Suppose an object were to fall into the inner solar system, solely under the influence of gravity, from infinity, or from almost infinity.
Is it possible that this object could fall into an almost perfectly circular orbit of the Earth?
And at what height and speed would the object end up orbiting the Earth?
Soso said:
Suppose an object were to fall into the inner solar system, solely under the influence of gravity, from infinity, or from almost infinity.Is it possible that this object could fall into an almost perfectly circular orbit of the Earth?
And at what height and speed would the object end up orbiting the Earth?
it would be making a beeline for the sun, if it misses it will most likely have gained so much speed from being accelerated that it would be slung out of the solar system
wookiemeister said:
Soso said:
Suppose an object were to fall into the inner solar system, solely under the influence of gravity, from infinity, or from almost infinity.Is it possible that this object could fall into an almost perfectly circular orbit of the Earth?
And at what height and speed would the object end up orbiting the Earth?
unlikelyit would be making a beeline for the sun, if it misses it will most likely have gained so much speed from being accelerated that it would be slung out of the solar system
wookiemeister said:
most things passing earth do so at great speed they wouldn’t go into orbit around the earth they are travelling too fast
umm a lot of stuff falls in.. but anything passing.. is doing just that.
roughbarked said:
wookiemeister said:most things passing earth do so at great speed they wouldn’t go into orbit around the earth they are travelling too fast
umm a lot of stuff falls in.. but anything passing.. is doing just that.
most stuff passes by at great speed
theres a bit that hits the earth but it wouldn’t have come from being in orbit from the earth, the earth was just in the way of where it was going
Economists are warning an increase of casual and part-time work means Australia’s unemployment rate is higher than we think.
The unemployment rate is currently 5.5 per cent, but official figures show another 7 per cent of workers in casual or part-time roles are willing and able to work more hours.
http://www.abc.net.au/news/2013-06-12/australia-casual-workforce-masking-unemployment-figures/4749900?section=business
wookiemeister said:
Economists are warning an increase of casual and part-time work means Australia’s unemployment rate is higher than we think.The unemployment rate is currently 5.5 per cent, but official figures show another 7 per cent of workers in casual or part-time roles are willing and able to work more hours.
http://www.abc.net.au/news/2013-06-12/australia-casual-workforce-masking-unemployment-figures/4749900?section=business
There is a heck of a lot that isn’t on record.
Soso said:
Suppose an object were to fall into the inner solar system, solely under the influence of gravity, from infinity, or from almost infinity.Is it possible that this object could fall into an almost perfectly circular orbit of the Earth?
And at what height and speed would the object end up orbiting the Earth?
If the object had no relative motion, it would just plow headlong into the sun.
If the object had enough relative motion to miss the upper layers of the sun, it would head back out of the solar system on the ellipse that it entered on.
If you are expecting an object falling into the solar system to suddenly change direction and start orbiting the earth, you have as much chance of expecting a speeding freight train to turn 90 degrees because a fly on it farted at right angles to its direction.
Kingy said:
If you are expecting an object falling into the solar system to suddenly change direction and start orbiting the earth, you have as much chance of expecting a speeding freight train to turn 90 degrees because a fly on it farted at right angles to its direction.
:)
Kingy said:
Soso said:
Suppose an object were to fall into the inner solar system, solely under the influence of gravity, from infinity, or from almost infinity.Is it possible that this object could fall into an almost perfectly circular orbit of the Earth?
And at what height and speed would the object end up orbiting the Earth?
If the object had no relative motion, it would just plow headlong into the sun.
If the object had enough relative motion to miss the upper layers of the sun, it would head back out of the solar system on the ellipse that it entered on.
If you are expecting an object falling into the solar system to suddenly change direction and start orbiting the earth, you have as much chance of expecting a speeding freight train to turn 90 degrees because a fly on it farted at right angles to its direction.
Soso said:
Suppose an object were to fall into the inner solar system, solely under the influence of gravity, from infinity, or from almost infinity.Is it possible that this object could fall into an almost perfectly circular orbit of the Earth?
And at what height and speed would the object end up orbiting the Earth?
Earth would need to be a lot denser for that to be possible, and even if that were the case, the path of the body would have to be lined up fairly accurately.
As it is, it can’t happen because a body falling from infinity towards the Sun would be going too fast when it passed the Earth, so it couldn’t be captured in a closed orbit by the Earth.
