Orbital speed

[Nachtwind]

Hi,

I was thinking about a mind experiment and i wonder where i go wrong because this cant be right at all...

So if you launch a craft from Earth the speed for a stable orbit decreases with altitude. So.. the higher you go the less speed you need to stay in said orbit. I hope we can agree on that part

So.. my problem is.. if you go higher and higher in altidude - and if you werent affected by any other sources of gravity (for instance you make a solar orbit and increase its altitude) you reach a point where it takes you 1m/s to stay on the orbit.. and what then? If you go up further your relative speed tends to 0... but is that even possible? I mean.. at one point your relative speed will be so close to 0 that pretty much no movement is needed anymore, is it (of course this is ridicolous altitude we are talking here.. but still..)? Is there even a point where relative speed can drop to 0 at all? That question sounds stupid to me, but since velocity tends to 0 it should at some point reach it, or not?

[Holo]

Hi,

I was thinking about a mind experiment and i wonder where i go wrong because this cant be right at all...

So if you launch a craft from Earth the speed for a stable orbit decreases with altitude. So.. the higher you go the less speed you need to stay in said orbit. I hope we can agree on that part

So.. my problem is.. if you go higher and higher in altidude - and if you werent affected by any other sources of gravity (for instance you make a solar orbit and increase its altitude) you reach a point where it takes you 1m/s to stay on the orbit.. and what then? If you go up further your relative speed tends to 0... but is that even possible? I mean.. at one point your relative speed will be so close to 0 that pretty much no movement is needed anymore, is it (of course this is ridicolous altitude we are talking here.. but still..)? Is there even a point where relative speed can drop to 0 at all? That question sounds stupid to me, but since velocity tends to 0 it should at some point reach it, or not?

Velocity does tend to 0, but you need to be an infinite distance away from the parent body for that to happen. The rest is all correct - as you move far away, gravity becomes so weak that barely any speed is needed to counteract it.

[Ralathon]

Yea you're correct. If you have 2 masses at infinite distance of one another their relative velocity for an orbit would be 0. This makes sense if you look at the equations for (newtonian) gravity:

F = G*M*m/r^2. If you move 2 objects apart the upper term would stay the same but the lower term would quickly become huge. At infinite distance you get:

F = x/infinite = 0. So there is no pull between the objects. Without pull you can't make an orbit with a speed above 0.

[Kerbart]

Is there even a point where relative speed can drop to 0 at all? That question sounds stupid to me, but since velocity tends to 0 it should at some point reach it, or not?

Theoretically no, as that distance would be "infinity" but there are some practical limitations to that:

• The size of the universe is limited (we think)
  
• Gravity of earth will become such a small force that it gets "overruled" from other planets/stars
  

Keep in mind that this is basically how you calculate the escape velocity--how much energy does it take to reach an infinite distance (where speed required for orbit is 0) and then express that as all velocity at the surface.

[Rjhere]

Well, if you were in a universe with only one gravitational object, no matter were you are, billions upon billions of light years away from... say Earth, eventually you will be dragged against the object. Black holes in, let's say the Triangulum galaxy affects us. Gravity affects everything app. infinite. But yea, there's a distance where the gravitational pull from the object is insignificant.

[Mr Shifty]

The Earth's SOI is about 925,000km. Further away than that, Sol's gravity dominates. So it's not possible to get an infinite distance away from the Earth while still subject solely to Earth's gravity. If you're going exactly escape velocity, your relative speed at the edge of Earth's SOI would be about 925 m/s. (Contrast with orbit speed in LEO of about 7500 m/s.)

[WestAir]

Assuming the Earth is the ONLY gravitational object in the universe (besides yourself), assuming the Universe is finite in size, and assuming that there is a point where information can be made no smaller (Plank Length) that exists, the answer in practice is yes, you can orbit at 0 velocity.

The reason is that, while mathematically you should always have a velocity above 0, if there is a point where information can be made no smaller, than there's a point where you can travel no slower (which would be something on the order of 1 Plank Length per Age of the Universe), which would be equal to zero, yet still be a viable orbital velocity at a given distance and beyond.

[Nachtwind]

Thanks for the interestering answers. Ralathon your answer is, though mathematical, nice to understand and westair, yours is nice to imagine!

Well, thanks for the insight :0)