The radius of the earth is approximately 6371 km.If the international space station (ISS) is orbiting 353 km above the earth, find the distance from the ISS to the horizon(x)
x^2 + 6371^2 = (6371+353)^2
x = 2150
To find the distance from the ISS to the horizon, we can use the Pythagorean theorem. Let's consider a right triangle with the following dimensions:
- The radius of the earth (r) = 6371 km
- The altitude of the ISS (h) = 353 km
- The distance from the ISS to the horizon (x) = ?
Using the Pythagorean theorem, the equation becomes:
(r + h)² = r² + x²
Substituting the given values, we have:
(6371 + 353)² = 6371² + x²
Simplifying:
(6724)² = 40482641 + x²
44992776 = 40482641 + x²
44992776 - 40482641 = x²
4510135 = x²
Taking the square root of both sides:
x = √4510135
Hence, the distance from the ISS to the horizon is approximately 2125.50 km.