Precession Of The Orbital Plane In Non-Spherical Gravitational Fields

[spacerider]

Why the orbital plane of a satellite, in polar orbit, rotates slowly in time?

 

Problem:

A satellite rotates in a polar orbit around a hypothetical stationary planet that does not spin and does not turn around any star. The planet rests isolated in space, far away from any celestial body. However, its gravitational field does not have spherical symmetry, being more intense at the poles and less powerful at the equator.

 

Question: Why does the orbital plane, of the satellite which turns around the planet, slowly rotate around the axis that unites the two poles?

 

I would like an explanation as simple and as intuitive as possible.

I am working on a CubeSat pico satellite project (see: http://cubesat.ifastnet.com/forum/viewforum.php?f=5 ) and one of the problems I have encountered is this drift (precession), in non spherical gravitational fields, whose cause I do not understand.

[Tormod]

Hey and welcome to Hypography! I can't answer your question, but I am sure someone else here will be happy to give it a shot.

[Qfwfq]

Why does the orbital plane, of the satellite which turns around the planet, slowly rotate around the axis that unites the two poles?

Are you sure it does? Angular momentum ought to be conserved...

[spacerider]

Are you sure it does? Angular momentum ought to be conserved..

In a spherical gravitational field, maybe yes but I am not sure about the conservation of momentum in arbitrarily shaped gravitational fields.

[Qfwfq]

If the force is central it is conserved. In your specific case, for such a precession to occur, the force would have to at least sometimes not be in the plane of the current orbit or, IOW, the plane given by the radius vector and the velocity vector.

[erKa]

the force would have to at least sometimes not be in the plane of the current orbit or, IOW, the plane given by the radius vector and the velocity vector.

..elseway there could be more than a single gravity vector acting on the mass of the satellite. F.e. MASCONS (Mass Concentrations) afflicted deeply sats orbiting the Moon but the same occurred to all sats orbiting Earth. You must add the pulling&pushing action due to moving gravity vectors of Moon and Sun ruling their own orbital periods, Sun = 24h and Moon = 28 days. Following the mutual actraction rules of Poincarè you must consider the mutual attraction of n bodies with n = infinite but for engineering purposes and terrestrial sats could be relevant the gravitational actractions of a few bodies like Moon, Sun and closest planets like Venus and Mars reducing the problem to the Laplace's easier solution.

[Qfwfq]

there could be more than a single gravity vector acting on the mass of the satellite

I was talking about the total vector sum.

 

As far as I can understand the OP, it is describing a planet with a mass distribution having axial symmetry and this axis is in the plane of the orbit. This is why I don't see how there could be any precession. The orbit presumably woudn't be elliptic but it should be stable against precession of perigees too.

[erKa]

I was talking about the total vector sum.

But you have a good chance to resolve all MASCONs gravity vectors by summing all them in only one vector sum ONLY in the case the main distance of the satellite fom the geometrical center of the astronomic body is much more greater than the distance from MASCON to MASCON. :) In the specific case of the Moon during Apollo project it seemed that the Moon's gravitational vector sum was slowly moving (dutch-rolling) by complex rotative changes in direction and the phoenomenon was not accomplished by Newton laws without further investigating. The only theory allowed by NASA to explain the strange drift of the gravitational sum vector of the Moon was in the evidence that the center of gravity of the Moon is not the center of masses but there were some funny MASCONs spread under the surface of the Moon randomly and in allotropic manner. Allotropic means an irregular dinstribution of MASCONs far from the isotropic dinstribution of heavy elements expected before Apollo legendary flights.

[Qfwfq]

I don't see the use of these examples for predicting a precession in the case the OP asks about.

[erKa]

Because you have never heard something about GOCEESA project! :)

 

ESA's gravity mission GOCE

 

Launched on 17 March 2009, ESA's Gravity field and steady-state Ocean Circulation Explorer (GOCE) is bringing about a whole new level of understanding of one of Earth's most fundamental forces of nature – the gravity field.

 

Dubbed the 'Formula 1' of satellites, this sleek high-tech gravity satellite embodies many firsts in its design and use of new technology in space to map Earth's gravity field in unprecedented detail.

 

As the most advanced gravity space mission to date, GOCE is realising a broad range of fascinating new possibilities for oceanography, solid Earth physics, geodesy and sea-level research, and significantly contribute to furthering our understanding of climate change.

