https://community.wolfram.com RSS Feed for Wolfram Community showing questions tagged with Astronomy sorted by most viewed. https://community.wolfram.com/groups/-/m/t/251690 Dear community members, I'm currently try to use Wolfram Mathematica to some gravity research. But i can't find built-in methods do differential geometry calculations in Mathematica. For example, is there any way to compute Einstein or Ricci tensor by metric? Or something more complicate, like create manifold, some medium with fixed state equation and write Einstein equations for this system? Thanks, Boris Latosh Boris Latosh 2014-05-14T18:31:41Z https://community.wolfram.com/groups/-/m/t/293403 TL;DR --- I have three issues with getting sun positions in Mathematica V10: - It is extremely slow compared to V9 - It doesn't *seem* to yield correct results - a) It needs an Internet connection, which b) is not assured to always return results and c) if not used optimally can easily consume your monthly allowance of W|A calls Long story === With the advent of V10 `AstronomicalData` has been deprecated, as shown on its documentation page: ![enter image description here][1]. I'm not an astronomer, so my main use of this function has been restricted to its capability to get the sun position using functions calls like this: { AstronomicalData["Sun", {"Azimuth", {2013, 3, 1, #, 0, 0}, {52.37`, 4.89`}}, TimeZone -> 1], AstronomicalData["Sun", {"Altitude", {2013, 3, 1, #, 0, 0}, {52.37`, 4.89`}}, TimeZone -> 1] } & /@ Range[0, 23] > {{341.47732, -43.93930}, {2.33417, -45.21747}, {22.94232, -43.19133}, > {41.52167, -38.28400}, {57.55208, -31.30276}, {71.47253, -23.03159}, > {84.02194, -14.08294}, {95.91940, -4.92723}, {107.80166, 4.03418}, {120.23770, 12.40167}, {133.72303, 19.72563}, {148.59433, > 25.48377}, {164.84179, 29.12209}, {181.93103, 30.19428}, {198.91284, > 28.55117}, {214.89602, 24.41962}, {229.46400, > 18.28613}, {242.70064, 10.70703}, {254.98998, > 2.19073}, {266.84760, -6.82566}, {278.85594, -15.94505}, {291.66723, -24.75464}, {306.00911, -32.75641}, {322.57956, > -39.29877}} So, this gets me the sun positions in steps of an hour during a particular day in Amsterdam (TZ 1). The same call still works in V10, though it now returns numbers with units; degrees in this case. On its first call, it reads some paclet information from a Wolfram server, but on any successive call no Internet connection is needed. I will be going into detail about timing further on, but I'll say here that the V10 function takes about three times longer than its V9 namesake. I blame the addition of units for that. With `AstronomicalData` apparently deprecated we are supposed to use its successors. In this case I need `SunPosition`. A direct translation of the above would be: SunPosition[GeoPosition[{52.37`, 4.89`}], DateObject[{2013, 3, 1, #, 0, 0}, TimeZone -> 1]] & /@ Range[0, 23] > {{95.7, -5.1}, {107.6, 3.9}, {120.0, 12.3}, {133.5, 19.6}, {148.3, 25.4}, {164.5, 29.1}, {181.6, 30.2}, {198.6, 28.6}, {214.6, 24.5}, {229.2, 18.4}, {242.5, 10.9}, {254.8, 2.4}, {266.6, -6.7}, {278.6, -15.8}, {291.4, -24.6}, {305.7, -32.6}, {322.2, -39.2}, {341.3, -43.5}, {2.0, -44.8}, {22.5, -42.9}, {41.1, -38.0}, {57.1, -31.1}, {71.0, -22.9}, {83.6, -13.9}} As with the new `AstronomicalData` the output is actually in degrees which I have removed in the above output for the sake of clarity. There are a few things to note: - `SunPosition` uses position and date objects, the latter being new in V10 - `SunPosition` does not have a `TimeZone` option, but you can set it in `DateObject` - `SunPosition` can use the old lat/long list position indication. It also can use a date list to enter the date instead of a `DateObject`. In the latter case you are out of options with respect to time zones and you have to add the appropriate amount of time offset - It is extremely slow, and it may even time-out: ![enter image description here][2] - Last but not least: the results seem to be plain wrong. It suggests that sunrise is somewhat before 1 am, which is -of course- incorrect. I assume that this has something to do with a `$GeoLocation` setting for the observer of the sun positions, but I haven't managed to