# Calculators and Converters

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## Re: Calculators and Converters

Sorry, Airman, I have replied about the wrong graph!

This graph, and the distance vs angle graph, work quite strangely and I think this is because the angle does not change the force or distance. It changes how the force is applied, but not the value of the force. It needs looking into. I might drop these equations all together.

LongtimeAirman wrote:OBSERVATION. Graph of force vs angle F = W/dcos(θ) is surprising. Any comment?

This graph, and the distance vs angle graph, work quite strangely and I think this is because the angle does not change the force or distance. It changes how the force is applied, but not the value of the force. It needs looking into. I might drop these equations all together.

**Nevyn**- Admin
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## Updating

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From http://www.nevyns-lab.com/mathis/math/graphs.php I cannot get to the graphing calculators. In firefox the page is blank. In chrome and IE I get HTTP error 500. I can go to the non-graphing calculators.

I replaced my initial draft Angular and Angle Velocity Functions R code above http://milesmathis.the-talk.net/t315-calculators-and-converters#2592 with many corrections, including plot titles.

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From http://www.nevyns-lab.com/mathis/math/graphs.php I cannot get to the graphing calculators. In firefox the page is blank. In chrome and IE I get HTTP error 500. I can go to the non-graphing calculators.

I replaced my initial draft Angular and Angle Velocity Functions R code above http://milesmathis.the-talk.net/t315-calculators-and-converters#2592 with many corrections, including plot titles.

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**LongtimeAirman**- Admin
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## Re: Calculators and Converters

Thanks, Airman, I have fixed that now. I had actually fixed that problem in my dev environment, but when I checked the site it didn't show the symptoms, so I left it. I didn't realise that I had actually copied the code over to the server but hadn't deployed it. When I made a small change to another page yesterday, it deployed those changes as well.

What is the last line doing in this function:

It just specifies the main variable. Is that deleting it? Does that return it from the function?

What is the last line doing in this function:

- Code:

wvsradius <- function(){

w1 <- 0:10

r1 <- 1:10

v1 <- c(10,10,10,10,10,10,10,10,10,10)

for(i in r1){

w1<- sqrt(2*r1*sqrt((v1*v1)+(r1*r1))-2*r1*r1)

}

plot(r1,w1,main = "omega(w) vs. radius(r)\nw = sqrt(2rsqrt(v^2+r^2)-2r^2)")

w1

}

It just specifies the main variable. Is that deleting it? Does that return it from the function?

**Nevyn**- Admin
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## What is w1?

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What is w1? w1 tells the function wvsradius to list the w variables calculated. My plot area shows the plot. The console shows:

What is w1? w1 tells the function wvsradius to list the w variables calculated. My plot area shows the plot. The console shows:

- Code:
`> wvsradius()`

[1] 4.254380 5.726444 6.681455 7.359527 7.861514 8.242745 8.537668 8.769263

[9] 8.953504 9.101797

**LongtimeAirman**- Admin
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## Re: Calculators and Converters

Do you need to list the functions at the end or is that just invoking them?

- Code:

###########################################

#

# Function List

#

wvsradius()

wvsvelocity()

vvsradiusw()

vvsomega()

rvsvelocityw()

rvsomega()

avsradius()

avsvelocity()

vvsradiusa()

vvsangle()

rvsvelocitya()

rvsangle()

**Nevyn**- Admin
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## Re: Calculators and Converters

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The functions don't need to be listed. They are grouped for convenience. I use that list to invoke the function I want since my memory isn't good enough to just type them directly. Of course the other variables need to be reviewed or adjusted before

the function is run.

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The functions don't need to be listed. They are grouped for convenience. I use that list to invoke the function I want since my memory isn't good enough to just type them directly. Of course the other variables need to be reviewed or adjusted before

the function is run.

.

**LongtimeAirman**- Admin
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## Re: Calculators and Converters

Cool, thanks. I have the start of an R code generator working. I just took the javascript generator and converted it into R code. The graphing functions still need work but the structure is working as I want it to. It only works on the Velocity calculator as I need to add in the R code for each equation in the database and I have only done that one so far. I am just using Velocity as my testing ground.

You can have a look at it here: http://www.nevyns-lab.com/mathis/math/lib-r.php?type=velocity&equation=velocity

The calc* functions should be usable, but the calc*Vs* ones are not, they are still mostly javascript code.

