在python中的简单重力列车

问题描述

我想写一个程序简单描述苹果通过地球的运动，或者我们称之为重力列车，请参阅（维基百科的重力列车）通过超物理学的重力列车

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我想在时间内绘制移动速度和位置。



这是我制作的代码，但答案错误（速度和时间错误）。虽然我使用正确的方程式下降身体方程式维基百科 []

我得到的速度和距离值非常大我错了什么？在此先感谢Max



**我必须拥有的价值时间必须等于2530.30秒（接近42.2分钟）最高时速约为7 900米秒（28440公里/小时）。

I want to write a program describes in simple the movement of the apple through the earth, or what we call Gravity train ,see (Gravity train by wikipedia) Gravity train by hyperphysics
http://hyperphysics.phy-astr.gsu.edu/hbase/mechanics/earthole.html[^]

I want to draw movement speed and postion in the time.

This is my code that I made, but I got wrong answer ( wrong value for speed and time). although I used right the equations for a falling body falling body Equations wikipedia https://en.wikipedia.org/wiki/Equations_for_a_falling_body[^]
the value for velocity and distance that I got is very big what is my wrong ? Thanks in advance Max

**What the value that I must have The time must be equals 2530.30 seconds (nearly 42.2 minutes) The maximum speed is about 7 900 metres per second (28440 km/h).

 # -*- coding: utf-8 -*-
import math
import numpy as np
import matplotlib.pyplot as plt

# Please notice that we assume :air friction is neglected

G = 6.67408 * (10**-11)     # gravitational constant
M = 5.972 * (10**24)        # Earth  Mass in kg
r = 6371000                 # Earth radius per meter
p = 5514                    # Mean Earth density in kg\m3

time = 0   #  the begin time is zero
a=0     #  the begin acceleration g 
v=0
t=0

L_h = [] # list for postion (hight)
L_a = [] # list for acceleration
L_v = [] # list for speed
L_t = [] # list for time

# for_loop in the path that we walk
delta=1000
for h in np.arange(1,2*r,delta):

# (M_effective) is The effective mass of earth that changes when h changes 
# (M_effective) =         new sphere volume       * density
#    M_effective = (4./3) * (math.pi) * ((r-h)**3)   *  p
    M_effective = (4./3) * (math.pi) *   p * (math.pow((r-h),3))


    a = G * M_effective / (r**2)  # (a) is the acceleration 

    if a>0:
        a=a
        t=t+math.sqrt(2*delta/a)
        v=v+math.sqrt(2*delta*a)
    else:
        a=a
        t=t + math.sqrt(2*delta/(abs(a)))
        v=v - math.sqrt(2*delta*(abs(a)))


    L_h.append(h)
    L_t.append(t)
    L_v.append(v)
    L_a.append(a)




plt.subplot(121)
plt.title("Velocity ")
plt.xlabel("Time ")
plt.ylabel("Velocity m/s")
plt.plot(L_t, L_v, 'g-')


plt.subplot(122)
plt.title("distance ")
plt.xlabel("Time ")
plt.ylabel("distance  m")
plt.plot(L_t, L_h, 'b-')

plt.tight_layout()


plt.figure(2)
plt.plot(L_t, L_a , 'b-')
plt.title("acceleration in tijd")
plt.xlabel(" Time s")
plt.ylabel("acceleration (a) m/ss")


plt.show()
#Gravity train
#The travel time equals 2530.30 seconds (nearly 42.2 minutes),
#For a train that goes directly through the center of the Earth, the maximum speed is about 7 900 metres per second (28440 km/h).

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