sort out what I am supposed to enter to get the correct sun positions for the location provided in the same call. As to timing: I noticed very inconsistent timings for `SunPosition` compared to `AstronomicalData`, so I used the following code to collect a somewhat more statistical sound sample: SetAttributes[timingTest, HoldFirst]; timingTest[code_, repeats_Integer] := Table[ ClearSystemCache[]; code // AbsoluteTiming // First, {repeats} ] Using this, I collected timing of 20 calls to the following code snippets: - `AstronomicalData` V9 and V10: As above - `SunPosition`: As above - `SunPosition` without `GeoPosition`, just the lat/long list. - `SunPosition` without `GeoPosition`, and also without the `DateObject` date, just a classical date list (with the hour set to +1 to accommodate TZ 1) - `SunPosition` V10 without `GeoPosition` and with the `Map` (`/@`) gone and replaced by a `DateRange` inside the call. In the last case, the returned value is a `TimeSeries` object from which I extract the positions using the `"Paths"` method: SunPosition[{52.37`, 4.89`}, DateRange[{2013, 3, 1, 1, 0, 0}, {2013, 3, 1, 24, 0, 0}, "Hour"]]["Paths"][[1, All, 2]] The results were as follows: ![enter image description here][3] Clearly, the `SunPosition` results are very disappointing. Getting the sun positions with `SunPosition` is almost 40 times slower than using the old V9 method (which, I should add, wasn't particularly quick either. I have an implementation in Mathematica code which is faster). The V10 implementation of `AstronomicalData` is also more than three times slower than the V9 version. The `DateRange` version of the call saves a lot of communication overhead. Still, it is almost *five times slower* than in V9. The cause of all this slowness is that `SunPosition` simply does a call to Wolfram|Alpha. Sniffing the communication one sees the following string passed to the server: "1:eJxTTMoPSuNgYGAoZgESPpnFJcHcQEZwaV5AfnFmSWZ+XhoTsmxR/6GvGjH9wg4Qhr6XQxobsnzmXXYGhkxmIC+TEUSIgwggZihigIJgoAIGj/yizKr8PJigA5yBZtubwB1yrdxeDkXVIuvcH1aJOBRzAqUcS0vycxNLMpMBSAArww==" which can be turned into readable form using `Uncompress`: {"SunPosition", {4.89, 52.37}, {2013, 3, 1, 23, 0, 0.}, "Horizon", 2., 2., {52.09, 5.12}, Automatic} Here, we can recognize the lat/long of the position I used (but with lat/long reversed - Is this somehow significant?). At the end is my own `$GeoLocation`, but I don't believe it is used at all (and it shouldn't: I'm asking for the sun position over Amsterdam, not where I live). Changing it with `Block` I get the same results: Block[{$GeoLocation = GeoPosition[{52.37`, 40.89`}]}, SunPosition[{52.37`, 4.89`}, {2013, 3, 1, 1, 0, 0}]] Apart from the slowness, there's the issue of the necessary Internet connectivity (Want to give a demonstration and you don't have Internet? Sorry, you're out of luck). And what of the use of W|A calls? Each of the `SunPosition` tests (except the last one) took me 20 * 24 = 480 calls. So this part of my testing only already took 1440 calls, and one should be reminded that a typical Home Use license allows for only 3,000 calls per month. Things like this can go pretty fast. In fact, I once wrote an application that calculates the impact of building changes on shadows around your house throughout the year. It does in the order of 17,000 `AstronomicalData` calls. I couldn't implement that naively using `SunPosition` and have it actually work. Clearly, one should now use the `DateRange` version of the call as much as possible. ---------- To wrap up: I have one real question, i.e., how to get `SunPosition` to return the same values as `AstronomicalData`, and a request to the WRI team: please put `SunPosition` in the kernel and don't use W|A calls, because the situation as it is now is rather annoying and IMHO a real step backwards. [1]: /c/portal/getImageAttachment?filename=AstronomicalData.png&userId=43903 [2]: /c/portal/getImageAttachment?filename=timeout.png&userId=43903 [3]: /c/portal/getImageAttachment?filename=results.png&userId=43903 Sjoerd de Vries 2014-07-13T16:39:48Z https://community.wolfram.com/groups/-/m/t/772569 Hello, I’m a graphic artist working for an education company in Arizona. I