Why aren't artificial satellites ripped apart by gravitational tidal forces of the earth?
In short, the pieces of a satellite are held together by chemical, molecular bonds, which are strong compared to the tidal forces that are weak for objects the size of artificial satellites and gravity sources the strength of the earth.
A tidal force is the difference in attraction between two distances from a gravitational source. For a small object such as a natural satellite, that is just a few meters, gravity simply won't vary much between the nearest and farthest points unless you're talking about a orbiting a neutron star or black hole extremely closely.
For instance the ISS is 100m along its longest axis. Say that axis is perpendicular to the earth's surface. If its nearest point to earth is at 400km from the surface, the farthest point is therefore 400.1km. But earth is 5371km radius, so the distance from the center (where the gravity "seems" to be coming from) is 5771km and 5771.1km.
Gravity falls off at 1/(distance squared), so the difference in gravity is (1/(5771^2)) / (1/(5771.1^2)). That's a difference of 3*10^-8, or .000003% difference.
Gravity at earth's surface is 1G, giving 1kg mass 9.8N (newton) force (what you feel when you hold up 1kg on earth's surface). At 400km altitude it'd be 9.8*5371/(5371+400))^2=8.4N . So if you had even 1,000,000kg at each end of a 100m rope at that altitude, 1,000,000 * 8.4N * .000003% = .25N, about what you feel were you to pick up 25g of coins right now. (About 5 nickels.)
Even a human hair is strong enough to hold 25g at the earth's surface, and further, satellites aren't that heavy, and are far stronger than a hair.