What a great question! I love it. The answer is no, but there's much more to the story.

I'll begin to looking at how dust settles in calm air near the ground. That dust experiences its weight due to gravity, so it tends to descend. Each particle would fall like a rock except that it's so tiny that it experiences overwhelming air resistance. Instead of falling, it descends at an incredibly slow terminal velocity, typically only millimeters per second. It eventually lands on whatever is beneath it, so a room's floor gradually accumulates dust. But dust also accumulates on vertical walls and even on ceilings. That dust is held in place not by its weight but by electrostatic or chemical forces. When you go into an abandoned attic, most of the dust is on the floor, but there's a little on the walls and on the ceiling.

OK, now to the space shuttle. The shuttle is orbiting the earth, which means that although it has weight and is falling freely, it never actually reaches the earth because it's heading sideways so fast. Without gravity, its inertia would carry it horizontally out into space along a straight line path. Gravity, however, bends that straight line path into an elliptical arc that loops around the earth as an orbit.

So far no real surprises: dust near ground level settles in calm air and the shuttle orbits the earth. The surprise is that particles of space dust particles also orbit the earth! The shuttle orbits above the atmosphere, where there is virtual no air. Without air to produce air resistance, the dust particles also fall freely. Those with little horizontal speed simply drop into the atmosphere and are lost. But many dust particles have tremendous horizontal speeds and orbit the earth like tiny space shuttles or satellites.

Whether they are dropping toward atmosphere or orbiting the earth, these space dust particles are typically traveling at velocities that are quite different in speed or direction from the velocity of the space shuttle. The relative speed between a dust particle and the shuttle can easily exceed 10,000 mph. When such a fast-moving dust particle hits the space shuttle, it doesn't "settle." Rather, it collides violently with the shuttle's surface. These dust-shuttle collisions erode the surfaces of the shuttle and necessitate occasional repairs or replacements of damaged windows and sensors. Astronauts on spacewalks also experience these fast collisions with space dust and rely on their suits to handle all the impacts.

Without any air to slow the relative speeds and cushion the impacts, its rare that a particle of space dust lands gracefully on the shuttle's surface. In any case, gravity won't hold a dust particle in place on the shuttle because both the shuttle and dust are falling freely and gravity doesn't press one against the other. But electrostatic and chemical attractions can hold some dust particles in place once they do land. So the shuttle probably does accumulate a very small amount of accumulated space dust during its travels.

To the astronauts orbiting the earth, up and down have very little meaning. Because they are falling all the time, these astronauts have no feeling of weight and can't tell up from down without looking. If an astronaut were to look at a person walking on the ground below, that person might easily appear at a strange angle, depending on the astronaut's orientation and point of view.

One possible ion engine uses mercury as a propellant. The mercury starts as a liquid in a small tank, but its atoms slowly evaporate to form a low-density gas. An electric discharge through this gas, such as occurs inside a fluorescent lamp, knocks electrons off some of the mercury atoms. When a mercury atom loses an electron, it becomes a positively charged mercury ion and can be accelerated from the discharge by electric fields. In the ion propulsion engine, an electric field extracts and accelerates the mercury ions toward a hole in the side of a spaceship. The mercury ions are ejected into space at enormous speeds. As they accelerate, the mercury ions exert reaction forces on the engine and these forces are what propel the spaceship forward. Overall, the mercury ions accelerate in one direction while the spaceship accelerates in the other direction. To keep the spaceship electrically neutral, the engine also ejects electrons into space. However, mercury ions provide most of the engine's thrust.

The cart with the small wheels will be easiest to move. That's because, as the cart starts moving, each kilogram of mass in the wheels acquires twice as much energy as each kilogram of mass in the cart itself. Keeping the mass of the wheels low by making the wheels small reduces the energy in the overall cart and makes it easier to start or stop.

Some rockets probably reach the speed of sound in a few hundred feet heading upward, so that reaching the speed of sound in 30,000 feet heading downward would be a simple task. In fact, if you dropped a highly aerodynamic object such as a rocket from 30,000 feet, it could reach the speed of sound even without any propulsion! Gravity alone will accelerate it to about 130% of the speed of sound.

The tower was built long ago on unstable ground that was unsuitable for supporting such a tall and heavy masonry structure. For an object to remain upright indefinitely, its center of gravity must lie above its base of support and that base of support must be firm at all its edges. The tower's base of support had at least one edge that wasn't firm and that began to sink downward under the weight of the tower. Once this edge sunk a small distance, the tower's center of gravity shifted sideways so that it was above that weak portion of the base of support. This shift in the tower's center of gravity put even more stress on the weak part of the ground and caused additional sinking, additional tipping, and even more shifting of the tower's center of gravity. This process might have toppled the tower over by now were it not for recent efforts to stop the tipping. The base of the tower has been reinforced to prevent further tipping.

Yes, everything in the universe exerts gravitational forces on everything else in the universe. However, those forces are usually so small that they are undetectable. The gravitational forces between two bowling balls are only barely measurable in a laboratory. The gravitational forces between two atoms are so small as to be hopelessly undetectable.