You can have a look at it here: http://www.nevyns-lab.com/mathis/math/lib-r.php?type=velocity&equation=velocity

The calc* functions should be usable, but the calc*Vs* ones are not, they are still mostly javascript code.

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## Re: Calculators and Converters

I made some updates to the R code generator so that the functions are legal syntax and working. I have also added another function to plot the graph, using appropriate labels.

I copied the code into R and it ran beautifully.

If anyone has any other ideas on what could be possible in R (or any language), then post them and I will see what I can do. This covers what the other languages do and is probably enough, but if I can provide more then I am happy to do so.

I now have to write R versions of all of the equations. This should be fairly straight forward, but some of the complicated equations may cause slight nausea. Once that is done, I can add R as a language to the code generation buttons. I might even look into making those buttons dynamic such that they look to see what languages a particular equation has, and only supplies links to those languages.

I copied the code into R and it ran beautifully.

If anyone has any other ideas on what could be possible in R (or any language), then post them and I will see what I can do. This covers what the other languages do and is probably enough, but if I can provide more then I am happy to do so.

I now have to write R versions of all of the equations. This should be fairly straight forward, but some of the complicated equations may cause slight nausea. Once that is done, I can add R as a language to the code generation buttons. I might even look into making those buttons dynamic such that they look to see what languages a particular equation has, and only supplies links to those languages.

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## Re: Calculators and Converters

I have now done all of the motion and angular motion equations. Found and fixed a few bugs while I was testing them.

Motion: http://www.nevyns-lab.com/mathis/math/lib-r.php?subject=motion

Angular Motion: http://www.nevyns-lab.com/mathis/math/lib-r.php?subject=angular_motion

Motion: http://www.nevyns-lab.com/mathis/math/lib-r.php?subject=motion

Angular Motion: http://www.nevyns-lab.com/mathis/math/lib-r.php?subject=angular_motion

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## Re: Calculators and Converters

I am proud to announce the official release of the R Code Generator!

You can now access R code for any equation from the code generation buttons.

I also found and fixed a bug where it didn't limit the generated code to a specified equation. This happened because I took some common code from all of these calculator pages and put it into a library. I missed the target equation part of that when I did it, but all is fixed now.

As I copied the Java code to convert it into R code, I found a few errors in that as well. They were caused by copying the Javascript code to convert it into Java and missing some variable datatypes.

You can now access R code for any equation from the code generation buttons.

I also found and fixed a bug where it didn't limit the generated code to a specified equation. This happened because I took some common code from all of these calculator pages and put it into a library. I missed the target equation part of that when I did it, but all is fixed now.

As I copied the Java code to convert it into R code, I found a few errors in that as well. They were caused by copying the Javascript code to convert it into Java and missing some variable datatypes.

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## Gute Stoff hombre

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Nevyn, I think you've made quite an accomplishment. Hard for me to put it better because I'm still stunned. I've used and started reviewing your code, since I won't understand it otherwise. Even though you may have minimal experience in R I'm sure your work follows best practices and so it absolutely requires study. I must admit, my time and psyche are stretched a bit thin lately but you're providing positive guidance. Gute Stoff hombre.

.

Nevyn, I think you've made quite an accomplishment. Hard for me to put it better because I'm still stunned. I've used and started reviewing your code, since I won't understand it otherwise. Even though you may have minimal experience in R I'm sure your work follows best practices and so it absolutely requires study. I must admit, my time and psyche are stretched a bit thin lately but you're providing positive guidance. Gute Stoff hombre.

.

**LongtimeAirman**- Admin
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## Re: Calculators and Converters

Nevyn wrote:I am proud to announce the official release of the R Code Generator!

You can now access R code for any equation from the code generation buttons.

I also found and fixed a bug where it didn't limit the generated code to a specified equation. This happened because I took some common code from all of these calculator pages and put it into a library. I missed the target equation part of that when I did it, but all is fixed now.

As I copied the Java code to convert it into R code, I found a few errors in that as well. They were caused by copying the Javascript code to convert it into Java and missing some variable datatypes.

I must concur with LTAM...very cool Nevyn!

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## Re: Calculators and Converters

I don't know enough about R to know if I have used best practices or not. There really is minimal code though, so it shouldn't be too bad. That code is just repeated for each equation so it ends up looking like a lot of code. I found better ways in R to sequence the values when creating graph data, so I made use of that and restructured the rest. The graph labels were a bit tricky but I found a way to create the label array and pass the reference back to the caller.

