 94.5 x 10⁶ km.....(2)

We need to find the distance from the sun to the other focus. 

Subtracting (1) and (2) we have 

a + c – (a – c) = 152 x 10⁶ – 94.5 x 10⁶

a + c – a + c = 57.5 x 10⁶ km

So 2c will be the distance from sun to the other focus and it is 57.5 x 10⁶ km