地球引力模型程序代码

模型地球内部引力图

地球模型计算的引力外地核处引力最大, 外地核向内或向外均在减小，从地核核心区处逃离地球引力需要能量为W=3.822MgR,由于不均匀分布，势能增加了0.5MgR

实际引力为分层球体的引力标准线叠加的结果。

如果地球模型不错我们完全可以根据分层密度计算它的内引力图

半径R

1 0.99482 0.846178 0.544812 0.262282 0.194318

密度 2.75 3.4 5.35 10.7 12.3 12.5

R/N 1 1.005207 1.181784 1.835496 3.81269 5.146204

分层密度

2.75 0.65 1.95 5.35 1.6 0.2

把密度确定以后，我们再把密度分层，先按最小密度绘制大圆图，再把第二层密度减去第一层后绘图，如此循环，画到地核，再把所有值叠加起来，就是模型引力图了。。如果模型不错，那么地球的实际引力就会和所画图一样。当

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⎛⎫⎛⎫a a 22

1-a +1-a + ⎪ ⎪3g 03MG g(a ) =1+2a -⎪= 1+2a -⎪332 2R 2 2222⎪⎪(1-a ) +1(1-a ) +1 ⎪ ⎪

⎝⎭⎝⎭

a =sin δ, R sin δ为质点到球心的距离, g 0为地表重力加速度

AUTOcadvba 模型程序代码

Sub 地球引力模型() Dim ml As Object

Dim a As Variant, a1 As Variant, a2 As Variant, a3 As Variant, a4 As Variant

Dim v As Variant, v1 As Variant, v2 As Variant, v3 As Variant, v4 As Variant, v5 As Variant

Dim U As Variant, U1 As Variant, U2 As Variant, U3 As Variant, U4 As Variant

Dim co As Variant co = 3

Dim p(0 To 20001) As Double Dim i As Integer Dim J As Variant a

1.[1**********]556:

1.[1**********]396:

1.[1**********]78: a3 = 3.[1**********]163: a4 = 5.[1**********]066 b = 0.[**************]: b1 = 0.[**************]: b2 = 1.[1**********]455: 7.[1**********]727E-02 For i = 0 To 10000 Step 2

v = i / 1000: v1 = v * a: v2 = v * a1: v3 = v * a2: v4 = v * a3: v5 = v * a4 p(i) = i

0.[**************]:

If v1

U = 750 * b * (1 + v1 * 2 - (1 - v1 ^ 2 + (v1 ^ 4) / 3) / (1 + (1 - v1 ^ 2) ^ 1.5)) / a

ElseIf v1 > 1 And v1 a Then U3 = 0 End If If v2

U1 = 750 * b1 * (1 + v2 * 2 - (1 - v2 ^ 2 + (v2 ^ 4) / 3) / (1 + (1 - v2 ^ 2) ^ 1.5)) / a1

ElseIf v2 > 1 And v2 a1 Then U3 = 0 End If If v3

U2 = 750 * b2 * (1 + v3 * 2 - (1 - v3 ^ 2 + (v3 ^ 4) / 3) / (1 + (1 - v3 ^ 2) ^ 1.5)) / a2

ElseIf v3 > 1 And v3 a2 Then

U2 = 0 End If If v4

U3 = 750 * b3 * (1 + v4 * 2 - (1 - v4 ^ 2 + (v4 ^ 4) / 3) / (1 + (1 - v4 ^ 2) ^ 1.5)) / a3

ElseIf v4 > 1 And v4 a3 Then U3 = 0 End If If v5

U4 = 750 * b4 * (1 + v5 * 2 - (1 - v5 ^ 2 + (v5 ^ 4) / 3) / (1 + (1 - v5 ^ 2) ^ 1.5)) / a4

ElseIf v5 > 1 And v5 a4 Then U4 = 0 End If If v

p(i + 1) = 750 * (1 + v * 2 - (1 - v ^ 2 + (v ^ 4) / 3) / (1 + (1 - v ^ 2) ^ 1.5)) + U + U1 + U2 + U3 + U4 Else

p(i + 1) = 500 * (1 + b * a ^ -3 + b1 * a1 ^ -3 + b2 * a2 ^ -3 + b3 * a3 ^ -3 + b4 * a4 ^ -3) / v ^ 2 End If Next i

Set ml = ThisDrawing.ModelSpace.AddLightWeightPolyline(p) co = co + 1 ml.color = co End Sub