# On orbital mechanics and the standard model

Some Questions on Lagrange Points – According to Wicki, a Lagrange point is

The Lagrangian points are the five positions in an orbital configuration where a small object affected only by gravity can theoretically be stationary relative to two larger objects (such as a satellite with respect to the Earth and Moon). The Lagrange points mark positions where the combined gravitational pull of the two large masses provides precisely the centripetal force required to rotate with them. They are analogous to geostationary orbits in that they allow an object to be in a fixed position in space rather than an orbit in which its relative position changes continuously.

Evidently Lagrange points are calculated using Newtonian mechanics in a two body problem. According to Wicki, satellites have been sent into the Lagrange points, or at least to orbit the Lagrange points heer - http://en.wikipedia.org/wiki/Lagrang...point_missions [Broken]. Also according to Wicki, the earth orbits the sun in an ellipse, with a distance to the sun that varies over the year by about 5 million kms. When we look at the Lagrange points, L1 to L5 are all dependent upon the location of the sun and the earth. As such, the following questions are pertinent –

1. If a satellite was sent to L1, what is the force that causes the satellite to move closer and further away from the sun when the earth moves closer and further away from the sun during its elliptical orbit?

2. According to Newtonian mechanics, the gravity field is stronger when a body is closer to another body. When the satellite is at L1 and is closest to the sun when the earth is at perihelion, what then is the force that causes the satellite to move along with the earth as the earth gradually moves away from the sun, to its maximum distance at aphelion?

3. If the satellite is launched from the earth, with a velocity component of 30km/s, what is the velocity component of the satellite at L1? Is it 30km/s or other?

4. If the sun orbits the solar system barycenter, which is located outside the sun, what is the force that causes the satellite to move along with the change in suns position as the solar system barycenter location changes?

5. Lagrange points are said to be points where centrifugal and centripetal forces balance. Centripetal force is dependent upon the velocity of the moving mass and its orbital radius. As the earths mass is the same, but the orbital radius changes throughout the year, then the centripetal force required to keep the earth in orbit must change, thereby moving the Lagrange point. Yet, the formula for the distance to L2 (r), is only dependent upon relative masses of two bodies, http://en.wikipedia.org/wiki/Lagrang...nt#cite_note-9 [Broken] , which do not change during the year. How does the value of r change when the centripetal force on the earth changes throughout the year, but the value of the two masses do not change?

6. For a satellite to remain in the L1 position during the year, it must travel along in an elliptical orbit around the sun, even though the centripetal force from the sun and the gravity of earth cancel. Therefore according to Newtonian mechanics, there is no gravitational force to counter the centrifugal forces created by the satellites orbit. How does Newtonian orbital mechanics account for the satellite motion without a gravity force acting on the satellite?

7. If the satellite is sent to L1 as the Lagrange point between the sun and the moon, what is the effect of the position of the moon on L1? If there is no effect, then this means the moons gravity field has no effect on L1, yet modern physics says the moons gravity field is critical to determining the actions of the earth’s tides. Therefore this would mean that the moon has both no effect of Lagrange points, and have immense importance in calculating tides, both of which involve the moons gravity. Seems very odd indeed.

8. If there is an effect on L1 by the moon, then L1 must move with the moon on a monthly basis. As such, to remain in the L1 point, the satellite is required to move in a flower pattern around the sun, just as the earth moves in a flower pattern orbiting the sun, around the earth-moon barycenter. What is the cause of the motion of the satellite in a flower pattern, when the gravity and centrifugal forces on the satellite cancel in the sun-earth system?

9. If the gravity from the sun-earth system is zero at L1, shouldn’t the moons gravity field dominate the satellites motion? As such, shouldn’t the satellite tend to orbit in a large ellipse, following the motion of the moon? Or always tend towards the moon and therefore fall out of a Lagrange point?

10. As the moon is between the sun and the earth, then the moons gravity force is at its greatest when the satellite is at L1. In this example, the satellite will tend to move towards the moon, when in fact the L1 will move away from the moon, towards the sun. In this way, the satellite requires a force to move against the moon. What is this force?

