#! /usr/bin/env python
"""
 satellite.py is program which calculates the altitude of a circular 
 orbiting satellite for a given orbit period.

 The program asks the user to input the period T and 
 print out the value for the height (altitude) using the formula 
 h = ((G*M*T**2) / (4 pi**2))**(1/3) - R 
 where G is Newton's constant, M is the mass and R is the raduis of the Earth.

 derivation of the above equation

 F == ma 
 GmM/r**2 == w**2 r      
 with w == 2pi f & f == 1/T
 r**3 == GMT**2/(2pi)**2
 with r == R + h
 h ==  ( (G*M*T**2)/(4 pi**2) )**(1/3) - R 

 
### PROGRAM OUTPUT ###
hpc-login-24 522% satellite.py
Enter period in minutes: 90
Altitude is 279 km

hpc-login-24 523% satellite.py
Enter period in minutes: 45
Altitude is -2182 km

### DISCUSSION ###
Altitude is defined as the distance above 
the Earth's surface (i.e.: radial distance = R_Earth + altitude ).

A negative value for altidude implies an impossible orbital 
radius within the Earth's surface.

Note: changing the input line to the code below will check and require
the user to input a period which does not produce negative results.

h = -1
while h < 0:
    T = 60 * float(raw_input("Enter period in minutes: "))  # T is the orbital period in units of seconds
    # Calculate the satellite height
    h = (G*M*T*T/(4*pi*pi))**(1/3) - R
    if h < 0:
        print("Orbital period results in a negative altitude of {0:2.0f} m.".format(h) )

 ###
 Paul Eugenio 
 PHZ4151C
 Jan 15, 2019
"""

# program header code
from __future__ import division, print_function
from math import pi

# main body of program
G = 6.67e-11        # Newton's gravitational constant
M = 5.97e24         # Mass of the Earth (kg) 
R = 6371e3          # Radius of the Earth (m)

T = 60 * float(raw_input("Enter period in minutes: "))  # T is the orbital period in units of seconds  

# Calculate the satellite height
h = (G*M*T*T/(4*pi*pi))**(1/3) - R

print( "Altitude is {0:2.0f} km".format(h/1000) )