Rockets push stored materials in one direction and experience a thrust force in the opposite direction. They make use of the observation that whenever one object pushes on a second object, the second object exerts an equal but oppositely directed force back on the first object. This statement is the famous "action-reaction" concept that is generally known as Newton's third law. While it seems sensible that when you push on a wall it pushes back on you, this situation is extraordinarily general. For example, if you push a passing car forward, that car will still push backward on you with an equal but oppositely directed force. If you push on your neighbor, your neighbor will push back on you with an equal but oppositely directed force even if your neighbor is asleep! In the case of a rocket, the rocket pushes burning fuel downward and the burning fuel pushes upward on the rocket with an equal but oppositely direct force. If the rocket pushes its fuel downward hard enough, the fuel will push up on the rocket hard enough to overcome the rocket's weight and accelerate it upward into the sky and beyond.

Not only is it possible to use electrically powered propulsion, such systems are already in use on several spacecraft. While they don't scavenge atoms and molecules from space, these ion propulsion engines uses electric forces to accelerate ionized atoms to enormous speeds. As the engine pushes on the ions it accelerates, those ions push back on the engine. The ions rush out into space in one direction and the engine experiences a modest thrust in the opposite direction. While the overall thrust from an ion engine is small, it uses its stored-atom "fuel" very efficiently and can be sustained for a very long time in a solar- or nuclear-powered satellite. Ion engines are used in spacecraft that need small but steady thrust for a long time. Scavenging atoms from space would allow these engines to run for an even longer time, but it's probably not realistic. The atoms in space are typically so rare and so fast-moving that they would be more trouble than they're worth.

A mixture of 1 part hydrogen and 19 parts fluorine by weight is the most energetic possible mixture of chemicals, releasing approximately 13,600 joules of energy per gram. The next most potent mixture is 8 parts oxygen and 1 part hydrogen by weight, releasing approximately 13,400 joules of energy per gram. Because fluorine is such a vigorous oxidizer that tends to cause fires, it isn't practical for rocket propulsion. The hydrogen/oxygen mixture is the basis for the Single Stage to Orbit rockets that are currently being developed. -- Thanks to Gary V. Lorenz at NASA for help on this question.

If the orbiting object doesn't interact with anything but the earth, then the answer is: no, it will continue to orbit forever. That's because, although it is always falling and accelerating toward the earth, its sideways velocity continues to make it miss the earth. It just keeps on missing forever. Moreover, its total energy remains constant--the sum of its kinetic and gravitational potential energies. But if something removes some of its energy, it will gradually shift closer and closer to the earth and will reenter the atmosphere. That reentry occurs for low-lying satellites because they interact with the diffuse atoms in the extreme upper atmosphere. These satellites gradually lose energy and eventually come down in a blaze of frictionally heated material.

When gas is moving slowly through a channel, it can respond to obstacles by flowing around them. For example, when the gas encounters a constriction in the channel, it speeds up to flow quickly through the narrowing and its pressure drops. But when the gas is moving very fast through the channel, it has trouble avoiding obstacles and behaves differently at a constriction. Instead of speeding up to flow smoothly through the narrowing, the gas collides with the walls of the constriction and is pressure rises. It just wasn't able to "sense" the presence of the constriction before it actually hit the constriction. When gas moves faster than the speed of sound in that gas, it can't anticipate changes in its environment and it doesn't follow Bernoulli's equation. That's why the nozzle of a rocket flares outward to handle the supersonic gas that emerges from the nozzle's throat. That high-speed gas experiences a pressure drop as it spreads out into the broad portion of the nozzle. The gas's density drops and its pressure goes down.

Sticks and fins both shift a rocket's center of aerodynamic pressure (center of drag) toward the tail of the rocket and behind the rocket's center of mass. As a result, the tail of the rocket normally remains at the rear during flight. The passing air twists the tail of the rocket until it's at the rear of the moving object.

A rocket engine works by ejecting stored material. It pushes on this material to make the material accelerate and the material pushes back on the engine. If the force that the ejected material exerts on the engine is upward and greater than the rocket's weight, the rocket will accelerate upward.

Most rocket engines are chemical engines. They combine stored chemical fuels to produce hot, high-pressure gas. This gas is allowed to expand out of a narrow orifice--the throat of the engine's exhaust nozzle. Gases always accelerate toward lower pressure, so the high-pressure gas moves faster and faster as it rushes out of the nozzle. It reaches sonic velocity (the speed of sound) in the nozzle's throat and continues to move faster and faster as it flows out of the nozzle's widening bell. By the time the gas leave the engine completely, it's traveling several thousand meters per second. A liquid fuel rocket has an exhaust velocity of about 4,500 meters per second or about 3 miles per second. Accelerating the gas to this enormous speed takes a huge force--the engine pushes down hard on the gas. The gas pushes back and propels the rocket upward.

Momentum is a vector quantity, meaning that it has both an amount (a magnitude) and a direction. When two objects are moving rapidly away from one another, they each have momentums but those momentums are in opposite directions. When you add these momentums together to find the total momentum of the two objects, you must consider the directions of those individual momentums. If the two momentums are exactly equal in magnitude but opposite in direction, they will cancel when you add them together and the total momentum will be exactly zero.