was given the task of writing a twenty page reader about black holes for middle school students, and all of my research has gone well. But I’ve reached a dead end regarding time dilation. I’m writing a scenario where the reader visits a ten-solar mass black hole while his or her friend stays at a safe distance. I would like to write the following: > If you could stay just in front of the event horizon, you could watch > your ten year old friend turn 100 years old in just [*xxx* *amount of > time*]. Unfortunately, I can’t get an adequate answer to this. I was directed to the time dilation calculator here http://www.wolframalpha.com/input/?i=time+dilation+calculator , but I don’t know how to use it. Just playing with it I’ve gotten negative numbers, *i*, and “exceeds the speed of light’. I have no idea what any of this means. What’s the gravitational acceleration? What’s the rest frame? What’s the radius of what? I know the time should be very short, but “a blink of an eye” isn’t useful. Would some kind-hearted soul be willing to walk me through this in layman’s language? Or better yet, give me an accurate (but not necessarily precise) number. Any help is greatly appreciated. Thank you and best regards, Jack Jack M 2016-01-13T02:39:29Z https://community.wolfram.com/groups/-/m/t/126665 Could anyone help? Always getting errors when export simple data to FITS format. I'm using Macbook Air, OS X 10.8.4. Not sure if it's machine dependent.    e.g.,  [mcode]d = First@ Import["http://exampledata.wolfram.com/messier61.fits.gz", "RawData"]; Export["image.fits", d] ConstantArray::ilsmn: Single or list of non-negative machine-sized integers expected at position 2 of ConstantArray[32,{-17}]. >> Join::heads: Heads List and ConstantArray at positions 1 and 3 are expected to be the same. >> BinaryWrite::nocoerce: Join[{83,73,77,80,76,69,32,32,61,32,32,32,32,32,32,32,32,32,32,32,32,32,32,32,32,32,32,32,32,84,32,47,32,78,111,114,109,97,108,32,70,73,84,83,32,102,105,108,101,32,<<750>>},<<3>>,{32,32,32,32,32,32,32,32,32,32,32,32,32,32,32,32,32,32,32,<<13>>,32,32,32,32,32,32,32,32,32,32,32,32,32,32,32,32,32,32,<<27>>}] cannot be coerced to the specified format. >>[/mcode] XIN Wang 2013-09-19T19:44:31Z https://community.wolfram.com/groups/-/m/t/532744 I'm starting to think I wasted money on a product that doesn't work... I have the following code: (* Take inputs for ECEF *) x = Input["What is the x coordinate?"]; y = Input["What is the y coordinate?"]; z = Input["What is the z coordinate?"]; (* Put in Coordinate Form *) GeoPositionXYZ[{x, y, z}, "ITRF00"]; (* Convert to LLA *) GeoPosition[%]; (* Display Map *) GeoGraphics[GeoRange -> "World", GeoProjection -> "Robinson"]; It converts the given coords in ECEF to Latitude, Longitude, Height... then it's supposed to plot latitude and longitude on a map. 1) It won't display any output at all because Mathematica is garbage. How do I make the software I paid six months of grocery budget for and am now eating ramen noodles and unable to pay my bills do what it's supposed to do and give some damned output? 2) Once it's giving output, how do I plot the latitude and longitude on the map? Nathan Lundholm 2015-07-19T11:49:15Z https://community.wolfram.com/groups/-/m/t/574455 Please find attached a small routine that plots the intensity profile between two points in a circular image. I'd like a routine that was able to make several radial routes, such as the example, from the center of the image to its exterior. Perhaps with an adjustable angular variation. I am very grateful for any help. Antonio ![enter image description here][1] [1]: http://community.wolfram.com//c/portal/getImageAttachment?filename=sdf34546ygrwefads.png&userId=11733 Antonio de Oliveira 2015-10-02T19:52:07Z https://community.wolfram.com/groups/-/m/t/487004 I'm trying to use Mathematica to drive an autofocus system for a telescope and ccd camera. Three calculations are commonly used FWHM, HFD (half flux diameter) and sigma. So I need to be able to calculate those from a small (100x100) crop from an image produced by my tethering software. I found a Mathematica program to separate the stars out of the small image that works great so