Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: Petrochemicals on 14/10/2018 18:32:39
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I guess you can guess what the question is. Had a quick google just lots of stuff about the moons gravity.
With the moon over head of your earthly position is the acceleration due to gravity less than with the moon at the opposite position, that would be under your feet through the earth and on the other side. ?
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We can apply F=GMm/r2 to do a back-of-the-envelope calculation.
To get the relative strength of Earth & Moon's gravity on you, we can eliminate half of these parameters, since G & m (your mass) is common.
The mass of the Moon is about 1/80 mass of the Earth.
And the radius of the Earth at 6000km is around 1/60 the distance of the Moon.
So the relative gravitational force of the Moon on you is about (1/80)*(1/60)2, or 1 part in 300,000.
So if you mass 70kg, the position of the Moon makes a difference of about 0.2grams in the weight you feel.
This is much less than the forces on your body every time you take a step or have a sip of water.
And because the change occurs over 12 hours, the effect is imperceptible.
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We can apply F=GMm/r2 to do a back-of-the-envelope calculation.
To get the relative strength of Earth & Moon's gravity on you, we can eliminate half of these parameters, since G & m (your mass) is common.
The mass of the Moon is about 1/80 mass of the Earth.
And the radius of the Earth at 6000km is around 1/60 the distance of the Moon.
So the relative gravitational force of the Moon on you is about (1/80)*(1/60)2, or 1 part in 300,000.
So if you mass 70kg, the position of the Moon makes a difference of about 0.2grams in the weight you feel.
This is much less than the forces on your body every time you take a step or have a sip of water.
And because the change occurs over 12 hours, the effect is imperceptible.
The net weight difference is less than that. At the the center to center distance between Earth and Moon, the acceleration due to gravity caused by the Moon is 3.3e-5 m/s^2 at the near side of the Earth to the Moon it is 3.44e-5 m/s^2. Since the center of the Earth is in free fall with respect to the Moon, it is the difference between these values, or ~1.4e-6 m/s, that would result in a net lessening of weight. This is ~1.4e-7g. For a 70 kg person you get a net weight difference of ~ 0.01 gram.
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If you look up lunar Perigee and Apogee then you will see that the distance from moon to planet varies considerable monthly like next Perigee is 17 October 404,000km and Apogee is 31 October is 370,000km. What is the feedback mechanism that controls this elliptic orbit? Does it follow the suns 22 year cycle??
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According to Kepler, orbits in free space do not circularise.
I think the answer to the original question is "yes".
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According to Kepler, orbits in free space do not circularise.
I think the answer to the original question is "yes".
Kepler's laws don't take influences like tidal circularization into account. Just like they don't consider the tidal acceleration that is slowly increasing the size of the Moon's orbit.
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If you look up lunar Perigee and Apogee then you will see that the distance from moon to planet varies considerable monthly like next Perigee is 17 October 404,000km and Apogee is 31 October is 370,000km. What is the feedback mechanism that controls this elliptic orbit? Does it follow the suns 22 year cycle??
Elliptic orbits are the norm. Left to itself, an object in an elliptical orbit will remain in it unchanged forever. But, generally speaking, orbits aren't left alone. There is the tidal acceleration I mentioned earlier, and the gravitational tugs and pulls of other bodies or the fact that the body they are orbiting isn't perfectly spherical itself, and even to some degree, the effects of General Relativity.
These all can all combine to cause various changes in an object's orbit.
For example, if we take the Earth's Moon. its Sidereal orbital period (the time it takes to complete a full orbit with respect to the stars is ~27.32 days. Again, left to itself, this would also be the same amount of time that it would take to go from perigee to perigee. However, due to the various influences mentioned, it actually takes ~27.55 days to go from perigee to perigee. This difference results in what is called Apsidal precession (the more general term for the apogee and perigee is the apsides)
This precession itself has a period of ~8.85 years.
The only effect the Sun has on this is that fraction of the various gravitational pulls it provides.
