Question

An artificial satellite of the Earth releases a bomb. Neglecting air resistance, the bomb will never strike Earth

Why never striking earth? can you explain deeply? why it will continue to orbit and never actually fall to earth?

An astronaut in an orbiting space-craft feels weightless because she has the same acceleration as the space-craft why both in free fall?

Answer 1

An artificial satellite of the Earth releases a bomb. Neglecting air resistance, the bomb will never strike Earth because :-

It will continue to orbit and never actually fall on the earth, it will remain in orbit with the satellite. once something is in orbit, it requires energy (eg, a rocket) to leave orbit and return to earth.

At the current speed there is no RELATIVE force. The bomb stays in the same orbit as its satellite.
If you take energy from the bomb so it is slower than the satellite it goes into an elliptical orbit. At some points a bit closer to the earth.

When something "falls" it can be shown to be an elliptical orbit of width zero.
ie it has NO velocity perpendicular to the earth.
If you have "projectile motion" that too is part of an elliptical orbit.
It would orbit EXCEPT that the earth gets in the way.

So to actually reach the earth you need to slow the bomb down so much that its elliptical orbit actually intersects the earth so that it lands SOMEWHERE on earth.
Now the moving satellite ( or bomb) produces gravity that has tidal effects.
So they DO slow down eventually. One day they crash on the surface of the earth.
The location is usually only predictable within the last few days of its motion.
So all those thousands of satellites would eventually crash in unpredictable locations upon the earth.

2. Earth-orbiting astronauts are weightless for the same reasons that riders of a free-falling amusement park ride or a free-falling elevator are weightless. They are weightless because there is no external contact force pushing or pulling upon their body. In each case, gravity is the only force acting upon their body. Being an action-at-a-distance force, it cannot be felt and therefore would not provide any sensation of their weight.

But for certain, the orbiting astronauts weigh something; that is, there is a force of gravity acting upon their body. In fact, if it were not for the force of gravity, the astronauts would not be orbiting in circular motion. It is the force of gravity that supplies the centripetal force requirement to allow the inward acceleration that is characteristic of circular motion. The force of gravity is the only force acting upon their body. The astronauts are in free-fall.

Like the falling amusement park rider and the falling elevator rider, the astronauts and their surroundings are falling towards the Earth under the sole influence of gravity. The astronauts and all their surroundings - the space station with its contents - are falling towards the Earth without colliding into it. Their tangential velocity allows them to remain in orbital motion while the force of gravity pulls them inward.