that is all sorted. As I understand it you do a gaussian distribution on the pixel data then calculate the two values to use to figure out the direction and when you are in focus. I'm new to Mathematica discovered it when I bought a Raspberry Pi and since I can buy a copy for about half what commercial software to do autofocus costs I thought it would be the way to go as I can use Mathematica for so much more. But I'm not having any luck so far doing the GD. So any clues tips or links are very much appreciated. Dan Dan Pollock 2015-04-27T00:09:28Z https://community.wolfram.com/groups/-/m/t/466654 Hi, <BR> I am creating a powerpoint for a presentation I'm giving on black holes. I created a 3D revolution plot which requires computations (the resulting graphic that is displayed depends on the value of parameters chosen by sliders). I would like to export this interactive graphic into my powerpoint presentation. I assumed the CDF player would be the way to do this, but when I export it to CDF the graphic won't display, because CDF format does not allow for the computations required to manipulate the graphic. Does anyone know a way I can get the graphic into my powerpoint in a way that I can interact with it? Thanks, <BR> Jeremy Primus Jeremy K 2015-03-25T07:21:16Z https://community.wolfram.com/groups/-/m/t/420255 Galilei observed the moons of Jupiter and used it for the Determination of the Position on open sea. Which mathematical method was used to arrive at this result, and are there historical records of this calculation method. Sidereus nuncius describes only the observations. Was it actually used for the Determination of the longitude? Wim Schols 2015-01-09T23:29:41Z https://community.wolfram.com/groups/-/m/t/427526 I noticed that all important "Geoprojections" are available in projections for spherical reference models: GeoProjectionData function. 1 - How can I use the sinusoidal projection using astronomical data ? I want to use the frames of this projection to plot astronomical points in that map , using right ascension and declination as the coordinates, both in degrees. 2 - And what about the [Hammer-Aitoff Equal-Area Projection][1]? If that projection is not available, how do I make an astronomical plot using the equations ( also doing ticks, axis, frames, etc..)? In the link below is data that can be used. The format is { {RA,DEC, Velocity},....}. Just need the RA, DEC parameters. So [DataSample][2] EDIT 1: I did some tries, after reading maps and cartographies from Wolfram help: > GeoGraphics[{}, GeoRange -> All, GeoProjection -> "Sinusoidal", > GeoGridLines -> Automatic, GeoGridLinesStyle -> Directive[Thin, > Dashed, Yellow], GeoBackground -> Black, Frame -> True] And the result is: ![SInusoidalMap][3] But I need to insert the point data and make the coordinates range going -90 to 90 and 0 to 360 And one more challenge, I want to use a color range for every point using the parameter (Velocity). Is that possible? EDIT 2: Thanks to bbgodfrey, we did this (http://mathematica.stackexchange.com/questions/72426/using-map-projections-with-astronomical-data): ![Sinusoidal Mapping][4] Wolfram developers, don t you think it is time to create specific plotting functions for the astronomy area? [1]: http://mathworld.wolfram.com/Hammer-AitoffEqual-AreaProjection.html [2]: https://www.dropbox.com/s/n542435m9appl9l/DadosRad2014_RADECVELOC_15124_1024.dat?dl=0 [3]: /c/portal/getImageAttachment?filename=AnalisedoAnalyser.jpg&userId=33625 [4]: /c/portal/getImageAttachment?filename=MapaSinusRad2014_15125_1121.png&userId=33625 Marcelo De Cicco 2015-01-24T12:37:07Z https://community.wolfram.com/groups/-/m/t/217048 Hello, I have constructed a function which is simply a three-dimensional gaussian: As you can see, these are both gaussian terms, so they should be easy to integrate. I have tried many methods of NIntegrate, which do not converge or give a consistent answer. This function is very simple and well-behaved, it is a ball at r=0 and a shell at r=3, both of gaussian shape. How can I produce the definite integral of this function? [mcode]Conv[x_, y_, z_, xp_, yp_, zp_] := (1/4)*1/Sqrt[Pi]*Exp[-((xp - x)^2 + (yp - y)^2 + (zp - z)^2)] + (3/4)*(1/Sqrt[Pi])*Exp[-4*(Sqrt[(xp - x)^2 + (yp - y)^2 + (zp - z)^2] - 3.5)^2] [/mcode] C. E. Coppola 2014-03-11T19:12:07Z https://community.wolfram.com/groups/-/m/t/93435 Hello all, I've been playing around with OpenCL and I've run into a problem that I can't pin down. When running this n-body simulation, the amount of memory in use gradually increases with every time step (until I run out completely). I've tried using Bytecount[] on every variable that I can think of, and none of them seem to be the culprit. Anyway, the OpenCL code in question is here: [code]__kernel void nbody_kern( float timeStep, float eps, __global float4* position1, __global float4* velocity1, __global float4* acceleration1, __global float4* position2, __global float4* velocity2, __global float4* acceleration2, __local float4* localPosition ) { const float4 dt = (float4)(timeStep,timeStep,timeStep,0.0f); int idxGlobal = get_global_id(0); int idxLocal = get_local_id(0); int globalSize = get_global_size(0); int localSize = get_local_size(0); int blocks = globalSize / localSize; float4 currentPosition = position1[idxGlobal]; float4 currentVelocity = velocity1[idxGlobal]; float4 currentAcceleration = acceleration1[idxGlobal]; float4 newPosition = (float4)(0.0f,0.0f,0.0f,0.0f); float4 newVelocity = (float4)(0.0f,0.0f,0.0f,0.0f); float4 newAcceleration = (float4)(0.0f,0.0f,0.0f,0.0f); for(int currentBlock = 0; currentBlock < blocks; currentBlock++) { localPosition[idxLocal] = position1[currentBlock * localSize + idxLocal]; barrier(CLK_LOCAL_MEM_FENCE); for(int idx = 0; idx < localSize; idx++) { float4 dir = localPosition[idx] - currentPosition; float invRadius = rsqrt(dir.x * dir.x + dir.y * dir.y + dir.z * dir.z + eps); float magnitude = localPosition[idx].w * invRadius * invRadius * invRadius; newAcceleration += magnitude * dir; } barrier(CLK_LOCAL_MEM_FENCE); } // leapfrog integration newPosition = currentPosition + currentVelocity * dt + 0.5f * currentAcceleration * dt * dt; newVelocity = currentVelocity + 0.5f * (currentAcceleration + newAcceleration) * dt; position2[idxGlobal] = newPosition; velocity2[idxGlobal] = newVelocity; acceleration2[idxGlobal] = newAcceleration; }[/code]  and the Mathematica code is here:[mcode]initialVelocity[pt_] := Module[ {y, v0, \[Theta]}, y = Norm[pt[[1 ;; 3]]]/(2 rd); v0 = 4*\[Pi]*\[CapitalSigma]0*rd* y^2 (BesselI[0, y]*BesselK[0, y] - BesselI[1, y]*BesselK[1, y]); \[Theta] = ArcTan[pt[[1]], pt[[2]]]; {-v0 Sin[\[Theta]], v0 Cos[\[Theta]], 0.0, 0.0} + RandomVariate[NormalDistribution[0, .001], 4] ] Needs["OpenCLLink`"]; source = {"D:\\Google Drive\\Mathematica\\nbody.cl"}; stepSimulation = OpenCLFunctionLoad[ source, "nbody_kern", { "Float", "Float", {"Float", _, "Input"}, {"Float", _, "Input"}, {"Float", _, "Input"}, {"Float", _, "Output"}, {"Float", _, "Output"}, {"Float", _, "Output"}, {"Local", "Float"} }, 256, "ShellOutputFunction" -> Print ]; dt = .01; eps = .0001; rd = 1.0; \[CapitalSigma]0 = 0.3; len = 2^14; particles = (RandomVariate[ExponentialDistribution[rd]]*{Cos[#], Sin[#], 0.0, 0.0}) & /@ RandomReal[{0, 2 Pi}, len]; particles[[All, 4]] = 1.0/len; velocity = initialVelocity /@ particles; acceleration = Array[{0.0, 0.0, 0.0, 0.0} &, len]; position1 = OpenCLMemoryLoad[particles, "Float"]; velocity1 = OpenCLMemoryLoad[velocity, "Float"]; acceleration1 = OpenCLMemoryLoad[acceleration, "Float"]; position2 = OpenCLMemoryAllocate["Float", {len, 4}]; velocity2 = OpenCLMemoryAllocate["Float", {len, 4}]; acceleration2 = OpenCLMemoryAllocate["Float", {len, 4}]; pr = 8; memList = {MemoryInUse[]}; Graphics3D[{ PointSize[Small], Point[Dynamic[Refresh[ AppendTo[memList, MemoryInUse[]]; stepSimulation[dt, eps, position1, velocity1, acceleration1, position2, velocity2, acceleration2, 256*4, len]; stepSimulation[dt, eps, position2, velocity2, acceleration2, position1, velocity1, acceleration1, 256*4, len]; OpenCLMemoryGet[position1][[All, 1 ;; 3]], UpdateInterval -> 0]] ]}, PlotRange -> {{-pr, pr}, {-pr, pr}, {-pr/4, pr/4}}, ImageSize -> 1000 ] Dynamic[ListLinePlot[memList]] [/mcode] As far as I can tell, the code does what it's supposed to and I'm generally pleased with the results. This is what I get after a few