A body falling towards the sun from infinity has a speed (relative to the Sun) of around 42 km/s when its distance is 1 AU from the Sun, i.e., crossing the Earth’s orbit. The Earth’s mean orbital speed is just under 30 km/s. The velocity vectors of the Earth & the falling body are almost at right angles, so we can approximate their relative velocity using Pythagoras’s theorem, which gives us a figure of a little over 51.5 km/s.
The mean radius of an orbit of that mean speed around a body with the mass of the Earth is just under 150 km (assuming I haven’t made a mistake with my algebra or arithmetic). That’s not 150 km above sea level, that’s 150 km above the centre of the body. And as you may have noticed, the Earth’s radius is substantial larger than 150 km. :) So such an orbit is not possible… unless you want to squash the Earth a fair bit. :)
PM 2Ring said:
Soso said:
Suppose an object were to fall into the inner solar system, solely under the influence of gravity, from infinity, or from almost infinity.Is it possible that this object could fall into an almost perfectly circular orbit of the Earth?
And at what height and speed would the object end up orbiting the Earth?
Earth would need to be a lot denser for that to be possible, and even if that were the case, the path of the body would have to be lined up fairly accurately.
As it is, it can’t happen because a body falling from infinity towards the Sun would be going too fast when it passed the Earth, so it couldn’t be captured in a closed orbit by the Earth.
A body falling towards the sun from infinity has a speed (relative to the Sun) of around 42 km/s when its distance is 1 AU from the Sun, i.e., crossing the Earth’s orbit. The Earth’s mean orbital speed is just under 30 km/s. The velocity vectors of the Earth & the falling body are almost at right angles, so we can approximate their relative velocity using Pythagoras’s theorem, which gives us a figure of a little over 51.5 km/s.
The mean radius of an orbit of that mean speed around a body with the mass of the Earth is just under 150 km (assuming I haven’t made a mistake with my algebra or arithmetic). That’s not 150 km above sea level, that’s 150 km above the centre of the body. And as you may have noticed, the Earth’s radius is substantial larger than 150 km. :) So such an orbit is not possible… unless you want to squash the Earth a fair bit. :)
I prefer the fly fart analogy.
Kingy said:
Soso said:
Suppose an object were to fall into the inner solar system, solely under the influence of gravity, from infinity, or from almost infinity.Is it possible that this object could fall into an almost perfectly circular orbit of the Earth?
And at what height and speed would the object end up orbiting the Earth?
If the object had no relative motion, it would just plow headlong into the sun.
If the object had enough relative motion to miss the upper layers of the sun, it would head back out of the solar system on the ellipse that it entered on.
If you are expecting an object falling into the solar system to suddenly change direction and start orbiting the earth, you have as much chance of expecting a speeding freight train to turn 90 degrees because a fly on it farted at right angles to its direction.
No I understood this event would have a probability just shy of zero, but it seemed reasonable to me that since some stuff hits and some stuff misses, there must be a boundary between hitting and missing, and that should mean orbiting.
Actually I was pondering a sci-fi scenario where there was a panic about a major impact, with the odds of impact growing ever closer to 50%, and then at last instant…. the almost impossible….
PM 2Ring said:
Soso said:
Suppose an object were to fall into the inner solar system, solely under the influence of gravity, from infinity, or from almost infinity.Is it possible that this object could fall into an almost perfectly circular orbit of the Earth?
And at what height and speed would the object end up orbiting the Earth?
Earth would need to be a lot denser for that to be possible, and even if that were the case, the path of the body would have to be lined up fairly accurately.
As it is, it can’t happen because a body falling from infinity towards the Sun would be going too fast when it passed the Earth, so it couldn’t be captured in a closed orbit by the Earth.
A body falling towards the sun from infinity has a speed (relative to the Sun) of around 42 km/s when its distance is 1 AU from the Sun, i.e., crossing the Earth’s orbit. The Earth’s mean orbital speed is just under 30 km/s. The velocity vectors of the Earth & the falling body are almost at right angles, so we can approximate their relative velocity using Pythagoras’s theorem, which gives us a figure of a little over 51.5 km/s.
The mean radius of an orbit of that mean speed around a body with the mass of the Earth is just under 150 km (assuming I haven’t made a mistake with my algebra or arithmetic). That’s not 150 km above sea level, that’s 150 km above the centre of the body. And as you may have noticed, the Earth’s radius is substantial larger than 150 km. :) So such an orbit is not possible… unless you want to squash the Earth a fair bit. :)
Can we do that?
