Moon's eccentricity, apogee and perigee

[darkdave3000]

Why do these properties each have a range each instead of a fixed value? Is it because of the 8 year precession?

I'm writing a graphical software that will illustrate the lunar orbit. I planned to show the precession too but am unsure what values of apogee and perigee and even eccentricity because of the ranges given in Wikipedia.

Note the fixed values that are given are given as averages of the given ranges. Once again, why are there ranges?

 

[Janus]

The Sun exerts a tidal influence across the orbit of the Moon distorting its shape. As the Earth-Moon system orbits the Sun, the orientation of the line of apsides changes with respect to the radial line joining with the Sun, Thus the distortion of the Moon's orbital shape changes over the course of a year, altering the perigee and apogee.

 

[darkdave3000]

I get that there is precession caused by the sun so the moon-earth orbit rotates as Wikipedia shows, but how does this change the eccentricity and the resulting perigee and apogee? Is this change a cycle that repeats and is predictable? If so how do I calculate when the apogee will be at it's min and max end of it's range?

 

[phyzguy]

Figures 4-6 and 4-7 at this site show how the eccentricity, apogee, and perigee change with time. You would need to dig deeper to know exactly how those graphs are calculated.

 

[Janus]

I get that there is precession caused by the sun so the moon-earth orbit rotates as Wikipedia shows, but how does this change the eccentricity and the resulting perigee and apogee? Is this change a cycle that repeats and is predictable? If so how do I calculate when the apogee will be at it's min and max end of it's range?

While precession will change the direction of the line of apsides with respect to the the fixed stars over time, What I was talking about was how tidal forces of the Sun actually pull on and change the shape of the Moon's orbit. IOW, the Moon's orbit exhibits its own version of "tidal bulges". When these bulges align with the line of apsides, its eccentricity is increased and both perigee and apogee are pulled further from the Earth.

 

[darkdave3000]

Where can I find:

1) The location of the current apogee and perigee using the Earth Moon barycentre as a position reference?

2) Or their current distances from said reference frame?

3) Also where can I also find out the length of the current Semi Major Axis of the moon's orbit?

I'm asking since all of these numbers change with time after each new moon... surely there is a way to get their current values and perhaps also their past and future numbers? Since I'm building a simulator I need to know where to position these nodes according to the user specified calendar date.

If I cannot find these values, would it be fair to say that when the apogee is minimum the perigee will be maximum and vice versa? Can I use the min and max values of both nodes this way?

 

[Klystron]

Early solar system sim:

 

[phyzguy]

Where can I find:

1) The location of the current apogee and perigee using the Earth Moon barycentre as a position reference?

2) Or their current distances from said reference frame?

3) Also where can I also find out the length of the current Semi Major Axis of the moon's orbit?

I'm asking since all of these numbers change with time after each new moon... surely there is a way to get their current values and perhaps also their past and future numbers? Since I'm building a simulator I need to know where to position these nodes according to the user specified calendar date.

If I cannot find these values, would it be fair to say that when the apogee is minimum the perigee will be maximum and vice versa? Can I use the min and max values of both nodes this way?

The best place to get this kind of information is the JPL Horizons web site. It can tell you the position of any solar system body at any time. There is a page here that lists the orbital elements of the moon at a single time, but I don't see how to get these as a function of time. It has a reference that might be useful. Finding the data you are asking for will probably be a significant amount of work.

 

[darkdave3000]

Thanks for this, I was going to ask if I could do this:

"So if I was to use 0.7 X apogee's min-max range and add it to the apogee's minimum distance then the Perigee should be 0.3 X perigee's rage added to perigee's minimum right?"
or similarly:
"So if I was to use 0.5 X apogee's min-max range and add it to the apogee's minimum distance then the Perigee should be 0.5 X perigee's rage added to perigee's minimum right?"
"So if I was to use 1 X apogee's min-max range and add it to the apogee's minimum distance then the Perigee should be 0 X perigee's rage added to perigee's minimum right?"
"So if I was to use 0 X apogee's min-max range and add it to the apogee's minimum distance then the Perigee should be 1 X perigee's rage added to perigee's minimum right?"

