Projectiles And Orbits question--Newtons cannon (1 Viewer)

[Roobs]

"Ignoring Air Resistance, could an object be launched such that it lands 3/4 of the way around earth? Why?"

My initial thought was no, any more than half way around and the projectile would continue in an orbit, but i dont know if this is right or not

any help/thought appreciated, especially a way of proving the answer

thanks

 

[Riviet]

"Ignoring Air Resistance, could an object be launched such that it lands 3/4 of the way around earth? Why?"

This question is referring to the orbital velocity of an object. We know that when an object reaches a particular velocity, it will continue to orbit around the earth. If it is slightly faster, then its flight will follow an elliptical orbit. If the object is has a velocity that is slightly slower than the orbital velocity, then as it travels around the earth, it will curve around the earth, but since its velocity is not fast enough for it to curve away and maintain the orbit, it will very gradually approach the earth's surface due to the gravitational force overcoming it. Therefore it will eventually land on the ground.

 

[zeek]

If by air resistance you mean any type of resistance such as wind, cosmic particles etc. then no, it cannot land on the earth after it travels 3/4 of the earth's circumference. The reason for this is if the satellite were to travel 3/4 of the earth's circumference, then it would need to have reached escape velocity to get past half way or else it would be pulled to earth by gravity and atmospheric friction. Once it reaches escape velocity then it will begin orbital velocity and at this stage it will be past half way and gravity will have no effect on its orbital path. The only thing that can bring down the satellite would be atmospheric friction from particles however, in this case, it has been disregarded. So no, the satellite will not land after 3/4 of the earth's circumference.
Riviet, if you look at the orbital velocity formula, then you would find that the earth's gravity will have no effect on the velocity of the satellite; hence it cannot pull the satellite to the surface. Furthermore, for the satellite to even go past half way, it would have to be launched at an angle that would project it into space.

 

[Riviet]

Ah good point made, since the earth's gravitational force doesn't affect the orbital velocity, then I would agree that it can't land past half way of its orbit around the earth.

 

[Roobs]

thanks..good to have that one cleared up.....