Exploring Orbital Motion Around Earth

[Guiwee]

orbiting earth!

Hope iposted this question in the right spot!.
If i launched something in space and then stopped its forward momentum
wouldnt the Earth gradually move away from it and pick it up again so to speak..a year later?

 

[Filip Larsen]

Motion is always relative to something, so in this case I assume you mean to stop the motion of an object relative to the sun at some point near the Earth and then want to know if the Earth will move around the sun and then come back to this point a year later? If you were to ignore gravity on the object, then the answer would more or less be yes, but if you include gravity then the answer would be no, as the object would fall toward the sun.

 

[LURCH]

In fact, the object would fall toward the Sun and miss, which is kind of the definition of an orbit. Your object would be pulled into a very ellipticle orbit, with the highest point being equal to the distance from which it originaly fell, which is the distance from the Sun to the Earth (1 AU). Unless it made a close pass by Venus or Mercury, or had some other outside force change its orbit, it would continue going in close to the Sun and back out to where the Earth orbits until it eventually gets to Earth's orbit at the same time Earth is passing through that point in its orbit. Then, of course, it would hit Earth (or Earth would hit it).

 

[Filip Larsen]

In fact, the object would fall toward the Sun and miss, which is kind of the definition of an orbit. Your object would be pulled into a very ellipticle orbit, with the highest point being equal to the distance from which it originaly fell, which is the distance from the Sun to the Earth (1 AU). Unless it made a close pass by Venus or Mercury, or had some other outside force change its orbit, it would continue going in close to the Sun and back out to where the Earth orbits until it eventually gets to Earth's orbit at the same time Earth is passing through that point in its orbit. Then, of course, it would hit Earth (or Earth would hit it).

Any object that is even a bit slower than Earth at Earth's distance from the sun would be in an orbit with a different orbital time than earth, so after a year it it will not be where Earth is. If we assume this special object is put into an orbit where perihelios (closest point to sun) is approximately zero, the period of the object would be around 130 days.

 

[LURCH]

So, how many orbits before it would hit Earth?

 

[Filip Larsen]

So, how many orbits before it would hit Earth?

Well, after one year the object would have done 2 orbits and will be around 22 days from completing its third. In other words, everything else being equal it would miss Earth with 22 days on its third orbit.

 

[Dale]

By the way, the delta v required to get to the sun is very high, much higher than the delta v required to escape the sun. In that sense, the sun is the most difficult place to reach in the universe. You can get anywhere else with less fuel (ignoring, of course, fancy maneuvers like gravitational slingshot etc).

 

[LURCH]

Well, after one year the object would have done 2 orbits and will be around 22 days from completing its third. In other words, everything else being equal it would miss Earth with 22 days on its third orbit.

And, if my rough guesses are close, there is a point about 5 or 6 years out where it misses by lass than a week, and around 10 years down the road I think it gets so close that our gravity would do the rest. These are just estimates by picturing the orbits in my head, of course; I'll try to do the maths (internet has been down for almost a week).

The point is, the two cannot just keep crossing paths forever; they must eventually colide.