This week the moon is waxing and moving across familiar territory along the ecliptic past Jupiter and through Sagittarius. The moon is, of course, a satellite of the earth. That is to say, it is held in an orbit by earth's gravity and is close enough to the earth that when it is visible it dominates the night sky. There are, of course, many other satellites orbiting earth. These are man-made satellites and they too can be exciting to see in part due to their rarity and in part due to their unusual motion or brightness. The most distinctive satellite we can see on a regular basis is the International Space Station, also known as ISS. It orbits the earth every 90 minutes and is approximately 200 miles above the earth. It makes a fairly constant trip around the earth but each time it does so, the earth rotates part of the way through the day. ISS is quite large (about the size of a football field) and reflects sunlight very well, so when it passes directly overhead just after sunset or just before sunrise (when our skies are darkened but ISS is still in sunlight), it shines very brightly and moves quickly across the sky, much faster than airplanes.
If you want to get a look at this, you need clear skies, attentive eyes, and an accurate wristwatch. NASA maintains a website with all the details when it will appear over which parts of the United States. The website address is http://www.jsc.nasa.gov
Good luck and happy viewing.