Daniel O. answered • 12/12/12

Math and Physics Tutor, with a math and physics degree

The equation of the satellite's orbit is given in the form:

x^{2} + y^{2} = r^{2}

Which is the equation of a circle, where r is the radius. Since the equation is:

x^{2} +y^{2} = 2250000

r^{2} is therefore 2250000, so take the square root of it to find r

r^{2} = 2250000

r = √2250000 = 1500km

As Robert showed, you don't actually need to find the radius in this case, but you can use it if you like. Since the second satellite's radius is given by (r+200)km, to find how much further the second satellite travels, subtract the circumference of the first satellite from the circumference of the second:

2π(r+200) - 2πr = 2π(r+200-r) [I took out a common factor of 2π from both terms]

= 2π*200 = 400π km

If you did this using the radii, you'd do it like so:

2π*1700 - 2π*1500 = 2π(1700-1500) [again, I took out a common factor of 2π]

= 2π*200 = 400π km

So, you can see we get the same answer regardless of whether we actually use 1700km and 1500km, or (r+200) and r as the radii.

Sabrina Y.

I know r is the radius, but what is the radius?

12/11/12