Tell me what you think, in the mean time I will check out your references.

David

The best place to get this kind of information is the JPL Horizons web site. It can tell you the position of any solar system body at any time. There is a page here that lists the orbital elements of the moon at a single time, but I don't see how to get these as a function of time. It has a reference that might be useful. Finding the data you are asking for will probably be a significant amount of work.

 

[darkdave3000]

After reading the materials, the precession of the Moon's orbit does not explain the varying distances to the apogee and perigee. Can anyone else explain how the orbit changes shape? The precession of the orbit does not explain why or how it changes shape nor does it explain it. Are you sure that the precession of the orbit is directly influencing the changing shape of the orbit and the varying apogee?

Would it be more logical to reason that the apogee is at maximum when it faces the sun and minimum when the perigee faces the sun according to season?

 

[phyzguy]

No one said that it was just the precession that affects the shape of the orbit. I think the best answer is, "it's complicated." In the link I posted in post #4, it says:

"This dynamic behavior is due to the gravitational pull of the Sun on the Moon as it orbits Earth. Consequently, a continuous torque is applied to the lunar orbit in an unsuccessful effort to permanently align the major axis towards the Sun. The annual orbit of the Earth-Moon system around the Sun coupled with the Moon's synodic orbit around Earth mean that the conditions for such a permanent alignment are always changing. The overall effect is to twist and distort the shape and orientation of the Moon's elliptical orbit.

It was stated earlier that the Moon's mean orbital eccentricity is 0.0549, but this too is subject to large changes because of solar perturbations. Figure 4-6 plots the variation in the Moon's orbital eccentricity from 2008 through 2010. The instantaneous eccentricity (light gray curve) oscillates with a period tied to the synodic month and ranges from 0.0266 to 0.0762 over this 3-year interval. "

It is the changes in eccentricity that cause the changes in apogee and perigee, not the precession. As I said earlier, getting all of the details right will probably be a lot of work. I suspect you could spend years modeling the moon's orbit in detail, and I'll bet people have.

 

[darkdave3000]

Right right right! So what happens if the sun finally manages to get that semi major axis to turn toward the sun? 2012 disaster film? :)

Or will the alignment stay fixed toward the sun permanently?

 

[Janus]

After reading the materials, the precession of the Moon's orbit does not explain the varying distances to the apogee and perigee. Can anyone else explain how the orbit changes shape? The precession of the orbit does not explain why or how it changes shape nor does it explain it. Are you sure that the precession of the orbit is directly influencing the changing shape of the orbit and the varying apogee?

Would it be more logical to reason that the apogee is at maximum when it faces the sun and minimum when the perigee faces the sun according to season?

Here is the Moon's orbit at 4 different times of Earth's orbit. In the upper corner is its "normal" shape without tidal influence by the Sun. We will ignore any apsidal precession.

The red arrows show the tidal force "stretching" the Orbit. At the top and bottom this stretches the Moon's orbit along the major axis(pulling both perigee and apogee away from the Earth), and on either side , it stretches it along the minor axis.( The shapes here are exaggerated for visual effect.)
The tidal Influence from the Sun also produces an apsidal precession causing the line of apsides joining perigee and apogee to rotate with respect to the fixed stars. One complete rotation takes ~8.45 yrs. This simply means the the line of apsides won't align with the Sun at the same point of the orbit every time, and the times of the year when the perigee is at its furthest changes.

 

[Janus]

Right right right! So what happens if the sun finally manages to get that semi major axis to turn toward the sun? 2012 disaster film? :)

Or will the alignment stay fixed toward the sun permanently?

That can never happen. The tidal influence from the Sun has an effect that produces a torque that causes the line of apsides to rotate. It's like when you try to change the direction of the axis of a gyroscope; it twists in your hands and the "twist" is at right angles to the direction you were trying to turn it.