Why an object thrown into the air don't get left behind by earth as it rotates on its axis or moves about the sun?

Answer 1

The atmosphere (the air around the earth held there by gravity) is spinning with the earth so when you throw somthing into the air, the air will not stop the object which already was moving with the earth. Think about being in a car... you can throw a tennis ball up and down easily because the air inside your car is also moving. Try throwing it out the window and the stationary air (with respect to your car) will slow down the ball.

Answer 2

They do fall to earth.

To maintain long-term orbits, rockets are used to minimally boost the satellite's speed to maintain it's height above the earth.

When some satellites come to the end of their lives they are allowed to return to the atmosphere, where some of them burn up and the residue can fall harmlessly to earth.

answ2. Newton maintains that a body will continue in its position of motion or rest until a force acts on it.

A Body rotating at an altitude round the Earth, is at each individual moment moving at a tangent to its orbit. If the Earth's gravity were switched off at that moment, the body would continue along its straight line path (its 'tangent' path). And escape into space.

But equally, at each individual moment, the Earth's gravity exerts a pull on the body. If the gravity pull is exactly balanced by the tangent force, then the body will continue in its orbit.

If the gravity was stronger, (or the tangent force weaker) the body would spiral into the Earth.

If the Gravity were weaker (or the tangent force stronger), the body would escape into space.

In practice, even at altitude, there is some drag, and a satellite needs an occasional boost to maintain its orbit. Or it WILL fall.