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Kepler's laws don't take influences like tidal circularization into account. Just like they don't consider the tidal acceleration that is slowly increasing the size of the Moon's orbit.
So how does an orbit circularize? The tidal forces would seem to give the moon the greatest thrust at perigee, which increases the apogee, and the least thrust at apogee, which minimizes the lifting of perigee. So that would seem to amplify the eccentricity of the orbit, not circularize it.
Of course the duration of the thrust at preigee is less than the duration at apogee, so maybe that's what I'm missing.
There's also the fact that at perigee, the orbital speed is higher, which decreases the lag between tidal bulge and planet.
Take it to the point where the angular velocity at perigee equals the angular velocity of planet, and at perigee, the tidal acceleration drops to zero not effecting the apogee at all.
Increase the eccentricity even further so that perigee orbital angular velocity exceeds rotational speed and you have the apogee being draw in.
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So how does an orbit circularize?
In the far more extreme case of black holes or neutron stars in an elliptical orbit around their center of mass, gravitational waves do circularize the orbits, over time.
Gravitational wave radiation increases considerably when the two bodies are closest - it increases as 1/(radius cubed).
So most of the energy is radiated when the bodies are closest, which robs momentum that would be needed to reach the farthest point in their orbits.
This first results in the orbit circularizing, and then shrinking more rapidly, as the two bodies now spend more time close together.
https://en.wikipedia.org/wiki/Gravitational_wave#Binaries
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But if the closer proximity robs momentum of the moon then it will slow and re-enter the upper atmosphere and hit the planet. To stop that happening we need a feedback mechanism which is probably a magnetic repulsion. I have been puzzled for sometime as to why mercury and venus have such minimal magnetic fields but the reason could be that they have no moons to be pushed away.
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But if the closer proximity robs momentum of the moon then it will slow and re-enter the upper atmosphere and hit the planet. To stop that happening we need a feedback mechanism which is probably a magnetic repulsion. I have been puzzled for sometime as to why mercury and venus have such minimal magnetic fields but the reason could be that they have no moons to be pushed away.
The type of orbital decay caused by gravitational radiation as mentioned by evan_au is basically a non-factor when it comes to planets orbiting the Sun. At it present rate, the Earth is only moving closer to the Sun due to gravitational energy radiation at a rate that equal approximately the width of one proton per day. It would take many, many, many time the present age of the universe for the Earth to fall into the Sun due to gravitational radiation.
Mercury would take less time, but not a by any significant amount. (still much longer than the present age of the universe.
Long before that, other factors will have a much greater effect. The Sun is losing mass over time and its gravitational pull on the planets is slowly weakening for example. The effect of this far outweighs the loss of momentum through gravitational radiation for the planets of the Solar system. No feedback or magnetic repulsion is needed.
Another effect for a moon orbiting a planet is tidal acceleration. In this case, as long as the moon orbital period is longer than the time the planet takes to rotate, and the moon orbits in the same direction as the planet turns, tidal interact will transfer angular momentum from planet to Moon, slowly pushing it away from the planet (this is is what is happening to our Moon).
It only when the Moon orbits faster than the planet rotates or orbits in the opposite direction from the planet that this interaction draws the moon in (one example of the First case is the Martian moon Phobos, which orbits in less time than it takes for Mars to rotate, and is slowly falling in towards the planet. )
For our Moon, this leads to an increase in orbital distance of 4cm per year. This outpaces any loss due to gravitational radiation by several magnitudes.
Your last statement is a bit puzzling. It's not as if Mercury and Venus would say to themselves "Well, it looks like I don't have moon which I need to stabilize its orbit for, so I won't bother to generate a magnetic field." The Earth's magnetic field doesn't rely of the presence of the Moon, but is generated by a dynamo effect caused by its spinning core.
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Thank you Jason. I have just been reading about the ESA venus express and their discovery that the planet has magnetic reconnection beyond the planets orbit. Now this is not surprising as we know by the Norfolk island effect that radio coms are disrupted by sun spots and conclude therefore that the sun is magnetically linked to its planets and using the magnoflux spin effect is able to hold them in stable orbits. So why can't the planets do the same with their moons?