I don't really like the function names. They are too long, especially for R. I wrote them that way to be consistent with the other languages. I have managed to keep the same function signatures across 4 languages, which is no mean feat. I think I will remove the first namespace though. I used it for Javascript and kept it across the other languages. It works well in Java too, but it just makes the function names too long in R and C, which I am currently working on.

By the way, you can add another parameter to the url to get some debug code. Just append

http://www.nevyns-lab.com/mathis/math/lib-r.php?subject=angular_motion&debug=true

http://www.nevyns-lab.com/mathis/math/lib-r.php?debug=true

This is really helpful for me in R because I can paste in the code and then just call Equations.test() and it will generate every graph using the same parameters as my web pages. If there is an error anywhere in the code, it will fail and give me some idea of where the problem is.

I don't really like the function names. They are too long, especially for R. I wrote them that way to be consistent with the other languages. I have managed to keep the same function signatures across 4 languages, which is no mean feat. I think I will remove the first namespace though. I used it for Javascript and kept it across the other languages. It works well in Java too, but it just makes the function names too long in R and C, which I am currently working on.

By the way, you can add another parameter to the url to get some debug code. Just append

**&debug=true**if there are existing parameters, or add**?debug=true**if there are none.http://www.nevyns-lab.com/mathis/math/lib-r.php?subject=angular_motion&debug=true

http://www.nevyns-lab.com/mathis/math/lib-r.php?debug=true

This is really helpful for me in R because I can paste in the code and then just call Equations.test() and it will generate every graph using the same parameters as my web pages. If there is an error anywhere in the code, it will fail and give me some idea of where the problem is.

**Nevyn**- Admin
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## Solar System Properties

I have another treat for you all!

I extended the calculators database to include solar system bodies which I then use to present and calculate various properties of those bodies in a table. A second table allows you to find the relative values of those properties by comparing each body to a selected base body.

This is helpful for a lot of Miles' papers where he uses these relative values.

http://www.nevyns-lab.com/mathis/math/solar-system.php

I extended the calculators database to include solar system bodies which I then use to present and calculate various properties of those bodies in a table. A second table allows you to find the relative values of those properties by comparing each body to a selected base body.

This is helpful for a lot of Miles' papers where he uses these relative values.

http://www.nevyns-lab.com/mathis/math/solar-system.php

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## Interactive solar system diagram?

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Nevyn, You’re on a roll. Just this morning, I see an update.

PAPER UPDATE, added 6/2/17, The Cause of the Solar Cycles http://milesmathis.com/cycle.pdf . A reader has tracked the declination cycles of the big-four planets against sunspot activity in two charts, showing an almost perfect correlation. See end of paper.

Please consider creating an adjustable solar system with interactive diagram. Where we can observe the just Earth/Moon, or the Jovians and see the field strengths or interactions between bodies. What do you think? Don't go running off and building it without talking about it first!

.

Nevyn, You’re on a roll. Just this morning, I see an update.

PAPER UPDATE, added 6/2/17, The Cause of the Solar Cycles http://milesmathis.com/cycle.pdf . A reader has tracked the declination cycles of the big-four planets against sunspot activity in two charts, showing an almost perfect correlation. See end of paper.

Please consider creating an adjustable solar system with interactive diagram. Where we can observe the just Earth/Moon, or the Jovians and see the field strengths or interactions between bodies. What do you think? Don't go running off and building it without talking about it first!

.

**LongtimeAirman**- Admin
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## Re: Calculators and Converters

Well that kind of ties into what I am doing at the moment. I am adding a new section to the solar system page that calculates the distance of the magnetopause of each planet. It puts that data into a table, but I have thoughts on using that data to feed an animation of some kind. I'm not too sure of the details at this stage. I'm still working out the math for the magnetopause calculations. I have figures that are what I expect but am not entirely confident in the math to get them. I have to translate Miles' words into equations and then figure out how to put those equations together to get the data I want. It's not easy.

The main thing that is tripping me up is the 1/r^4 drop-off of charge density from a bodies surface. I was taking that r to mean a radius, but it turns out that it is not exactly a radius, but the coefficient of the radius. That is, r does not equal some distance. The actual distance is r * bodies radius. But then you have one side of the equation using the Sun's radius and the other side using the planets radius and I need to find where they are equal. Anyway, I am pretty close and the values coming out are what I expect but I am not too sure about the distance I am using in the equations.

