posted by sarah on .
The Hubble Space Telescope is orbiting Earth 600 km above Earth's surface. Earth's radius is about 6370 km. Use the Pythagorean Theorem to find he distance a from the telescope to Earth's horizon. Round your answer to the nearest ten kilometers.
Draw the figure. Note it is a right triangle, with hypotenuse of (Rearth+altitude), legs of Rearth, and of what you want to find.
There is a right trangle formed by points at the center of the Earth, the HST satellite and the point where a line from the satellite is tangent to the Earth. The hypotenuse (c) goes from the HST to the center of the Earth, and its length is 600 + 6370= 6970 km. The side that you want is
b^2 = c^2 - a^2, where a is the radius of the Earth.
b^2 = (6970)^2 - (6370)^2
b = 2829 km