## Traveling through the Solar System

tary probes. The shortest trips, to the Moon, take a few days. The longest trips, to the outer planets, take several years. By comparison, at the speeds of these probes, a trip to the nearest star would take about 20 000 years.

In this section, we look at the mechanics relating to space probes traveling to other planets. It is important to remember that during most of the flight of a planetary probe, it is unpowered. This means that it is simply in an orbit about the Sun. When we talk about orbiting space probes, the mass of the probe is much less than that of the Sun or any planet. We therefore do not have to consider the recoil of the Sun or any planet, making the problem a little easier.

Example 22.2 Orbit and escape from the Earth What is the speed for a circular orbit just above the Earth's atmosphere? How does this compare with the escape velocity?

solution

For an object of mass m, in a circular orbit of radius r, around a planet of mass M, the gravitational force must provide the acceleration for circular motion, so mv2rb _ GMm r r2

where vorb is the orbital speed. Solving for vorb gives