 

Although invisible, gravity is a complex force of nature that has an immeasurable impact on our everyday lives. It is often assumed that the force of gravity on the surface of Earth has a constant value, but in fact the value of 'g' varies subtly from place to place. These variations are due to a number of factors such as the rotation of Earth, the position of mountains and ocean trenches and variations in density of Earth's interior.

 

 

 

Mapping gravity as never before

 

GOCE to map gravity as never before

GOCE is mapping these global variations in the gravity field with extreme detail and accuracy. This will result in a unique model of the 'geoid', which is the surface of equal gravitational potential defined by the gravity field – crucial for deriving accurate measurements of ocean circulation and sea-level change, both of which are affected by climate change. GOCE-derived data are also much needed to understand more about processes occurring inside Earth and for use in practical applications such as surveying and levelling.

 

 

 

GOCE takes six simultaneous measurements of the gravity field

 

Since the gravitational signal is stronger closer to Earth, the 'arrow-like', five metre-long GOCE satellite was designed to cut through what remains of Earth's atmosphere at just 250 km above the surface. This low-orbiting satellite is the first mission to employ the concept of 'gradiometry' - the measurement of acceleration differences over short distances between an ensemble of proof masses inside the satellite.

 

 

GOCE is equipped with three pairs of ultra-sensitive accelerometers arranged in three dimensions that respond to tiny variations in the 'gravitational tug' of Earth as it travels along its orbital path. Because of their different positions in the gravitational field they all experience gravitational acceleration slightly differently. The three axes of the gradiometer allow the simultaneous measurement of six independent but complementary components of the gravity field.

 

In order to measure gravity, there can be no interference from moving parts so the entire satellite is actually one extremely sensitive measuring device.

 

 

Mission objectives

 

* to determine gravity-field anomalies with an accuracy of

1 mGal (where 1 mGal = 10–5 ms–2).

* to determine the geoid with an accuracy of 1-2 cm.

* to achieve the above at a spatial resolution better than

100 km.

 

First gravity field model

The first gravity field model will be released at ESA's Living Planet Symposium which takes place in Bergen, Norway, from 28 June to 2 July this year.

 

 

Last update: 20 May 2010

 

...anyway the term "accelerometer" let us think the mathematical way to determine the strength and direction of the gravitational forces acting on GOCE in any moment is (not easily) achieved by closely integrating the 1st, 2nd, and 3rd therms of the motion rule of GOCE respect with a dual 6 axis Cartesian spaces. The 1st 3-axis space is the space is the space of velocities (derivative) affecting orbital speed respect with the ideal forecasted orbital velocity.The 2nd cartesian space is the space of the linear distance (derivative of derivative) from ideal orbital path starting ccomputing from initial circular 1st orbit in any moment. No changes by solving polar equations instead of Cartesian spaces. Equations of motion are on wikipedia, no news abut them. :)

[Qfwfq]

Because you have never heard something about GOCEESA project!

No it's because, if you take the care to read the OP properly, it isn't talking about this planet, nor about its moon or any other existing one. It asks about an example of a hypothetical isolated planet.

 

That's why your examples don't constitute a reason for the precession. Please try to keep to the topic of threads.

[erKa]

No it's because, if you take the care to read the OP properly, it isn't talking about this planet, nor about its moon or any other existing one. It asks about an example of a hypothetical isolated planet.

 

That's why your examples don't constitute a reason for the precession. Please try to keep to the topic of threads.

..but I have read the OP properly and the lacks are exactly in the rough definition of the celestial body: spacerider's fictionary body is a flat disk not any sort of celestial body! ..and this is only a 1st trap: no true differences between spherical gravitational field of Newton's body and the thorical gravitational field of spacerider's body. And there is a 2nd trap: no difference if the orbit of the satellite is polar or equatorial or a simple mix of both. Another further trap... :esmoking: Simply the 2nd law of thermodynamics suggest us that the energy spent by the satellites while orbiting cannot be equal to the labour done while orbiting because universal entropy affects their sum. Angular momentum ought to be conserved...but only for a while. :thumbs_up ..Universal Entropy slowly affects both orbital period and orbital apogee by increasing them. Some eons far in the past the main orbital period of the Moon was much more shorter than 28 days as the mean distance from Earth's surface was far less than 400 thousands Km... :shrug: Finally spacerider's space cannot be half fictionary and half real... in the real universe there is entropy always working but in the spacerider's dish-alike universe there could be entropy, nothing or sintropy. :naughty: Without better definition from spacerider or from QfWfq I ought think there is a standard entropy... I am allowed to think so Taken from italian wiki:

 

The syntropy principle is symmetrical and opposite to that of physical entropy. Entropy theorizes and measures the energy degradation that occurs in a system according to the second law of thermodynamics and the fact that in any physical transformation that not all energy is in the initial system and is the initial body instills and finds system and body finish. In fact, some of the energy is absorbed in the work (required for processing) and dissipates as heat. A striking example is provided by incandescent light bulbs in which not all the electricity used is converted into light (good) but some is lost as heat. (Useless for lighting).