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Now this is not surprising as we know by the Norfolk island effect that radio coms are disrupted by sun spots and conclude therefore that the sun is magnetically linked to its planets and using the magnoflux spin effect is able to hold them in stable orbits.
This is an erroneous conclusion. Sun spot interference has nothing to do with any magnetic linking between the Sun and the planets. Sunspots are a effect of increased Solar activity which includes an increase production of radiation in the form of ions and x-rays. It is this radiation impinging on our atmosphere that produces the interference. While sunpots are the result of the magnetic field of the Sun, this effect is localized to the Sun itself.
The typical magnetic field strength of the Sun at its surface is only about twice that at the Earth's field strength at its surface. Now consider that even get a compass needle to point keep pointing North you have to make sure that the friction between needle and pivot point is very small. Magnetic forces fall off very rapidly with distance. Given that the Earth is some 215 times further from the Sun's surface than the surface is from its center, The idea that the Sun's magnetic influence on the Earth has any effect on the Earth's orbit is beyond ridiculous. Nor is there any reason for it. Orbital mechanics based simply on gravitational attraction and momentum are quite sufficient to explain the Earth's, or any other planet's, present orbit.
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How about the effect of photons striking the surface of teh earth moon system. The photons strike the moon as it is motion toward the sun and away from the sun. If the solar radiation is like earth 1366w/m2 at its equator, it has a cross section area of square meters. 9x12 square metres. That equals alot of watts
As the photons re admit, with the moon toward the sun they should slow the moon, and as the moon moves away they should drive the moon faster. Coupled with the radiation emmision from earth which must be also be being driving the earth away from the sun, but a slower rate due to greater mass to surface area of the earth, plus the solar winds driving both bodies at there surface area/mass rate, surely the moon is being driven elliptical with a close pass on the earth sun side. This will however only draw the earth back toward the sun as well as simultaniously giving the moon a faster motion. Where does it all end ?
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How about the effect of photons striking the surface of teh earth moon system. The photons strike the moon as it is motion toward the sun and away from the sun. If the solar radiation is like earth 1366w/m2 at its equator, it has a cross section area of square meters. 9x12 square metres. That equals alot of watts
As the photons re admit, with the moon toward the sun they should slow the moon, and as the moon moves away they should drive the moon faster. Coupled with the radiation emmision from earth which must be also be being driving the earth away from the sun, but a slower rate due to greater mass to surface area of the earth, plus the solar winds driving both bodies at there surface area/mass rate, surely the moon is being driven elliptical with a close pass on the earth sun side. This will however only draw the earth back toward the sun as well as simultaniously giving the moon a faster motion. Where does it all end ?
1363 w/m^2 over the cross section of the Moon creates 4.3e7 Newton's of force in radiation pressure. While this may seem like a lot, the Moon has a mass of 7.35e22 kg. That much force acting on that mass would only generate an acceleration of ~6e-16 m/sec^2.
Also, You are not going to get that much net acceleration. The Moon, like the Earth, rotates with respect to the Sun and due to the Moon's low albedo, 78% percent of solar radiation falling on it is absorbed and then re-radiated away into space when the that side has rotated away form the Sun (day side of Moon absorbs radiation, nightside radiates it away). This re-radiation from the night side cancels out any outward momentum gained by absorption on the day side.
In addition, the orientation of the Moon's orbit is fixed relative to the stars ( plus some precession) Since the Earth-Moon system orbits the Sun relative to the stars, The Moon's orbital orientation with respect to the Sun changes over the course of a year. (for example, if the Moon's perigee is on the Sun side of the Earth at one point of the year, 6 month later, it will be the apogee that will be on the Sun side of the Earth.)
