拋物線運動 - 重力隨高度變化

Question

問題是必須在重力不穩定的情況下進行拋射運動。所以位置s（t）= -0.5 g t2 + v0 t和g（s）= G∙ME /（RE + s）2。其中G，ME和RE都是常數。因此，新方程是s（t）= -0.5 g（s）t2 + v0 t。

我得出一個假設，即每0.005秒的速度是恆定的，所以方程必須每0.005秒更新一次。所以s（t）= s（t-Δt）+ v（t）∙Δt其中v（t）= v（t-Δt）-g（s（t-Δt））∙Δt。

我的代碼現在的問題是

# Assigning Variables 
G = 6.6742*10**(-11) # Gravitational Constant 
M_e = 5.9736*10**(24) # Mass of Earth 
R_e = 6371000 # Radius of Earth 
t = float(input('Time (in seconds)')) # Asking user to input total time, t 
v_0 = float(input('initial velocity')) # Asking user to input initial velocity 
t_0 = .005 # Time before first recalculation 
g = 9.81 # initial gravity 

# Derivative of s(t) = s't = v(t) 
# v(t) = -g(s)*t+v_o 

while t != t_0: 
    s = v_0*t_0 
    g = (g*M_e)/(R_e+s)**2 
    v = -g*s*t_0+v_0 
    t_0=t_0+.005 
    if int(t_0) == t_0: 
     print'Gravity is {%f}, position is {%f}, and velocity is {%f} at time {%.0f}' %(g, s, v, t_0) 
print'Projectile has reached your time {%f}, with gravity {%f}, position {%f}, and velocity {%f}'%(t,g,s,v) 

我真的不知道我應該如何改變它，所以它會奏效。

所以我更新了它作爲我得到的建議。現在，當我運行它時，我的程序要求時間和初始速度和時間（以秒爲單位）。但它甚至不會產生輸出。

時間（單位：秒）5

初始velocity5

這就是結果的樣子時，我對兩個輸入5。

Answer 1

我已經給你的代碼添加了評論，以及一些改變，所以程序將運行（至少在2.7.6）。然而，雖然它會運行，它不會真正的工作。你應該看看你的函數s，g和v - 它們是不正確的。例如R_e * s不會給你距離地球中心的距離，因爲它的單位現在是米^ 2。

# Assigning Variables 
G = 6.6742*10**(-11) # Gravitational Constant 
M_e = 5.9736*10**(24) # Mass of Earth 
##### In your code the commas are making this a tuple, not an integer - it needs to be defined without commas. 
R_e = 6371000 # Radius of Earth 
t = float(input('Time (in seconds)')) 
v_0 = float(input('initial velocity')) 
t_0 = .005 
#You need to define an initial g 
g = 9.81 

while t != t_0: 
    ####In your code you had a typo here - t_o instead of t_0 
    s = v_0*t_0 
    ####If you don't initialise g, this function does not know what g is. 
    g = (g*M_e)/(R_e*s)**2 
    v = -g*s*t_0+v_0 
    t_0=t_0+.005 
    #####If you want to check if the type of t_0 is an integer, you need to use the type function. It will also never be an integer, as you are always adding a float to a float in the line above this. 
    if type(t_0) == int: 
     print('Gravity is {%f}, position is {%f}, and velocity is {%f} at time {%.0f}' %(g, s, v, t_0)) 
####No need for an if statement to tell if the while loop is finished - just put the print statement after the while loop. 
print('Projectile has reached your time {%f}, with gravity {%f}, position {%f}, and velocity {%f}'%(t,g,s,v))