No? Oh well thanks for the answer anyway.
The only way it could happen is with a lot of perfectly aligned aero braking through our atmosphere. Very, very unlikely.
Another solution would be for the infalling body to impact the moon. If it was small enough to not disturb the moons orbit to much, then it would end up in a nearly circular orbit around the earth.
Stealth said:
Another solution would be for the infalling body to impact the moon. If it was small enough to not disturb the moons orbit to much, then it would end up in a nearly circular orbit around the earth.
I really like this idea for a story.
podzol said:
Stealth said:
Another solution would be for the infalling body to impact the moon. If it was small enough to not disturb the moons orbit to much, then it would end up in a nearly circular orbit around the earth.
I really like this idea for a story.
If it is an object falling from infinity(or beyond) it is likely to be Buzz Lightyear in a future Toy Story.
Riff-in-Thyme said:
podzol said:
Stealth said:
Another solution would be for the infalling body to impact the moon. If it was small enough to not disturb the moons orbit to much, then it would end up in a nearly circular orbit around the earth.
I really like this idea for a story.
If it is an object falling from infinity(or beyond) it is likely to be Buzz Lightyear in a future Toy Story.
lol.
I love the Toy Story movies!
Falling from infinity, not only would the object not orbit the earth, but it wouldn’t orbit the sun either. Ignoring gravitational radiation (by considering the falling object to be a “test mass”), gravitation is a conservative “force”, so that unless the falling object can somehow reduce its total energy (by frictional collisions), the object will return to infinity (such a trajectory will either be parabolic or hyperbolic depending on the initial velocity at infinity).
Soso said:
it seemed reasonable to me that since some stuff hits and some stuff misses, there must be a boundary between hitting and missing, and that should mean orbiting.
Not if the mathematical function is discontinuous.
If it hit the moon and created a ring of smashed up material around earth it might look like this (not saying it could happen!):
http://io9.com/if-earth-had-a-ring-like-saturn-508750253
KJW said:
Falling from infinity, not only would the object not orbit the earth, but it wouldn’t orbit the sun either. Ignoring gravitational radiation (by considering the falling object to be a “test mass”), gravitation is a conservative “force”, so that unless the falling object can somehow reduce its total energy (by frictional collisions), the object will return to infinity (such a trajectory will either be parabolic or hyperbolic depending on the initial velocity at infinity).
Hmm, okay I read up on the origin problem for Phobos and Deimos after reading this. But how does relate to “gravity assists” used to slow spacecraft?
Soso said:
Hmm, okay I read up on the origin problem for Phobos and Deimos after reading this. But how does relate to “gravity assists” used to slow spacecraft?
Ah, a spacecraft has an engine, so it’s not purely at the mercy of gravity.
With current technology, spacecraft can’t run their engines through the whole journey, so they’re free-falling for most of their trajectory and only burn their precious fuel at strategic points on their path where it’ll have the most effect.
The “gravity assists” thing utilises the Oberth effect
the Oberth effect is where the use of a rocket engine when travelling at high speed generates much more useful energy than one at low speed. Oberth effect occurs because the propellant has more usable energy (due to its kinetic energy on top of its chemical potential energy) and it turns out that the vehicle is able to employ this kinetic energy to generate more mechanical power.
PM 2Ring said:
Soso said:
Hmm, okay I read up on the origin problem for Phobos and Deimos after reading this. But how does relate to “gravity assists” used to slow spacecraft?
Ah, a spacecraft has an engine, so it’s not purely at the mercy of gravity.
With current technology, spacecraft can’t run their engines through the whole journey, so they’re free-falling for most of their trajectory and only burn their precious fuel at strategic points on their path where it’ll have the most effect.The “gravity assists” thing utilises the Oberth effect
the Oberth effect is where the use of a rocket engine when travelling at high speed generates much more useful energy than one at low speed. Oberth effect occurs because the propellant has more usable energy (due to its kinetic energy on top of its chemical potential energy) and it turns out that the vehicle is able to employ this kinetic energy to generate more mechanical power.
The wikipedia article treats the use of fuel during a gravity assist as an optional extra however.
Soso said:
Suppose an object were to fall into the inner solar system, solely under the influence of gravity, from infinity, or from almost infinity.Is it possible that this object could fall into an almost perfectly circular orbit of the Earth?
And at what height and speed would the object end up orbiting the Earth?
