Q&A on Orbits: Throwing Balls in Space

[yalgaar]

I am new to this forum so do not know all the rules of posting. So please don't mind if I have missed something. I have not been doing any physics and stuff for many many years, but have been having lots of curiosity about stuff, so will dare to ask it here.

I understand that orbits are due to gravity. I have read ton of articles on this but it still does not make sense to me. So in my example I will exclue moon an sun so to get a better idea.

If I throw a ball in the space, it will come back to earth.

If I throw a ball at much fast speed, it will come down but will have a little curve.

If I throw it fast enough, it will form an orbit around earth.

Bases on my 3 statements above, following are my questions:

1) Are all my statements above true?
2) How fast I need to throw the ball so that it forms an orbit around earth?
3) How far will be the orbit from Earth and why?
4) What will be the shape of the orbit? will it be perfect circle or ellipical?
5) How fast I have to throw so that it just blows away in the space, free of gravity of earth?

I know the above questions are pretty basic, but I am really trying hard to understand and reading so much articles are just confusing me more and more.

Thanks in Advance.

 

[mgb_phys]

You are almost there - it is a question of both speed and direction.
If you throw an obect straight up with enough speed that it's kinetic energy eqauals the gravitational potential energy it will travel away for ever. This speed is called the escape velocity and is approx 11km/s for Earth.

To get into orbit you have to fire an object perpendicular to the surface. For any given height there is a speed which will cause it to fall at just the correct rate to follow the curvature of the Earth, so it will be in orbit. There is nothing special about space, you could be in orbit at ground level if it wasn't for the atmosphere slowing you down, the only reason rockets go up first is to get out of the atmosphere. Without an atmosphere on eg. the moon you could fire a bullet into orbit at head height!.

The usual example of this is a cannon firing from the top of a mountain, as in this game
http://spaceplace.nasa.gov/en/kids/orbits1.shtml

You can easily work out the time for one orbit (called the period ) and so the speed from the equation:
Time = 2 * pi * sqrt ( a^3 / G M )
Where, a is the radius of the orbit (from the centre of earth) M is the mass of the Earth and G is the gravitational constant.

The lowest practical orbit (high enough to avoid atmospheric drag) is about 500km above the surface with a period of 90mins and a speed of around 7km/s.

Orbits are elliptical, but without anything to disturb them are almost circular. Remember a circle is just a special ellipse and like a straight line doesn't exist in nature - which is why we say orbits are elliptical.

 

[pixel01]

1) Not all, in the 1st statement, you should mention the velocity.
2)You have to throw at least at ~7.5 km/s to bring the object to the near orbit of the Earth
3)Theoretically, the orbit can be just above the surface. But there is the dense atmosphere so all the satellites should fly at about more than ~200km.
4)The shape of orbit normally eliptical. Satellites need to use jet engines to drive themselves into circle orbits.
5)That's the escape velocity : about 11.2km/s.

Hope this helps.

 

[yalgaar]

You are almost there - it is a question of both speed and direction.
If you throw an obect straight up with enough speed that it's kinetic energy eqauals the gravitational potential energy it will travel away for ever. This speed is called the escape velocity and is approx 11km/s for Earth.

To get into orbit you have to fire an object perpendicular to the surface. For any given height there is a speed which will cause it to fall at just the correct rate to follow the curvature of the Earth, so it will be in orbit. There is nothing special about space, you could be in orbit at ground level if it wasn't for the atmosphere slowing you down, the only reason rockets go up first is to get out of the atmosphere. Without an atmosphere on eg. the moon you could fire a bullet into orbit at head height!.

The usual example of this is a cannon firing from the top of a mountain, as in this game
http://spaceplace.nasa.gov/en/kids/orbits1.shtml

You can easily work out the time for one orbit (called the period ) and so the speed from the equation:
Time = 2 * pi * sqrt ( a^3 / G M )
Where, a is the radius of the orbit (from the centre of earth) M is the mass of the Earth and G is the gravitational constant.

The lowest practical orbit (high enough to avoid atmospheric drag) is about 500km above the surface with a period of 90mins and a speed of around 7km/s.

Orbits are elliptical, but without anything to disturb them are almost circular. Remember a circle is just a special ellipse and like a straight line doesn't exist in nature - which is why we say orbits are elliptical.

Thanks a lot for your reply. The link you sent me was pretty good. Made things even more clear for me. I still have more questions.

1) You say orbits are almost circular if nothing to disturb them. In this case what is distrubing all the planents? I believe none of the orbits of any of the planets is circular?

2) In the cannnonball example, once you shoot it with a certain speed, it stays in the orbit. Am I right to think that this is becuase there are 2 forces acting on this. 1) the Gravity of Earth 2) the force that I created on the cannonball by throwing it at certain speed and becuase of Newtons law of motion where a moving body keeps moving, the force stay on the ball forever?

 

[yalgaar]

1) Not all, in the 1st statement, you should mention the velocity.
2)You have to throw at least at ~7.5 km/s to bring the object to the near orbit of the Earth
3)Theoretically, the orbit can be just above the surface. But there is the dense atmosphere so all the satellites should fly at about more than ~200km.
4)The shape of orbit normally eliptical. Satellites need to use jet engines to drive themselves into circle orbits.
5)That's the escape velocity : about 11.2km/s.

Hope this helps.

Great! Thanks a lot. More Questions so I can understand this better.

1) So basically anything with less then 7.5 km/s velocity will fall back on Earth and anything with more then 11.2 km/s velocity will escape Earth into space?

2) What kind of orbits will be formed when they are thrown at a velocity of a) 7.5 km/s b) 8.5 km/s c) 9.5 km/s and d) 10.5 km/s

 

[Janus]

You actually need to reach a little over 7.9 km/ sec to achieve orbit, but you get a little assist from the fact that the Earth turns, and at the equator gives you an extra 463 km/sec. So if you throw in the same direction as the Earth is turning you only have to supply the 7.5 km/sec
With these answers I'll assume that that the speeds are the Throwing speed and that you are throwing from the equator and in the direction of Earth's rotation. I will also ignore atmospheric drag.

a. nearly circular with a period of 1.4 hrs

b. elliptical with an apogee altitude (greatest distance from the surface of the Earth) of 8407 km and a period of 2.3 hrs
c. elliptical with an apogee altitude of 19256 km and a period of 5.3 hrs
d. ellipitical with an apogee altitude of 242922 km and a period of 67.5 hrs

 

[russ_watters]

1) You say orbits are almost circular if nothing to disturb them. In this case what is distrubing all the planents? I believe none of the orbits of any of the planets is circular?

The planets disturb each other, mostly.

2) In the cannnonball example, once you shoot it with a certain speed, it stays in the orbit. Am I right to think that this is becuase there are 2 forces acting on this. 1) the Gravity of Earth 2) the force that I created on the cannonball by throwing it at certain speed and becuase of Newtons law of motion where a moving body keeps moving, the force stay on the ball forever?

The force doesn't stay on the ball forever, Newton's first law says a force is required to change the speed.