月球与地球公转立体示意图
2019-04-24 02:44
本范例通过三维立体图形展示了月球绕地球公转的运动过程。图中使用了向量、圆、直线和平移等几何构造命令,结合参数曲线和三角函数来模拟天体运行的轨道。需要注意的是,为了演示效果,图中天体的大小和距离并未按照真实宇宙比例绘制。该模型直观地呈现了空间几何中的轨道运动与坐标变换。
所属专题
太阳系的奥秘
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.533.0" app="classic" platform="offline" id="585790cb-8e56-4438-89f5-b108066ac153" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="1464" height="843" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.6591530054644809" orientation="1" />
</panes>
<views>
<view id="4" toolbar="0 || 2020 , 2021 , 2022 , 66 || 2001 , 2003 , 2002 , 2004 , 2005 || 2040 , 2041 , 2042 , 2044 , 2043" visible="false" inframe="false" stylebar="true" location="1,1" size="291" window="100,100,600,400" />
<view id="2" visible="false" inframe="false" stylebar="true" location="3,3" size="380" window="100,100,250,400" />
<view id="8" toolbar="1001 | 1002 | 1003 || 1005 | 1004 || 1006 | 1007 | 1010 || 1008 1009 || 66 68 || 6" visible="false" inframe="false" stylebar="false" location="1,3" size="300" window="100,100,600,400" />
<view id="1" visible="true" inframe="false" stylebar="false" location="1" size="491" window="100,100,600,400" />
<view id="16" visible="false" inframe="false" stylebar="false" location="1" size="141" window="50,50,500,500" />
<view id="32" visible="false" inframe="false" stylebar="true" location="1" size="270" window="50,50,500,500" />
<view id="64" toolbar="0" visible="false" inframe="false" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="128" visible="false" inframe="false" stylebar="false" location="1" size="480" window="50,50,500,500" />
<view id="4097" visible="false" inframe="false" stylebar="true" location="1" size="336" window="570,22,700,550" />
<view id="70" toolbar="0 || 2020 || 2021 || 2022" visible="false" inframe="false" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="43" visible="false" inframe="false" stylebar="false" location="1" size="450" window="50,50,500,500" />
<view id="512" toolbar="0 | 1 501 5 19 , 67 | 2 15 45 18 , 7 37 | 514 3 9 , 13 44 , 47 | 16 | 551 550 11 , 20 22 21 23 , 55 56 57 , 12 | 69 | 510 511 , 512 513 | 533 531 , 534 532 , 522 523 , 537 536 , 535 | 521 520 | 36 , 38 49 560 | 571 30 29 570 31 33 | 17 | 540 40 41 42 , 27 28 35 , 6 , 502" visible="true" inframe="false" stylebar="false" location="3" size="965" window="100,100,600,400" />
</views>
<toolbar show="true" items="0 39 | 1 501 67 , 5 19 , 72 | 2 15 45 , 18 65 , 7 37 | 4 3 8 9 , 13 44 , 58 , 47 | 16 51 64 , 70 | 10 34 53 11 , 24 20 22 , 21 23 | 55 56 57 , 12 | 36 46 , 38 49 50 , 71 | 30 29 54 32 31 33 | 17 26 62 73 , 14 68 | 25 52 60 61 | 40 41 42 , 27 28 35 , 6" position="1" help="false" />
<input show="true" cmd="true" top="algebra" />
<dockBar show="false" east="false" />
</perspective>
</perspectives>
<labelingStyle val="0"/>
<font size="12"/>
</gui>
<euclidianView>
<viewNumber viewNo="1"/>
<size width="490" height="789"/>
<coordSystem xZero="195.5501355209942" yZero="298.20668399463096" scale="9.610735086567301" yscale="9.610735086567312"/>
<evSettings axes="false" grid="false" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" checkboxSize="26" gridType="0"/>
<bgColor r="255" g="255" b="255"/>
<axesColor r="0" g="0" b="0"/>
<gridColor r="192" g="192" b="192"/>
<lineStyle axes="1" grid="0"/>
<axis id="0" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="1" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
</euclidianView>
<algebraView>
<mode val="1"/>
<collapsed val="0"/>
</algebraView>
<kernel>
<uses3D val="true"/>
<continuous val="false"/>
<usePathAndRegionParameters val="true"/>
<decimals val="2"/>
<angleUnit val="degree"/>
<algebraStyle val="0" spreadsheet="0"/>
<coordStyle val="0"/>
<startAnimation val="true"/>
</kernel>
<tableview min="-2" max="2" step="1"/>
<scripting blocked="false" disabled="false"/>
<euclidianView3D>
<coordSystem xZero="0.9060161618627944" yZero="-5.29834786972868" zZero="-1.3386447310863585" scale="15.958107494497138" xAngle="9" zAngle="-251"/>
<evSettings axes="false" grid="false" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" gridType="0"/>
<axis id="0" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="1" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="2" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<plate show="false"/>
<bgColor r="255" g="255" b="255"/>
<clipping use="true" show="true" size="1"/>
<projection type="0"/>
</euclidianView3D>
<construction title="月球地球公轉立體圖(大小並不合比例)" author="" date="">
<expression label="node" exp="5°"/>
<element type="angle" label="node">
<angleStyle val="3"/>
<value val="0.08726646259971647"/>
<show object="false" label="true" ev="4"/>
<objColor r="0" g="100" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="1"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
<arcSize val="30"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<element type="numeric" label="time">
<value val="224"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="0" max="2000" absoluteScreenLocation="true" width="200" x="44" y="35" fixed="true" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="1" speed="0.1" type="1" playing="true"/>