steps: [img=width: 400px; height: 334px;]http://i.imgur.com/hQFbPZO.png[/img] However, the memory problem limits how long I can run this thing for. This plot shows the amount of memory in use with respect to the number of steps completed in the simulation. [img=width: 360px; height: 209px;]http://i.imgur.com/SGWx0aP.png[/img] The only way I've been able to free up all that memory is by quitting the kernel, which is hardly ideal. I'm guessing that I'm just missing some important aspect of OpenCL programming. If anyone is more familiar with this stuff and has some ideas, I'd be thrilled to hear them. Richard Hennigan 2013-08-09T17:18:48Z https://community.wolfram.com/groups/-/m/t/212730 I am looking to make a physics based Mathematica project. Ideally the project would take around 12 hours, gathering any experimental data and analyse the findings. I'd have full access to university physics labs. The project would be for 2nd year physics students in the end and would aim to introduce using Mathematica in their work.   Liam Walker 2014-03-06T13:43:34Z https://community.wolfram.com/groups/-/m/t/763123 I would ask for some help to implement a code to be able to find the center of mass of an annular image of light projection from a fiber optics. The center of mass should be the point where it originates the average radius. On the other hand, the average radius ends at the point, inside the annulus, where the light intensity is maximum. Basically, an initial center is chosen (may be the center of the frame), then 18 sectors are built from that center to the larger circle of the annulus, which is contained in the frame. The fix for the assumed center is calculated as the sum of the average radius times the cosine (in x) and sine (for y) sectors around the circle. The center is shifted to there and the process repeated. In another words, the new coordinates obtained, original center plus delta x and delta y, must to shift the original center closer to the correct center of mass. However the operation should be performed some times until convergence is complete or that the residual value is less than or equal to 1 pixel. This should probably happen after two or three interactions, depending of course the amount initially chosen for the original center. So far, the current code is able to find the value delta x and delta y to be added to the center originally preset. My difficulty is define a loop to redo the operation as many times as necessary. I would really appreciate some help to finish this code to obtain the final value of the center of mass coordinates. Thanks for any help... Antonio de Oliveira 2015-12-23T18:26:51Z https://community.wolfram.com/groups/-/m/t/440994 Dear friends, I have a lot of Raw images in .NEF format (NIKKON). So, I read the section : [http://reference.wolfram.com/language/LibraryLink/tutorial/ImageProcessing.html][1] But I did not understand how implement these libraries in order to work with .NEF extension images, for astrophotography. EDIT 1: a sample of image *.NEF: [https://www.dropbox.com/s/2n5y5xjhhqeh7k0/DSC_5133.NEF?dl=0][2] [1]: http://reference.wolfram.com/language/LibraryLink/tutorial/ImageProcessing.html [2]: https://www.dropbox.com/s/2n5y5xjhhqeh7k0/DSC_5133.NEF?dl=0 Marcelo De Cicco 2015-02-12T13:19:44Z https://community.wolfram.com/groups/-/m/t/389820 I am interested in creating an orrery, ideally with SystemModeler. I have been experimenting with the MultiBody library since that allows you to do animations. The most relevant example seems to be Modelica.Mechanics.MultiBody.Examples.Elementary.PointGravity, but the problem is that it has a single point of gravity. You can change the gravity from the earth's gravity to something else, but for my orrery I would think each body needs to have gravity/mass. The bodies do have a settable mass, though, so does this mean I can just create one body for each planet, set the mass correctly and it will work? So, in other words one way to set up the model would seem to be to make the "world" have the gravity of the sun and gravity type of PointGravity, then have the planets as bodies moving around it. However, I don't think this will work right because