Gravity

Mathematically, this gravitational force between two objects can be represented as:

where M₁ is the mass of the first object (in kilograms), M₂ is the mass of the second object (in kilograms), k is a gravitational constant always equal to 6.67 x 10¹¹ newton m²/kg², and the pro duct of all three is divided by the square of the distance, d (in meters), between the two objects. By canceling all the units (which is the key to doing physics well), you can see that the force of gravity is expressed in newtons, named aft er you know who! From this relationship, we can see that the greater the masses of the attracting objects, the greater the force of attraction between them. We can also see that the farther apart the objects are from each other, the less the attraction.

Because of the Earth's large mass, compared with ours, and because we are usually very close to the Earth (unless we are taking a plane trip), we stay firmly attached to the surface. However, the farther we distance ourselves from the center of the Earth, the weaker that pull of gravity becomes. When an astronaut is circling the Earth in a spacecraft, the Earth's gravity still tries to pull the spacecraft back to Earth. However, the velocity (speed) of the spacecraft can overcome the Earth's downward pull if the spacecraft is traveling fast enough.

One way to envision this effect is to imagine a person here on Earth throwing a baseball in the horizontal direction (Figure 6). What happens? The ball starts to fly forward but immediately begins to drop towards the ground after leaving the person's hand. The ball is eventually pulled to the ground by gravity. If that person were to throw the ball faster, gravity would pull it down at a farther point. If that person could throw the ball fast enough to overcome the downward force of gravity, and if the ball were able to continue at this velocity, the ball would orbit the Earth. One important fact to remember is that orbits within the Earth's atmosphere do not really exist. Atmospheric friction caused by the molecules of air (causing a frictional heating effect) will slow any object that could try to attain orbital velocity within the atmosphere.

Figure 6. The Earth's gravity pulls everything toward the Earth. In order to orbit the Earth, the velocity of a body must be great enough to overcome the downward force of gravity (although within the Earth's atmosphere, it is actually impossible to attain the velocity necessary to orbit continuously).

In space, with virtually no atmosphere to cause friction (at least above 100 miles in altitude), the space shuttle can travel at velocities strong enough to counteract the downward pull of Earth's gravity (over 17,000 miles per hour). If the spacecraft were not orbiting the Earth with enough velocity to balance out the pull of gravity, it would fall back to Earth. (In fact, the space shuttle returns to Earth by slowing down and allowing gravity to recapture its hold on the spacecraft.) Everything inside the spacecraft is also traveling at this same velocity, including the human beings! The speed of the spacecraft "forward" creates an outward (centrifugal) force that balances the "downward" gravitational force on the spacecraft and everything inside it. The spacecraft and the astronauts inside are said to be in free fall, which is the same as "floating."

A good way to imagine free fall using an Earthbound example is to consider two people in an elevator. If the elevator cable were to break, the elevator and the people inside would begin to fall and eventually reach the same velocity. The people would begin to float inside the elevator car until the car slowed down, thanks to the special umbrella emergency system! We have all felt the effects of a fast-moving elevator where it feels like it left us behind for a moment. Unfortunately, or fortunately considering the consequences, the elevator usually does not go fast enough for us to float.

As a spacecraft orbits the Earth, the astronaut experiences weightlessness because nearly all the forces on the body are balanced. If astronauts could somehow step on a normal bathroom scale in space, although they could not do this without tying themselves down, the scale would read zero. Because of weightlessness, many actions that are impossible on Earth become possible in space. For instance, crew members can turn somersaults with ease as they float through the spacecraft. Very heavy objects that might take two or three strong adults to move even an inch on Earth can be moved with merely a pinkie finger in space.