This also means that if at some point of the Year the moon is slightly accelerated by radiation pressure on one side of its orbit and deccelerated on the other side, Six months later the decelerated side will be the accelerated side and vice-versa. In other words, the net effect on the shape of the Moon's orbit will be zero over the course of a year and the effect doesn't compound.
But all-in all, the effect of radiation pressure on the Earth-Moon system is really, really small, and insignificant compared to other influences.
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So how does an orbit circularize?
They don't. A circle is just a special case of an ellipse with eccentricity = 0, which is a most improbable orbit.
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Just looked up Jupiters moons and it has found that the moons like our moon always have the same surface inwards according to NASA who quote below.
Three of the moons influence each other in an interesting way. Io is in a tug-of-war with Ganymede and Europa, and Europa's orbital period (time to go around Jupiter once) is twice Io's period, and Ganymede's period is twice that of Europa. In other words, every time Ganymede goes around Jupiter once, Europa makes two orbits and Io makes four orbits. The moons all keep the same face towards Jupiter as they orbit, meaning that each moon turns once on its axis for every orbit around Jupiter.
Now this always facing towards the planet means that their magnetic cores are locked together and synchronised which means that if the moons start to slow down the planets magnetic field will speed them up again and they will ellipse rather than rotate.
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Just looked up Jupiters moons and it has found that the moons like our moon always have the same surface inwards according to NASA who quote below.
Three of the moons influence each other in an interesting way. Io is in a tug-of-war with Ganymede and Europa, and Europa's orbital period (time to go around Jupiter once) is twice Io's period, and Ganymede's period is twice that of Europa. In other words, every time Ganymede goes around Jupiter once, Europa makes two orbits and Io makes four orbits. The moons all keep the same face towards Jupiter as they orbit, meaning that each moon turns once on its axis for every orbit around Jupiter.
Now this always facing towards the planet means that their magnetic cores are locked together and synchronised which means that if the moons start to slow down the planets magnetic field will speed them up again and they will ellipse rather than rotate.
Again, magnetic fields have nothing to do with this behavior. It is all due to gravitational interaction. Ganymede and Europa are in a resonance with each each other because this is a stable orbital configuration for them to be in due to gravitational interactions. Moons near in to Jupiter are locked into one rotation per orbit by gravitationally induced tides. (though Just because their orbits and rotations are synchronized, this doesn't mean that they keep the exactly the same face pointed at Jupiter at all times. Each of these Moons have a small eccentricity to their orbits, which means their orbital velocity varies slightly, but the rotational speed remains fixed. This causes a libration where the side facing Jupiter rocks back and forth over a small angle.)
Europa doesn't have it own independent magnetic field. It's magnetic field is an induced one caused by its passage through Jupiter's field and the fact that its orbit is at an angle to Jupiter's field.
The idea that tidal locking is caused by magnetic interaction is an unwarranted conclusion, based on nothing.
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I am not aware of any of Newtons laws of gravity that indicate a moon would be held in synchronised with its planet. However, it is very common with electromagnetic rotors.
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I am not aware of any of Newtons laws of gravity that indicate a moon would be held in synchronised with its planet.
It's called tidal forces. The difference in gravitational pull caused by different points of its body being different distances from the planet cause a differential called a tidal force. This results in the Moon bulging along the line joining it with the Planet. due to friction, a Moon that rotates relative to this tidal bulge experiences a drag that tends pull it into a matching rotation with the bulge. This final match occurs when the rotational period and orbital periods equalize.
There is even an equation for determining the time scale in which this will happen:
T = w a^2 I Q / (3 G M^2 k2 R^5)
w is the initial angular velocity of the rotating Moon
a is the semi-major axis of its orbit
I is the rotational moment of inertia for the Moon (0.4 m R^2, with m being the mass of the moon)
M is the mass of the Planet
R is the radius of the Moon
G is the universal Gravitational constant.
Q and K2 are coupling constants that depend on the makeup of the Planet and Moon.
Just because you are not aware of something doesn't mean that it does not exist. Tidal locking is a well known phenomena.