 

The principle of entropy, originally stated by the German physicist Clausius, leads to the conclusion that, ultimately, because there is more energy-heat in the work required to transform the physical processes of transformation, the universe will eventually heat death.

 

Syntropy The principle states that the entropy is closely related within each system and the universe and every living system can not die because, in the face of entropy that operates that system, there is a process opposite of reinstatement for an injection of energy from new energy or hired from outside the system. A striking example is given by the metabolism of living organisms in which to meet the catabolism leading to consumption and destruction of tissue by the body to live there anabolism, which reconstitutes these tissues through food intake , ie of substances taken from the outside. The principle of syntropy was affirmed first by the Italian physicist Luigi Fantappié and was then resumed and continued with contributions from several other independent scholars, including Salvatore Arcidiacono and Leonardo Sinisgalli.

 

The principle of syntropy is also taken by the spiritualist philosophy to say that man (body + mind) does not die for the entropic decay of his body, but survives death as a spirit for spiritual energy ratio.

[Doctordick]

Question: Why does the orbital plane, of the satellite which turns around the planet, slowly rotate around the axis that unites the two poles?

 

I would like an explanation as simple and as intuitive as possible.

The problem is that what you are asking for (an intuitive solution) is simply not possible. You are reducing the problem to a compartmentalized version of the issue and, by doing so, eliminating the very issues which require the precession you are interested in.

 

No it's because, if you take the care to read the OP properly, it isn't talking about this planet, nor about its moon or any other existing one. It asks about an example of a hypothetical isolated planet.

Qfwfq, this is an excellent example of exactly what happens when one constrains oneself to compartmentalized thinking. Now I don't know if you have the ability to follow what I am about to say but I will try anyway.

 

The problem this fellow is trying to resolve is fundamentally identical to the precession of the orbit of Mercury required by proper GR calculations. To see that, consider the ideal example of Schwarzschild solution to Einstein's field equations for a spherically symmetric gravitational source (the ideal “compartmentalized” picture of the orbit of Mercury). The solution ends up with a precession not found in Newton's solution.

 

Now examine that solution in the absence of the distant star fields. How in the world would one identify the fact that the orbit was precessing? One has no reference for establishing the direction of the major axis of what is for all practical purposes an elliptical orbit. It should be clear to you that the correct problem includes the existence of those distant objects. The same thing goes for spacerider's precession. One needs the correct holistic solution.

 

Sorry spacerider, some things just are not trivial.

 

Have fun -- Dick

[erKa]

The problem is that what you are asking for (an intuitive solution) is simply not possible. You are reducing the problem to a compartmentalized version of the issue and, by doing so, eliminating the very issues which require the precession you are interested in.

 

 

Qfwfq, this is an excellent example of exactly what happens when one constrains oneself to compartmentalized thinking. Now I don't know if you have the ability to follow what I am about to say but I will try anyway.

 

The problem this fellow is trying to resolve is fundamentally identical to the precession of the orbit of Mercury required by proper GR calculations. To see that, consider the ideal example of Schwarzschild solution to Einstein's field equations for a spherically symmetric gravitational source (the ideal “compartmentalized” picture of the orbit of Mercury). The solution ends up with a precession not found in Newton's solution.

 

Now examine that solution in the absence of the distant star fields. How in the world would one identify the fact that the orbit was precessing? One has no reference for establishing the direction of the major axis of what is for all practical purposes an elliptical orbit. It should be clear to you that the correct problem includes the existence of those distant objects. The same thing goes for spacerider's precession. One needs the correct holistic solution.

 

Sorry spacerider, some things just are not trivial.

 

Have fun -- Dick

:shrug: ..agree 100% with you even if I never thought before to a relativistic precession. But the spacerider's fictionary cosmo could be relativistic, not relativistic or relativistic in a different manner f.e. by doubling/halving "c" velocity... why not?

[Qfwfq]

The problem this fellow is trying to resolve is fundamentally identical to the precession of the orbit of Mercury required by proper GR calculations.

