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Gravity
Gravity is an attractive force that acts on all objects with mass. It pulls massive objects towards more massive ones. For example, everything on Earth is constantly pulled toward the ground because of the large mass of the planet. However, objects on Earth are also pulling the ground towards them --- but the difference in mass between, for example, a person and the Earth is so huge that this pull is not noticeable.
Gas-filled Objects
Objects filled with low density gas appear to go against gravity. Gravity is acting on these objects, but because of their low mass the force is not enough to pull them toward the ground. What causes these objects to move up through the air away from Earth is that their density is lower than that of the air on the atmosphere. For example, a helium filled balloon will float up because helium gas has a density lower than that of air.
Aircraft
Aircraft appear to go against gravity. They fall into two categories: lighter-than-air and heavier-than-air. Those that are lighter-than-air rely on the same principle as low density gas filled objects to stay in the air, but have equipment that allows the pilot to steer the aircraft and prevent it from floating upwards without stopping. Aircraft that are heavier-than-air, such as airplanes and helicopters, use aerodynamic principles. Wings on an airplane divert the air down and make it flow under the wing faster than it flows over it, giving the airplane lift.
Rockets
Rockets fly so fast that they can escape Earth's gravity. To do this, the kinetic energy given to the rocket during take off must be greater or equal to the gravitational force that pulls the rocket back to the surface of Earth. Escape velocity is the speed the rocket needs to reach to have enough kinetic energy, and it depends only on the mass and radius of Earth. The rocket mass is neglected because it is so small in comparison to the Earth mass. The escape velocity for Earth is approximately 25,000 miles per hour.