Not possible, but is possible to fall into an elliptical orbit around the Earth. To do that, the easiest way is for it to first make a close pass of Jupiter. This close pass of Jupiter would (with 50% probability) rob the infalling object of some energy, it’s the opposite of a gravitational slingshot – a gravitational slowdown. All the periodic comets became periodic in this way, by passing close to Jupiter on their way in from the Oort Cloud.
Now let’s have a look at the periodic comet Encke, this has a period of 3.3 years around the Sun, an Aphelion of 4.11 AU and a Perihelion of 0.33 AU. This has an inclined orbit that doesn’t cross the Earth’s, but suppose that our infalling object has the same period, aphelion and perihelion but does cross the Earth’s orbit. The the infalling object could have a close encounter with Earth (or Venus). Let the object have a close encounter with Earth in such a way that it is robbed of energy. In this case it becomes possible for it to become trapped in a highly eccentric orbit about the Earth. An analogy (though not a perfect one) was comet Shoemaker-Levy 9 (SL9). SL9 after having a close encounter with Jupiter was diverted into an orbit around Jupiter. Similarly, an incoming object similar to similar to Comet Encke could be diverted after a close encounter with the Earth into an elliptic orbit about the Earth.
I don’t know what the parameters of such an orbit would be, but I can guess. The maximum distance from the Earth would be less than one twentieth of an astronomical unit, less than 25 times the Earth-Moon distance. The minimum distance could be anything.
The object could make a pass through the earth’s atmosphere, slowing it down enough to sub-escape-speeds. If it then got a bit of a tweak from the moon, it could end in a moderately stable elliptical earth orbit.
So arseholes Uzbekistan have a pretty good chance of qualifying for the world cup eh?
Scusi
> The object could make a pass through the earth’s atmosphere, slowing it down enough to sub-escape-speeds. If it then got a bit of a tweak from the moon, it could end in a moderately stable elliptical earth orbit.
Yes.
> The minimum distance could be anything.
Did you spot my lie here? The minimum distance (perigee) would have to be very close. Without doing the calculations I don’t know how close, but WELL within the orbit of geostationary satellites (35,000 km). I’d hazard a guess of about 500 km, give or take a factor of 5.
> And at what height and speed would the object end up orbiting the Earth?
Maximum speed slightly less than twice that of a LEO satellite, which translates to about 15 km/s.
Soso said:
KJW said:
Falling from infinity, not only would the object not orbit the earth, but it wouldn’t orbit the sun either. Ignoring gravitational radiation (by considering the falling object to be a “test mass”), gravitation is a conservative “force”, so that unless the falling object can somehow reduce its total energy (by frictional collisions), the object will return to infinity (such a trajectory will either be parabolic or hyperbolic depending on the initial velocity at infinity).
Hmm, okay I read up on the origin problem for Phobos and Deimos after reading this. But how does relate to “gravity assists” used to slow spacecraft?
Hmmm. I think I need to refine my statement. Actually, the conservative nature of gravitation appears to require a stationary spacetime. In the stationary frame of reference, a gravitational potential field can be defined such that the energy required to transfer a mass from one location to another is dependent only on the two locations and independent of the path between the two locations (the independence of the path is what defines the conservative nature) . But with all the planets orbiting the sun, there is no stationary frame of reference, and the velocity of the various objects removes the conservative nature (a gravitational potential field can no longer be defined). What this means is that in the frame of reference of the sun, kinetic energy can be transferred from the moving planets to the falling object or visa versa.
KJW said:
Hmmm. I think I need to refine my statement. Actually, the conservative nature of gravitation appears to require a stationary spacetime. In the stationary frame of reference, a gravitational potential field can be defined such that the energy required to transfer a mass from one location to another is dependent only on the two locations and independent of the path between the two locations (the independence of the path is what defines the conservative nature) . But with all the planets orbiting the sun, there is no stationary frame of reference, and the velocity of the various objects removes the conservative nature (a gravitational potential field can no longer be defined). What this means is that in the frame of reference of the sun, kinetic energy can be transferred from the moving planets to the falling object or visa versa.
In the case of a single planet with a circular orbit around the sun, (ignoring the rotations of the sun and planet) a stationary frame of reference does exist. However, this is the non-inertial frame of reference that rotates with the planet’s orbital motion, and the conservative nature of the object’s trajectory has to be viewed from this frame of reference.
KJW said:
(ignoring the rotations of the sun and planet)
As well as gravitational radiation.