In my previous attempts I was trying to use the absolute distance between the bodies surfaces and I think I still need to use that, but I'm not convinced that the equation I have developed is using it correctly. I redeveloped the equations and it used a distance variable and, not thinking clearly, I used the distance I already had and the values come out right but on closer inspection I don't think it is the right distance for that equation or, more likely, I need to redevelop the equation to use the right distance. My guess is that the current values are wrong, but only slightly which is because the distance I am using is only slightly bigger than the distance the equation wants.

I'll just keep working through it until it makes sense.

The main thing that is tripping me up is the 1/r^4 drop-off of charge density from a bodies surface. I was taking that r to mean a radius, but it turns out that it is not exactly a radius, but the coefficient of the radius. That is, r does not equal some distance. The actual distance is r * bodies radius. But then you have one side of the equation using the Sun's radius and the other side using the planets radius and I need to find where they are equal. Anyway, I am pretty close and the values coming out are what I expect but I am not too sure about the distance I am using in the equations.

In my previous attempts I was trying to use the absolute distance between the bodies surfaces and I think I still need to use that, but I'm not convinced that the equation I have developed is using it correctly. I redeveloped the equations and it used a distance variable and, not thinking clearly, I used the distance I already had and the values come out right but on closer inspection I don't think it is the right distance for that equation or, more likely, I need to redevelop the equation to use the right distance. My guess is that the current values are wrong, but only slightly which is because the distance I am using is only slightly bigger than the distance the equation wants.

I'll just keep working through it until it makes sense.

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## Magnetopause Eh?

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When I was programming boids I tried to model the charge field E/M emissions about each particle (planet) as a D field function, a dual torus. So that normal approaches directly in toward the poles experienced the least emission resistance; most emission resistance would occur at +/-30. Does that even sound vaguely ...? I'll be ok.

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Sounds interesting. I guess there must be a large dominant E/M field - the Sun - that interacts with the Earth E/M field. What is the magnetopause used for? How do you define it? Is it a single boundary or one of many Charge field equal strength contour surfaces? If I follow you, I see the magnetopause extends in a flame-like column far beyond the planets' orbits; almost out to the next orbiting body. If so, I believe it would be very unhealthy to pass under the magnetopause of Venus. EU cataclysm stuff.I am adding a new section to the solar system page that calculates the distance of the magnetopause of each planet.

When I was programming boids I tried to model the charge field E/M emissions about each particle (planet) as a D field function, a dual torus. So that normal approaches directly in toward the poles experienced the least emission resistance; most emission resistance would occur at +/-30. Does that even sound vaguely ...? I'll be ok.

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## Re: Calculators and Converters

Yes, the magnetopause is really just an expression of the charge-pause. That is, the distance where the planet charge density equals that of the dominant body, the Sun in our case. The charge-pause is fairly constant but the magnetopause can vary slightly. It will always average out to the charge pause, but the magnetopause relies on ions being present but the charge-pause does not. Which is just to say that you need ions to measure magnetism. The underlying magnetism is still there, but we won't be able to see it without the ions.

I don't think the magnetopause is used for anything, it is just something we found when we started to orbit the Earth. Of course, it does protect us from the Solar Wind, but I don't know if humans are using it for anything explicitly.

The magnetopause is just the distance from a planet, or body, where its own magnetic field stops and the magnetic field of the dominant body starts, from the perspective of that planet. It is the point where the charge from each body cancels each other. It is always an interaction between two bodies. It requires two charge fields in opposition which means we are calculating the minimum radius of the magnetopause (in a direct line between the two bodies) and not the radius to the sides or rear. The so-called tail does stretch a long way and this is the result of the two charge streams merging at the sides and also because the planet blocks the Suns charge from that area so its own charge field can use it almost freely. We may find that other planets that are in higher orbits actually squash that tail a bit when they are inline with the planet and Sun.

I don't think it will be a problem to pass through another planets charge sheath. It would be if we didn't have our own, but the Earth's charge field can block the Sun's charge, so it will have no problem with that of Venus or even a Jovian. Of course, that depends on the distance. If we were very close to Jupiter we might have something to worry about but then again, Mercury can withstand the Sun at its distance and it is a lot smaller than the Earth (38% of it according to some informative web site I just happened to find ).