</element>
<expression label="C" exp="((14.96 * cos((0.02 * time))), (14.96 * sin((0.02 * time))))" type="point" />
<element type="point" label="C">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="153" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="3"/>
<coords x="-3.445331992603598" y="-14.557859989048602" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
<caption val="地球"/>
</element>
<command name="Vector">
<input a0="C"/>
<output a0="u"/>
</command>
<element type="vector" label="u">
<show object="false" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-3.445331992603598" y="-14.557859989048602" z="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<coordStyle style="cartesian"/>
</element>
<command name="Intersect">
<input a0="xAxis" a1="yAxis"/>
<output a0="A"/>
</command>
<element type="point" label="A">
<show object="true" label="true" ev="4"/>
<objColor r="255" g="127" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="3"/>
<coords x="0" y="0" z="1"/>
<pointSize val="9"/>
<pointStyle val="0"/>
<caption val="太陽"/>
</element>
<element type="numeric" label="moon">
<value val="29.530588"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="29.530588" max="29.530588" absoluteScreenLocation="true" width="200" x="46" y="74" fixed="true" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="0.05" speed="1" type="0" playing="false"/>
</element>
<element type="numeric" label="earth">
<value val="365.25"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="365.25" max="365.25" absoluteScreenLocation="true" width="200" x="105" y="126" fixed="true" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="0.05" speed="1" type="0" playing="false"/>
</element>
<element type="numeric" label="orbitalm">
<value val="3.844"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="3.844" max="3.844" absoluteScreenLocation="true" width="200" x="35" y="114" fixed="true" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="0.05" speed="1" type="0" playing="false"/>
</element>
<element type="numeric" label="orbitale">
<value val="14.95978707"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="14.95978707" max="14.95978707" absoluteScreenLocation="true" width="200" x="67" y="157" fixed="true" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="0.05" speed="1" type="0" playing="false"/>
</element>
<command name="Circle">
<input a0="A" a1="orbitale"/>
<output a0="c"/>
</command>
<element type="conic" label="c">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="10" typeHidden="1"/>
<eigenvectors x0="1" y0="0" z0="1.0" x1="0" y1="1" z1="1.0"/>
<matrix A0="1" A1="1" A2="-223.7952291797392" A3="0" A4="0" A5="0"/>
<eqnStyle style="specific"/>
</element>
<expression label="B" exp="C + ((orbitalm * cos((0.21 * time))), (orbitalm * sin((0.21 * time))))" type="point" />
<element type="point" label="B">
<show object="true" label="true" ev="4"/>
<objColor r="102" g="255" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="3"/>
<coords x="-7.275813849778415" y="-14.235765683208582" z="1"/>
<pointSize val="3"/>
<pointStyle val="0"/>
<caption val="月球"/>
</element>
<command name="Line">
<input a0="C" a1="A"/>
<output a0="a"/>
</command>
<element type="line" label="a">
<show object="false" label="true" ev="4"/>
<objColor r="255" g="255" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-14.557859989048602" y="3.445331992603598" z="0"/>
<lineStyle thickness="2" type="20" typeHidden="1"/>
<eqnStyle style="implicit"/>
</element>
<command name="Translate">
<input a0="Rotate[Circle[A, 3.844], node, xAxis]" a1="u"/>
<output a0="d"/>
</command>
<element type="conic3d" label="d">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="20" typeHidden="1"/>
<eigenvectors x0="1" y0="0" z0="1.0" x1="0" y1="1" z1="1.0"/>
<matrix A0="1" A1="1" A2="-14.776335999999999" A3="0" A4="0" A5="0"/>
<eqnStyle style="specific"/>
</element>
<command name="Circle">
<input a0="C" a1="B"/>
<output a0="e"/>
</command>
<element type="conic" label="e">
<show object="false" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eigenvectors x0="1" y0="0" z0="1.0" x1="0" y1="1" z1="1.0"/>
<matrix A0="1" A1="1" A2="209.02526400000005" A3="0" A4="3.445331992603598" A5="14.557859989048602"/>
<eqnStyle style="specific"/>
</element>
<expression label="D" exp="C + (cos(1.16239), 0, sin(1.16239))" type="point" />
<element type="point3d" label="D">
<show object="false" label="true" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-3.0481847610743897" y="-14.557859989048602" z="0.9177549109041506" w="1"/>
<pointSize val="5"/>
</element>
<command name="Line">
<input a0="C" a1="D"/>
<output a0="axis"/>
</command>
<element type="line3d" label="axis">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<coords ox="-3.445331992603598" oy="-14.557859989048602" oz="0" ow="1" vx="0.39714723152920817" vy="0" vz="0.9177549109041506" vw="0"/>
<eqnStyle style="parametric" parameter="λ"/>
</element>
</construction>
</geogebra>