the "world" object's gravity is constant, but in the solar system the force of gravity is a function of the distance. Another idea I had was to make the "world" object have type NoGravity, but then how do I constrain the planets? If I add in the sun as a body, and give the planets and the sun appropriate masses and distances and velocities will the simulator compute the instantaneous gravity between them, ie, solve the N-body problem automatically? Afterthought: is there a way to customize the look of the "bodies"? In the example they are just blue spheres and you can change their color and size but that is it. Hairy Thoughter 2014-11-14T23:53:02Z https://community.wolfram.com/groups/-/m/t/108668 I have one Graphics3D and one ParametricPlot3D, which I need to combine. Unfortunately, the Show[] Command does not work here, maybe because I use a Manipulate[] Command. The Prolog-> also does not work. Plot1, the Graphics 3D, is a set of 3 Points (the initial positions of Plot2): [mcode](* Plot 1 *) P1 = {0, 0, 0}; P2 = {-1, 0, 2}; P3 = {-3, 4, -2}; Plot1 = Graphics3D[Point[{P1, P2, P3}], PlotRange -> {{-5, 5}, {-5, 5}, {-3, 7}}, AspectRatio -> 1];[/mcode] Plot 2, the ParametricPlot3D, is a 3D simulation of the three-body-problem. I need to have the Plot1 plotted right into Plot2: (Edit: I dont know if the Code gets lost due conversion to plain text. If so, see .nb File at http://yukterez.ist.org/3kp/3k3D.nb [mcode](* Plot 2 *) G = 667384/ 10^16;(* Gravitationskonstante *) M1 = 100000000; M2 = 70000000; \ M3 = 50000000;(* Massen 1,2,3 in kg *) v1x = 1/70; v1y = -1/130; v1z = 1/20;(* v0 von M1 in m/sek *) v2x = -1/150; v2y = 1/100; v2z = 1/90;(* v0 von M2 in m/sek *) v3x = 1/200; v3y = 1/110; v3z = -1/170;(* v0 von M3 in m/sek *) P1 = {0, 0, 0}; (* Position 1 XYZ *) P2 = {-1, 0, 2}; (* Position 2 XYZ *) P3 = {-3, 4, -2}; (* Position 3 XYZ *) (* Container *) Funktion[{{x10_, y10_, z10_}, {x20_, y20_, z20_}, {x30_, y30_, z30_}}, {{vx10_, vy10_, vz10_}, {vx20_, vy20_, vz20_}, {vx30_, vy30_, vz30_}}, {m1_, m2_, m3_}, T_, plotType : ("x" | "v"), plotOptions___] := Module[{nds, Tmax, prolog, funcToPlot}, (* Differentialgleichung *)nds = NDSolve[{ x1'[t] == vx1[t], y1'[t] == vy1[t], z1'[t] == vz1[t], x2'[t] == vx2[t], y2'[t] == vy2[t], z2'[t] == vz2[t], x3'[t] == vx3[t], y3'[t] == vy3[t], z3'[t] == vz3[t], vx1'[ t] == -((G m2 (x1[t] - x2[t]))/ Sqrt[((x1[t] - x2[t])^2 + (y1[t] - y2[t])^2 + (z1[t] - z2[t])^2)^3]) - (G m3 (x1[t] - x3[t]))/ Sqrt[((x1[t] - x3[t])^2 + (y1[t] - y3[t])^2 + (z1[t] - z3[t])^2)^3], vy1'[ t] == -((G m2 (y1[t] - y2[t]))/ Sqrt[((x1[t] - x2[t])^2 + (y1[t] - y2[t])^2 + (z1[t] - z2[t])^2)^3]) - (G m3 (y1[t] - y3[t]))/ Sqrt[((x1[t] - x3[t])^2 + (y1[t] - y3[t])^2 + (z1[t] - z3[t])^2)^3], vz1'[ t] == -((G m2 (z1[t] - z2[t]))/ Sqrt[((x1[t] - x2[t])^2 + (y1[t] - y2[t])^2 + (z1[t] - z2[t])^2)^3]) - (G m3 (z1[t] - z3[t]))/ Sqrt[((x1[t] - x3[t])^2 + (y1[t] - y3[t])^2 + (z1[t] - z3[t])^2)^3], vx2'[t] == (G m1 (x1[t] - x2[t]))/ Sqrt[((x1[t] - x2[t])^2 + (y1[t] - y2[t])^2 + (z1[t] - z2[t])^2)^3] - (G m3 (x2[t] - x3[t]))/ Sqrt[((x2[t] - x3[t])^2 + (y2[t] - y3[t])^2 + (z2[t] - z3[t])^2)^3], vy2'[t] == (G m1 (y1[t] - y2[t]))/ Sqrt[((x1[t] - x2[t])^2 + (y1[t] - y2[t])^2 + (z1[t] - z2[t])^2)^3] - (G m3 (y2[t] - y3[t]))/ Sqrt[((x2[t] - x3[t])^2 + (y2[t] - y3[t])^2 + (z2[t] - z3[t])^2)^3], vz2'[t] == (G m1 (z1[t] - z2[t]))/ Sqrt[((x1[t] - x2[t])^2 + (y1[t] - y2[t])^2 + (z1[t] - z2[t])^2)^3] - (G m3 (z2[t] - z3[t]))/ Sqrt[((x2[t] - x3[t])^2 + (y2[t] - y3[t])^2 + (z2[t] - z3[t])^2)^3], vx3'[t] == (G m1 (x1[t] - x3[t]))/ Sqrt[((x1[t] - x3[t])^2 + (y1[t] - y3[t])^2 + (z1[t] - z3[t])^2)^3] + (G m2 (x2[t] - x3[t]))/ Sqrt[((x2[t] - x3[t])^2 + (y2[t] - y3[t])^2 + (z2[t] - z3[t])^2)^3], vy3'[t] == (G m1 (y1[t] - y3[t]))/ Sqrt[((x1[t] - x3[t])^2 + (y1[t] - y3[t])^2 + (z1[t] - z3[t])^2)^3] + (G m2 (y2[t] - y3[t]))/ Sqrt[((x2[t] - x3[t])^2 + (y2[t] - y3[t])^2 + (z2[t] - z3[t])^2)^3], vz3'[t] == (G m1 (z1[t] - z3[t]))/ Sqrt[((x1[t] - x3[t])^2 + (y1[t] - y3[t])^2 + (z1[t] - z3[t])^2)^3] + (G m2 (z2[t] - z3[t]))/ Sqrt[((x2[t] - x3[t])^2 + (y2[t] - y3[t])^2 + (z2[t] - z3[t])^2)^3], x1[0] == x10, y1[0] == y10, z1[0] == z10, x2[0] == x20, y2[0] == y20, z2[0] == z20, x3[0] == x30, y3[0] == y30, z3[0] == z30, vx1[0] == vx10, vy1[0] == vy10, vz1[0] == vz10, vx2[0] == vx20, vy2[0] == vy20, vz2[0] == vz20, vx3[0] == vx30, vy3[0] == vy30, vz3[0] == vz30}, {x1, x2, x3, y1, y2, y3, z1, z2, z3, vx1, vx2, vx3, vy1, vy2, vy3, vz1, vz2, vz3}, {t, 0, T}]; If[Head[nds] =!