I don't think the magnetopause is used for anything, it is just something we found when we started to orbit the Earth. Of course, it does protect us from the Solar Wind, but I don't know if humans are using it for anything explicitly.

The magnetopause is just the distance from a planet, or body, where its own magnetic field stops and the magnetic field of the dominant body starts, from the perspective of that planet. It is the point where the charge from each body cancels each other. It is always an interaction between two bodies. It requires two charge fields in opposition which means we are calculating the minimum radius of the magnetopause (in a direct line between the two bodies) and not the radius to the sides or rear. The so-called tail does stretch a long way and this is the result of the two charge streams merging at the sides and also because the planet blocks the Suns charge from that area so its own charge field can use it almost freely. We may find that other planets that are in higher orbits actually squash that tail a bit when they are inline with the planet and Sun.

I don't think it will be a problem to pass through another planets charge sheath. It would be if we didn't have our own, but the Earth's charge field can block the Sun's charge, so it will have no problem with that of Venus or even a Jovian. Of course, that depends on the distance. If we were very close to Jupiter we might have something to worry about but then again, Mercury can withstand the Sun at its distance and it is a lot smaller than the Earth (38% of it according to some informative web site I just happened to find ).

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## Re: Calculators and Converters

This is the source material that I am working with:

It does sound pretty simple, but you have to be careful with these relative values. They don't always mean what you think they mean. In this case, I had to realise that the Sun's charge was expressed in Sun radii and the planets charge was expressed in its own radii. Now I just need to find a way to link them together so that I can solve one equation with two unknowns. If I can get that working, I will attempt to remove all of the relative values and see if I can find an equation using straight radii values.

Miles Mathis wrote:

Wiki tells us that the magnetopause is 10-12 earth radii in the direction of the Sun. Using my mechanics, we can calculate that distance directly—something the standard model never does and cannot do. The mass of the Sun is 332,990 Earth's and its density is .255 Earth's. We seek a charge density on the surface of the Sun, and we can get that by just looking at the words. We seek a “charge density”. That could be written “charge x density”, and, as I have shown, charge is just a variant definition of mass. Therefore, we re-write the product as “mass x density.” M x D = 84,986. The Sun's charge density is 84,986 times that of the Earth. So we find by simple math that the charge field density is vastly different than the material density. We are finding the charge field density at the surface of the Sun, so we must sum all the mass “behind” that surface. All that mass emits charge photons.

Now we seek the point between Earth and Sun where the two charge densities are equal. Since I have proved elsewhere that the charge field, when emitted by spheres, diminishes as 1/r^{4}, we can solve. If the Sun's relative charge density is 84,986 at 1 Sun radius, at 214 Sun radii it will be .00004052. If the Earth's density is 1 at 1 Earth radius, at 12.53 Earth radii it will be .00004057. That is where the charge field strengths match. Since Wiki is measuring from the Earth's surface, we must subtract one Earth radius, giving us 11.53 Earth radii for the charge-pause.

It does sound pretty simple, but you have to be careful with these relative values. They don't always mean what you think they mean. In this case, I had to realise that the Sun's charge was expressed in Sun radii and the planets charge was expressed in its own radii. Now I just need to find a way to link them together so that I can solve one equation with two unknowns. If I can get that working, I will attempt to remove all of the relative values and see if I can find an equation using straight radii values.

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## Solar System

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First, I see that my firefox displays http://www.nevyns-lab.com/ properly. I haven’t checked since our last go round. Did you make a fix or I’ll just be grateful that being slow is better than never.

At http://www.nevyns-lab.com/mathis/math/solar-system.php . Looking at General Properties.

Please confirm your mass values. You show the Sun Mass to be 1.989e+24. I believe that number should be 1,988,500e+24. Likewise, Earth Mass is shown to be 5.993e+18, shouldn’t that be – 5.993e+24? If that column is off, then the Charge Density column is off too.

Miles has shown how the planetary tilt is a function of the charge field. I guess you’ll enter orbital data at some point. Aren't all orbits ellipses?

And all the moons!

I believe I recall seeing your solar system model, I may very well be confused. I don’t recall any problem with it, the scale was daunting (large spaces between tiny bodies). I believe Jared cited a solar system simulator in one of our discussions (maybe Saturn).