11. Likewise, the moons gravitational force is smallest when it is on the far side of the earth. In this example, the satellite will only slightly tend to move towards the moon, whereas L1 will move towards the sun at a greater rate to that of the satellite. In this way, the satellite requires a force to move with L1, towards the moon. What is this force?

12. When a satellite is at L2, the combined gravity and centrifugal forces of the sun and earth on the satellite is zero. What is the cause of the force that causes the satellite to remain in orbit, to counter the centrifugal force of the orbiting satellite around the sun, when the resultant forces due to the sun and earth on the satellite is zero? According to this scenario the sun has no net force on the satellite, yet there is a centrifugal force generated by the satellites motion around the sun. If there is no counter force acting on the satellite, then the satellite will drift out of the Lagrange point.

13. If satellites orbit the sun at any Lagrange point, this means the satellite is orbiting the sun, without the sun-earth system having any net force placed on the satellite. This is gravitationally similar to a satellite orbiting in space around nothing, which is therefore very similar to sciences rejected notion of epicycles. How then does modern science explain the motion of satellites around the sun in Lagrange points, when such motions are mechanically the same as the rejected planetary epicycles?

14. The following link http://www.esa.int/esaSC/SEMM17XJD1E_index_0.html shows the motion of the Lagrange points along with the earth. According to this model, the earth orbits the sun in a circle. Why does the modern explanation of Lagrange points require the earth to orbit the sun in a circle, when Newtonian/Kepler mechanics demands that it orbit the sun in an ellipse?

15. Derivation of the Lagrange points is merely based upon Newton’s formulas, only assuming two bodies in the problem. For example, distance to L1 is shown here – http://www.phy6.org/stargaze/Slagrang.htm between the sun and the earth. Yet in the real, there are many bodies, including the moon, Jupiter, Saturn, Uranus and Neptune, which all have an influence one the gravitational force acting on a body. As the gravitational force is constantly changing, then the location of all the Lagrange points must also be constantly changing relative to the earth. Yet the standard representation of Lagrange points do not show change in the location of the points. How is the standard presentation a reflection of the real Lagrange points used to provide destinations for satellites?

16. Lagrange points in the real are dependent upon centripetal and centrifugal forces that cancel at points around an orbiting body. As the Milky Way is moving through space at 600km/s then the location of the planets and sun relative to earth must account for aberration of light to locate the real positions of those bodies. Only after the real locations of bodies are known relative to earth, can the maths be done to calculate the real location of the Lagrange points. As aberration is not used in the calcs for the Lagrange points, then only apparent locations of bodies are used and therefore the Lagrange points are always in error. How can erroneous Lagrange points be used to determine the location of the destination of satellites such as SOHO?

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Bill_K
Can I pick just one to answer, or must I answer all 16 to get full credit??
For a satellite to remain in the L1 position during the year, it must travel along in an elliptical orbit around the sun, even though the centripetal force from the sun and the gravity of earth cancel. Therefore according to Newtonian mechanics, there is no gravitational force to counter the centrifugal forces created by the satellites orbit. How does Newtonian orbital mechanics account for the satellite motion without a gravity force acting on the satellite?
There are two forces acting on the satellite, the gravitational attraction of the Earth and Sun. These forces together supply the centripetal force needed to keep the satellite at the L1 point.

All right, one more.
If a satellite was sent to L1, what is the force that causes the satellite to move closer and further away from the sun when the earth moves closer and further away from the sun during its elliptical orbit?
L1 is a point of stable equilibrium. That means the balance mentioned above holds exactly at the exact L1 point, and when the satellite is slightly away from L1, tends to hold it in an orbit about L1, as seen in the rotating frame.

The answer to the other 14 questions are basically all the same: you need to understand the concept of "small perturbation." The effects of the Earth's elliptical orbit, the moon, planets, Milky Way, etc etc are all small perturbations. You're welcome to calculate the solution to the exact equations of motion including all of these effects if you care to use a computer, but to be able to describe it simply in words and pictures we ignore the small perturbations.