#PYTHON CODE--> make the necessary changes to run the code properly as per the instructions given

# A rocket orbits the earth at an altitude of 200 km, not firing its engine. When # it crosses the negative part of the x-axis for the first time, it turns on its # engine to increase its speed by the amount given in the variable called boost and # then releases a satellite. This satellite will ascend to the radius of # geostationary orbit. Once that altitude is reached, the satellite briefly fires # its own engine to to enter geostationary orbit. First, find the radius and speed # of the initial circular orbit. Then make the the rocket fire its engine at the # proper time. Lastly, enter the value of boost that will send the satellite # into geostationary orbit. #

import math from udacityplots import *

earth_mass = 5.97e24 # kg earth_radius = 6.378e6 # m (at equator) gravitational_constant = 6.67e-11 # m3 / kg s2

total_duration = 9. * 3600. # s marker_time = 0.25 * 3600. # s tolerance = 100000. # m

# Task 1: Use Section 2.2 and 2.3 to determine the speed of the inital circular orbit. initial_radius = # your code here initial_speed = # your code here final_radius = 42164e3

# Task 3: Which is the appropriate value for the boost in velocity? 2.453, 24.53, 245.3 or 2453. m/s? # Change boost to the correct value. boost = 42. # m / s

def acceleration(position): return -gravitational_constant * earth_mass / numpy.linalg.norm(position)**3 * position

@show_plot def send_to_geostationary(): position = numpy.array([initial_radius , 0.]) # m velocity = numpy.array([0., initial_speed]) # m/s current_time = 0. h = 0.1 # s, set to initial step size but will store current step size h_new = h # s, will store the adaptive step size of the next step previous_marker_number = -1; geostationary_time = 0.

boost_done = False radius_reached = False while current_time < total_duration: acceleration0 = acceleration(position) velocityE = velocity + h * acceleration0 positionE = position + h * velocity velocityH = velocity + h * 0.5 * (acceleration0 + acceleration(positionE)) positionH = position + h * 0.5 * (velocity + velocityE)

# Task 2: When the rocket crosses the negative part of the x axis, # fire its engine to increase the speed by the amount given in the variable boost. if not boost_done and # fill this in:

# your code here

velocity = velocityH position = positionH error = numpy.linalg.norm(positionE - positionH) + total_duration \ * numpy.linalg.norm(velocityE - velocityH) h_new = h * math.sqrt(tolerance / error)

h_new = min(0.5 * marker_time, max(0.1, h_new))

if current_time >= marker_time * previous_marker_number: previous_marker_number += 1 matplotlib.pyplot.scatter(position[0], position[1], s = 2., facecolor = 'r', edgecolor = 'none') current_time += h h = h_new

if not radius_reached and abs(numpy.linalg.norm(position) - final_radius) <= 150e3: radius_reached = True geostationary_time = current_time

axes = matplotlib.pyplot.gca() axes.set_xlabel('Longitudinal position in m') axes.set_ylabel('Lateral position in m') axes.add_patch(matplotlib.patches.Circle((0., 0.), earth_radius, facecolor = 'b', edgecolor = 'none')) axes.add_patch(matplotlib.patches.Circle((0., 0.), final_radius, facecolor = 'none', edgecolor = 'g')) matplotlib.pyplot.axis('equal')

return radius_reached, geostationary_time send_to_geostationary()