Orbital math/tiny object orbits - questions

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Sword7

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Hello folks,

Ok, thanks for many replies about gravity. I have two questions for you...

I have a question about orbit with small objects like hammer, golf ball, etc.. In space, can tiny objects (some inches to 3-4 feet diameters) like hammer, ball, etc. orbit each others? Is that possible to try them inside space station? If so, how fast do they orbit each others?

Also, I have another question about speed setting for spacecrafts or planets. How do I set a speed in vector for each object to orbit? If no speed set, it would fall toward other larger object, etc. I was looking for formula through my astrodynamc book but can't find them. Does anyone have any resources about formula for speed settings for orbit, etc?

Thanks!
Tim
 
Yes, it is possible for any object with mass to orbit a heavier object.

With some simple formulae the velocity can be worked out.
 
Getting two objects of small size and low density to orbit each other is very difficult (if not impossible given real world perturbations).

To illustrate this, take two golf balls of maximum density allowed by regulations (mass=1.620oz, diameter=1.680in) and separate them by an infinitesimally small distance. The escape velocity of the golf balls with respect to each other would be only 0.017mm/s! This is a kinetic energy of only 41MeV, so a single cosmic ray could cause this orbital system to be torn apart.
 
Actually, getting two very small objects to orbit each other is not possible in low Earth orbit due to the tidal force of the earth. One of your two objects is going to be slightly further away from the earth, and experience a slightly less pull toward Earth. The net effect is that the two object get pulled apart by the Earth's gravity field. If your two objects are massive enough and close enough to overcome this tidal stretch, then you can orbit.

Regards
 
Two Bowling balls made of lead will orbit perfectly in an empty universe, but I don't live in an empty universe.

Regards
 
If two lead bowling balls exist in an otherwise completely empty universe and no-one is around to witness it, do they really orbit each other?

Ah, philosophy... ;)
 
While gravity acts everywhere, the gravity potential of a object does not need to be powerful enough to allow orbiting.

The diameter of the hill sphere (the rough region where the gravity of an object would dominate) is pretty small, when you attempt this close to really strong gravity fields... for a golf ball, the ideal place to attempt it would be somewhere between two galaxies.

Just as example: The radius of the hill sphere of a space shuttle in low earth orbit (300 km) is only 120 cm.
 
And what about a big and a small object orbiting each other? For example in LEO, the shuttle's mass is several tonnes and the astronaut's much less. Can possibly the astronaut "orbit" the shuttle? I guess it would have to be at a very small velocity.

And what if the shuttle's mass is like.. 100x its real weight, would the orbital velocity increase a lot, or a little?
 
Whatu said:
And what about a big and a small object orbiting each other? For example in LEO, the shuttle's mass is several tonnes and the astronaut's much less. Can possibly the astronaut "orbit" the shuttle? I guess it would have to be at a very small velocity.

And what if the shuttle's mass is like.. 100x its real weight, would the orbital velocity increase a lot, or a little?
Click to expand...

Like I wrote above - the maximum possible orbital radius for the Shuttle is 120 cm.

If the Shuttle would weight 100 times more, the maximum possible radius would grow only by 100^1/3 = 4.6 - 5.5m radius.
 
Whatu said:
And what about a big and a small object orbiting each other? For example in LEO, the shuttle's mass is several tonnes and the astronaut's much less. Can possibly the astronaut "orbit" the shuttle? I guess it would have to be at a very small velocity.

And what if the shuttle's mass is like.. 100x its real weight, would the orbital velocity increase a lot, or a little?
Click to expand...

In LEO nothing can orbit anything in any sort of stable manner. When you're inside the sphere of influence of a major body like earth, you won't be able to orbit anything except earth.

Take Phobos for example. Get in a delta glider and get a circular orbit around Phobos. Yes, you can obtain a nearly 0 eccentricity orbit, but watch the orbit map as time goes on... Because Phobos orbits inside of the Martian sphere of influence, you won't even make one orbit around Phobos before mars ruins it all... And here you're dealing with a much larger object than the shuttle, or a golf ball...

I agree, in a true 0 G environment (maybe between 2 galaxies), you could get a golf ball to orbit a bowling ball, but it would be at a ridiculously slow velocity, and the slightest force would result in escape velocity for the golf ball...
 
reverend said:
Take Phobos for example. Get in a delta glider and get a circular orbit around Phobos. Yes, you can obtain a nearly 0 eccentricity orbit, but watch the orbit map as time goes on... Because Phobos orbits inside of the Martian sphere of influence, you won't even make one orbit around Phobos before mars ruins it all... And here you're dealing with a much larger object than the shuttle, or a golf ball...
Click to expand...

Actually, you can orbit phobos - you just have to be extremely close to it and it requires lots of fuel for staying there. But orbiting something at the speed of a pedestrian has some advantages.
 
Urwumpe said:
Actually, you can orbit phobos - you just have to be extremely close to it and it requires lots of fuel for staying there. But orbiting something at the speed of a pedestrian has some advantages.
Click to expand...

Yes, you can hang a rope ladder from the hatch and astronauts on the surface can hop on or hop off at will, like getting ona slow-moving train.:lol:

Not really, of course. You'd have a hard time walking or even standing still on Phobos without kicking yourself away. And the act of grabbing the robe ladder would be a significant force on the spacecraft, you might even pull it down and cause it to crash if it doesn't compensate with thrusters...
 
Urwumpe said:
Actually, you can orbit phobos - you just have to be extremely close to it and it requires lots of fuel for staying there. But orbiting something at the speed of a pedestrian has some advantages.
Click to expand...
Allow me to correct myself, an unpowered object cannot orbit it, ie: a golf ball....
 
reverend said:
Allow me to correct myself, an unpowered object cannot orbit it, ie: a golf ball....
Click to expand...

I think tony once tried the impossible - he simulated unpowered objects orbiting phobos. ;)
 
Another thing worth mentioning about trying to get small things to orbit each other in LEO is the effect that the direction of gravity won't be the same for the two objects. If the two objects are at the same height, but slightly apart, the two vectors from the two golf balls to the centre of the earth will not be parallel, but will point ever so slightly towards one another. This will have the effect of 'pulling' the two balls together ever so slightly. I can't remember off the top of my head what this effect is called
 
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