Question

Two satellites are orbiting Earth. The path of one satellite has the equation x^2 + y^2 = 56250000. The orbit of the other satellite is 200km farther from the centre of Earth. In one orbit, how much farther does the second satellite travel than the first satellite?

Answer 1

1,257 km

Explanation:

The path of one satellite has the equation

`x^2 + y^2 = 56,250,000\\ \\x^2+y^2=7,500^2`

This is the equation of the circle with the center at the origin (Eartg) and the radius of 7,500 km.

The orbit of the other satellite is 200 km farther from the centre of Earth, so the radius of this orbit is 7,700 km.

Find the distances travelled by two satellites:

1st satellite:

`D_1=2\pi r_1=2\pi \cdot 7,500=15,000\pi \ km`

2nd satellite:

`D_2=2\pi r_2=2\pi \cdot 7,700=15,400\pi \ km`

Difference:

`D_2-D_1=15,400\pi -15,000\pi =400\pi \approx 1,257\ km`