The problem, as stated in the OP, has nothing to do with the exact radial dependence. It explicitly states that the dependence isn't only radial and it would appear to have axil symmetry even though "this fellow" wasn't overly explicit about it:

However, its gravitational field does not have spherical symmetry, being more intense at the poles and less powerful at the equator.

He does not seem concerned with the radial dependence and I don't see the Schwartzschild solution vs. the inverse square being crucial.

 

Now examine that solution in the absence of the distant star fields. How in the world would one identify the fact that the orbit was precessing? One has no reference for establishing the direction of the major axis of what is for all practical purposes an elliptical orbit. It should be clear to you that the correct problem includes the existence of those distant objects. The same thing goes for spacerider's precession. One needs the correct holistic solution

The OP doesn't imagine nothing else exists in the universe, Dick, read it properly. It says:

The planet rests isolated in space, far away from any celestial body.

So it clearly isn't a problem of non inertial choice of coordinates.

 

spacerider's fictionary body is a flat disk not any sort of celestial body!

The OP does not state this and it would give the opposite effect of what he says::

...more intense at the poles and less powerful at the equator.

With a disk the field would be weaker around the axis than around its plane.

 

no difference if the orbit of the satellite is polar or equatorial or a simple mix of both.

Actually there is a difference.

 

In the case of the OP an equatorial orbit would be an instable equilibrium. As soon as it deviates it would gradually go toward some polar orbit.

 

In the disk case any orbit comprising the axis would be an instable equilibrium and the stable one would be in the disk's plane.

 

Simply the 2nd law of thermodynamics suggest us that the energy spent by the satellites while orbiting cannot be equal to the labour done while orbiting because universal entropy affects their sum. Angular momentum ought to be conserved...but only for a while. B) ..Universal Entropy slowly affects both orbital period and orbital apogee by increasing them. Some eons far in the past the main orbital period of the Moon was much more shorter than 28 days as the mean distance from Earth's surface was far less than 400 thousands Km... :lol: Finally spacerider's space cannot be half fictionary and half real... in the real universe there is entropy always working but in the spacerider's dish-alike universe there could be entropy, nothing or sintropy. :o Without better definition from spacerider or from QfWfq I ought think there is a standard entropy... I am allowed to think so :mellow: Taken from italian wiki:

I see no point in all this and if you want to discuss syntropy as theorized by Szent-Gyorgyi you should start a thread in Alternative Theories if not Theology, since the concepts is popular among Creationists.

 

Again, folks, try not to drag threads too far from their point.

[erKa]

The problem, as stated in the OP, has nothing to do with the exact radial dependence. It explicitly states that the dependence isn't only radial and it would appear to have axil symmetry even though "this fellow" wasn't overly explicit about it:He does not seem concerned with the radial dependence and I don't see the Schwartzschild solution vs. the inverse square being crucial.

 

The OP doesn't imagine nothing else exists in the universe, Dick, read it properly. It says:So it clearly isn't a problem of non inertial choice of coordinates.

 

The OP does not state this and it would give the opposite effect of what he says::With a disk the field would be weaker around the axis than around its plane.

 

Actually there is a difference.

 

In the case of the OP an equatorial orbit would be an instable equilibrium. As soon as it deviates it would gradually go toward some polar orbit.

In the disk case any orbit comprising the axis would be an instable equilibrium and the stable one would be in the disk's plane.

 

I see no point in all this and if you want to discuss syntropy as theorized by Szent-Gyorgyi you should start a thread in Alternative Theories if not Theology, since the concepts is popular among Creationists.

 

Again, folks, try not to drag threads too far from their point.

You excluded a Schwartzschild solution for relativistic precession and any kind of syntropy and I have no further interest in Szent-Gyorgyi theory.The contrary of a Gyroscope: disk fixed while gimbal rotates so there is a sort of gyroscopic precession due to the evidence that the sat is less gravitationally attracted when it is in gimbal axis position than closer to disk's edge and this waving sinusoidal change of scalar gravity could be considered a torque acting on sat. Nothing more nothing less than inverted conventional gyroscopical precession

[Qfwfq]

the sat is less gravitationally attracted when it is in gimbal axis position than closer to disk's edge

Have you still not read in the OP that it is the other way around? You keep barking up the wrong tree.

 

In the case described in the OP polar orbits are the stable equilibrium (apart from their apogees and perigees, which we lack any inf to work out). The instable equilibrium is the equatorial case and all those in between will go toward some polar orbit.