4. consider a satellite orbiting the earth at a height h above the surface. (assume the earth to be spherical with a smooth surface and planetary radius re).
(a) derive an expression for the field-of-view (solid angle) of the earth from the satellite in terms of h and re, what total area can be seen by the satellite at any instant in time?
(b) evaluate these two expressions for (i) a typical polar orbiting satellite (h ~850 km), and (ii) a geostationary satellite ( h ~ 36,000 km). note: one way to check your answer to (a) is to check the limit as h-> 0, and h-> ∞. what should the answers be in these two limiting cases?

the design of a ski jumping suit involves a trade-off between giving the skiers lift to get higher jumps and ensuring the skier does not face a lot of drag before the jump itself. an expansive suit may to lift the skier higher, but at the same time, it will also increase the air resistance. higher air resistance as the skier goes down the slope limits the speed of the jump. a big suit also increases the risk of losing balance or control, especially if there's a strong gust of wind. while technologically enhanced suits a lot, clothing is not the only factor in a ski jumper’s success. gathering speed while skiing down the slope, ensuring good speed on the ramp, and maintaining good body posture and form in the air all contribute to a ski jumper's success.