1. **State the problem:** We have two satellites orbiting Earth. The first satellite's orbit is a circle with equation $x^2 + y^2 = 56250000$. The second satellite's orbit is 200 km farther from the center of the Earth. We need to find how much farther the second satellite travels in one orbit compared to the first. 2. **Identify the radius of the first orbit:** The equation $x^2 + y^2 = r^2$ represents a circle with radius $r$. Here, $r^2 = 56250000$, so $$r = \sqrt{56250000}$$ Calculate $r$: $$r = 7500 \text{ km}$$ 3. **Radius of the second orbit:** The second satellite's orbit radius is 200 km farther, so $$r_2 = 7500 + 200 = 7700 \text{ km}$$ 4. **Calculate the circumference of each orbit:** The circumference $C$ of a circle is given by $$C = 2\pi r$$ For the first satellite: $$C_1 = 2\pi \times 7500 = 15000\pi \text{ km}$$ For the second satellite: $$C_2 = 2\pi \times 7700 = 15400\pi \text{ km}$$ 5. **Find the difference in distance traveled:** $$\text{Difference} = C_2 - C_1 = 15400\pi - 15000\pi = (15400 - 15000)\pi = 400\pi \text{ km}$$ 6. **Calculate the numerical value:** $$400\pi \approx 400 \times 3.1416 = 1256.64 \text{ km}$$ **Final answer:** The second satellite travels approximately 1256.64 km farther in one orbit than the first satellite.