If an astronaut is weightless orbiting the earth at 100 miles up would you experience weightlessness at the top of a 100 mile step ladder What equations would prove or disprove?

Answer 1

The person on the ladder would not feel weightless because they are not in orbit, they are simply at a high altitude. If they let go, they would fall straight down towards the earth's center just as any other object which is being pulled on by gravity.

Orbit is achieved through velocity. With enough thrust, a rocket is able to propel an astronaut to a speed which will send him beyond the earth's gravitational field and straight into space (ie: "escape velocity"). However, by controlling the level of thrust and angle of inclination, the astronaut can be placed in an area of space that is somewhere "in-between" the pull of earth's gravity and the escape velocity. This is called "orbital velocity". The astronaut achieves ORBIT, and he is in a constant free-fall circling around the earth: not quite fast enough to escape the earth's gravity, but not so slow that he falls back to earth.

When a spacecraft needs to return to earth, thrusters are fired in the direction of orbit, which decreases forward speed, and allows the craft to return to earth via the earth's gravitational field with help from atmospheric drag.