A charge field based solar system is a fine goal.

P.S. I think I see that each magnetopause must be calculated with greatly varying charge density values. The sun's field strength diminishes greatly as approach the edge the solar system. At the edge we can have very isolated and cold bodies.

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First, I see that my firefox displays http://www.nevyns-lab.com/ properly. I haven’t checked since our last go round. Did you make a fix or I’ll just be grateful that being slow is better than never.

At http://www.nevyns-lab.com/mathis/math/solar-system.php . Looking at General Properties.

Please confirm your mass values. You show the Sun Mass to be 1.989e+24. I believe that number should be 1,988,500e+24. Likewise, Earth Mass is shown to be 5.993e+18, shouldn’t that be – 5.993e+24? If that column is off, then the Charge Density column is off too.

Miles has shown how the planetary tilt is a function of the charge field. I guess you’ll enter orbital data at some point. Aren't all orbits ellipses?

And all the moons!

I believe I recall seeing your solar system model, I may very well be confused. I don’t recall any problem with it, the scale was daunting (large spaces between tiny bodies). I believe Jared cited a solar system simulator in one of our discussions (maybe Saturn).

A charge field based solar system is a fine goal.

P.S. I think I see that each magnetopause must be calculated with greatly varying charge density values. The sun's field strength diminishes greatly as approach the edge the solar system. At the edge we can have very isolated and cold bodies.

.

Last edited by LongtimeAirman on Wed Jun 07, 2017 3:08 pm; edited 1 time in total (Reason for editing : Added PS)

**LongtimeAirman**- Admin
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## Re: Calculators and Converters

I have made various changes to the main page, but I don't know what I did to fix your issue. I just added a cache manifest file so that the images in the main page are cached in your browser. This should make that page load faster after the images are cached. I have also been thinking of removing all of the apps from the main page and put them into an Applications page or something like that. This would reduce the number of sections and hence the number of images to load.

The Sun's mass is slightly different because the radius and density values are slightly different. The values may also be rounded. Be careful of the units too. I have converted all of my values to use the same units and I chose km instead of m and the density is often specified in kg/m^3 where-as I am using kg/km^3. This will change the position of the decimal place. Maybe I didn't convert the density correctly, I'll check it.

I had access to the orbital data and thought about putting it in the database for future use, but I'm not sure what I want to do with it yet so I didn't.

Another section for tilt would be a good idea. I think the tilt includes the influences from other bodies, not just the Sun, so I will have to see what I can do about that. If so, then you can only get a value for tilt for a specific time because the layout of the planets becomes important. I'll look into it once I get the magnetopause data working.

If I can get these data tables working for the various equations needed to specify orbits, then I can figure out how to put that all into an app and get a fully functional Mathis Orbital Simulator. That really would be an awesome outcome.

The Sun's mass is slightly different because the radius and density values are slightly different. The values may also be rounded. Be careful of the units too. I have converted all of my values to use the same units and I chose km instead of m and the density is often specified in kg/m^3 where-as I am using kg/km^3. This will change the position of the decimal place. Maybe I didn't convert the density correctly, I'll check it.

I had access to the orbital data and thought about putting it in the database for future use, but I'm not sure what I want to do with it yet so I didn't.

Another section for tilt would be a good idea. I think the tilt includes the influences from other bodies, not just the Sun, so I will have to see what I can do about that. If so, then you can only get a value for tilt for a specific time because the layout of the planets becomes important. I'll look into it once I get the magnetopause data working.

If I can get these data tables working for the various equations needed to specify orbits, then I can figure out how to put that all into an app and get a fully functional Mathis Orbital Simulator. That really would be an awesome outcome.

**Nevyn**- Admin
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Join date : 2014-09-11

## Re: Calculators and Converters

I have miscalculated the density conversions. I naively converted kg/m^3 into kg/km^3 by multiplying by 1000, the ratio of a km to a m. What I should have done is multiplied by 1000^3, so all of my density values are off by a million. I'll fix that later tonight.

This does not affect the relative values, since they are, well, relative! As long as both parts of the ratio are off by the same factor, it will still give the same answer.

This does not affect the relative values, since they are, well, relative! As long as both parts of the ratio are off by the same factor, it will still give the same answer.

**Nevyn**- Admin
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Join date : 2014-09-11

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