Chapter 1.7, Problem 34ES

An Earth-observing satellite has horizon sensors that can measure the angle $\theta$ shown in the accompanying figure on the next page. Let $R$ be the radius of the Earth (assumed spherical) and $h$ the distance between the satellite and the Earth’s surface.

(a) Show that $\sin \theta =\frac{R}{R+h}$ .

(b) Find the angle $\theta ,$ to the nearest degree, for a satellite that is $10,000\text{ km}$ from the Earth’s surface (use $R=6378\text{ km}$ ).