= NDSolve, Tmax = nds[[1, 1, 2, 1, 1, 2]]; funcToPlot = If[plotType === "x", {{x1[t], y1[t], z1[t]}, {x2[t], y2[t], z2[t]}, {x3[t], y3[t], z3[t]}}, {{vx1[t], vy1[t], vz1[t]}, {vx2[t], vy2[t], vz2[t]}, {vx3[t], vy3[t], vz3[t]}}] /. nds[[1]]; (* Plot Specifications *) prolog = {PointSize[0.3], Point[{P1, P2, P3}]}; ParametricPlot3D[Evaluate[funcToPlot], {t, 0, Tmax}, PlotStyle -> {Red, Blue, Green}, (* Plot Range und Seitenverhältnis *) PlotRange -> {{-5, 5}, {-5, 5}, {-3, 7}}, AspectRatio -> 1, (* Prolog -> prolog, *) MaxRecursion -> ControlActive[3, 9], Axes -> True, plotOptions], Text["Yukterez Mod. of demonstrations.wolfram.com/PlanarThreeBodyProblem"]]] // Quiet Plot2 = Manipulate[Funktion[ (* Positionen xy *){P1, P2, P3}, (* Geschwindigkeiten xy *){{v1x, v1y, v1z}, {v2x, v2y, v2z}, {v3x, v3y, v3z}}, (* Massen *){M1, M2, M3}, (* Regler *)T, xv, ImageSize -> {320, 320}], {{xv, "x", "Position/Geschwindigkeit"}, {"x" -> "Position", "v" -> "Geschwindigkeit"}}, {{T, 1, "Zeit"}, 1, 200}, ControlPlacement -> {Bottom}] [/mcode] (* http://yukterez.ist.org/3kp/3k3D.html *) Simon Tyran 2013-08-28T17:09:03Z https://community.wolfram.com/groups/-/m/t/240312 Dear All, I am using NonlinearModelFit to fit data with a function with 4 parameters. With Marquardt Levenberg Algorithm the errors are considered independent, but in reality errors are dependent each other. Is there a build in function which  I can use that when I type nonlimearmodelfit["ParameterErrors"] I can obtain an evaluation of the errors that takes into consideration that they are dependent each other? Many thanks, Best regards, Maria Maria Giovanna Dainotti 2014-04-21T13:05:46Z https://community.wolfram.com/groups/-/m/t/574679 I need help figuring out how to have a Mathematica script open a file. Each line of the script is in the format: C Name t_i t_f x y z x_dot y_dot z_dot x_sig y_sig z_sig x_dot_sig y_dot_sig z_dot_sig I have attached the file. I need my script to open the file, and for each satellite it needs to take the first row, take Name, X, Y, Z... so the second column, 5th column, 6th column, and 7th column, for the first row of the file for each satellite. (there are several satellites numbered GPS15, GPS24, GPS25, etc.... It then needs to map x, y, z for all of the satellites and label them on the map with their Name. I know it involves lists. I've tried, I can't figure out how to do this. Thank you so much! Nathan Lundholm 2015-10-03T19:31:11Z https://community.wolfram.com/groups/-/m/t/1500089 I am using Mathematica 10.3. I want fo perform a computational analysis of the motion of the Earth around the sun based on Kepler’s laws. Here is my code so far. eulerStep[{t_, state_List}, h_, f_List] := {t + h, state + h Through[f[{t, state}]]} solveSystemEuler [{t0_state0 _}, h_, n_Integer, f_List] := NestList[eulerStep[#, h, f] &, {t0, state0}, n] midptStep[{t_, state_List}, h_, f_List] := {t + h, state + h Through[ f[{t + 1/2 h, state + 1/2 h Through[f[{t, state}]]}]]} solveSytemMidPt[{t0_, state0_}, h_, n_Integer, f_List] := NestList[midptStep[#, h, f] &, {t0, state0}, n] L = 1/2 m (x'[t]^2 + y'[t]^2) + GMm/Sqrt[x[t]^2 + y[t]^2]; D[D[L, x'[t]], t] - D[L, x[t]] == 0 D[D[L, y'[t]], t] - D[L, y[t]] == 0 xdot[{t_, {x_, vx_, y_, vy_}}] := vx vxdot[{t_, {x_, vx_, y_, vy_}}] := -x/(x^2 + y^2)^(3/2) ydot[{t_, {x_, vx_, y_, vy_}}] := vy vydot[{t_, {x_, vx_, y_, vy_}}] := -y/(x^2 + y^2)^(3/2) start = {1, 0, 0, 1}; fcns = {xdot, vxdot, ydot, vydot}; orbit = solveSystemEuler[{0, start}, 0.01, 800, fcns]; << Statistics`DataManipulation` xypts = Column[Column[orbit, 2], {1, 3}]; ListPlot[xypts, PlotJoined -> True]; Running the program gave the following error messages. ![enter image description here][1] Please help me to fix my code. [1]: http://community.wolfram.com//c/portal/getImageAttachment?filename=Capture.JPG&userId=1499975 Senlau Minto 2018-10-08T03:45:10Z