How can projectile fall around the earth

We call this sideways motion tangential velocity. With sufficient tangential velocity, the Moon and all artificial Earth satellites fall around rather than into our planet. He reasoned that a projectile with sufficient speed could circle Earth without touching its surface Figure 1. He saw the Moon as a projectile.

Figure 1. This drawing by Isaac Newton shows that a cannonball fired fast enough from a tall mountain could fall all the way around Earth without touching its surface. If somehow gravity between Earth and the Moon suddenly vanished, then—like a stone released from a swinging slingshot—the Moon would fly off in a straight-line path. But because gravity does act on the Moon, it falls beneath the straight-line path it otherwise would follow Figure 2.

Figure 2. Two ways to know something falls: It gets closer to the floor left or farther from the ceiling right. Although a thrusting force put the ISS into orbit, once it attained sufficient tangential velocity it could orbit solely due to gravity. Except for small corrections, the only force keeping any Earth satellite in orbit is gravitational. How much velocity is needed for orbit? How much velocity does a projectile need to orbit Earth? The calculation is straightforward if we know two things.

A tossed object, whether a ball or satellite, falls vertically beneath where it would have been if there were no gravity. The dashed line in the figure shows the path that would be taken if gravity were absent. Figure 3. A horizontally tossed ball falls beneath the dashed line a vertical distance of 5 m in its first second of fall—regardless of its initial velocity. So the second thing to know to calculate orbital speed is that the surface of Earth curves a vertical distance of 5 m for each 8, m tangent Figure 4.

Therefore, if air resistance can be neglected, what minimum velocity is needed for a projectile to orbit Earth? Figure 4. Its curved path would match the curvature of Earth— and it would be in Earth orbit Figure 5.

Figure 5. The curved line shows the orbital path. Falling around Earth In the real world, air resistance and obstructions near the surface of Earth would not allow a projectile to maintain its orbital speed. Indeed, a satellite is accelerating towards the Earth due to the force of gravity. Finally, a satellite does fall towards the Earth; only it never falls into the Earth.

To understand this concept, we have to remind ourselves of the fact that the Earth is round; that is the Earth curves. In fact, scientists know that on average, the Earth curves approximately 5 meters downward for every meters along its horizon. If you were to look out horizontally along the horizon of the Earth for meters, you would observe that the Earth curves downwards below this straight-line path a distance of 5 meters.

In order for a satellite to successfully orbit the Earth, it must travel a horizontal distance of meters before falling a vertical distance of 5 meters. A horizontally launched projectile falls a vertical distance of 5 meters in its first second of motion. When launched at this speed, the projectile will fall towards the Earth with a trajectory which matches the curvature of the Earth.

As such, the projectile will fall around the Earth, always accelerating towards it under the influence of gravity, yet never colliding into it since the Earth is constantly curving at the same rate. Such a projectile is an orbiting satellite. To further understanding the concept of a projectile orbiting around the Earth, consider the following thought experiment.

Suppose that a very powerful cannon was mounted on top of a very tall mountain. Suppose that the mountain was so tall that any object set in motion from the mountaintop would be unaffected by air drag. The animations below depict these ideas. Two final notes should be made about satellite motion. Second, there is an upper limit on the orbital speed of a satellite.

If launched with too great of a speed, a projectile will escape Earth's gravitational influences and continue in motion without actually orbiting the Earth. Such a projectile will continue in motion until influenced by the gravitational influences of other celestial bodies.