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File:Ballistic-trajectories-planet2.svg

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Original file (SVG file, nominally 720 × 440 pixels, file size: 4 KB)

Summary

Description
English: Plot of two ballistic trajectories with identical initial velocity, one with a uniform gravity field (blue) and one in the central potential field of a planet (orange). The trajectories are one parabola and one ellipse, respectively. The graphical representation is accurately computed using the script, given below.
Date
Source Own work
Author Geek3
Other versions Ballistic-trajectories-planet.svg
SVG development
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The SVG code is valid.
 
This vector image was created with Python.
Source code
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Python code

Python svgwrite code
#!/usr/bin/python3
# -*- coding: utf8 -*-

try:
    import svgwrite
except ImportError:
    print("requires svgwrite library: https://pypi.org/project/svgwrite/")
    # documentation at https://svgwrite.readthedocs.io/
    exit(1)

from math import *

# document
size = 720, 440
name = "Ballistic-trajectories-planet2"
doc = svgwrite.Drawing(name + ".svg", profile="full", size=size)
doc.set_desc(name, name + """.svg
https://commons.wikimedia.org/wiki/File:""" + name + """.svg
rights: Creative Commons Attribution-Share Alike 4.0 International license""")

# background
doc.add(doc.rect(id="background", insert=(0, 0), size=size, fill="white", stroke="none"))

cx, cy = 72, 1720
R = 1500
lw = 5
dash = "5,9"
c1, c2 = "#0072bd", "#d95319"
vx, vy = 0.4, 0.4 # in units of sqrt(R*g)

# gradients
rgrad = doc.defs.add(doc.radialGradient(id='rgrad', center=(0.5,0.5), r=0.5, gradientUnits='objectBoundingBox'))
rgrad.add_stop_color(offset=0.93, color='#ffffff')
rgrad.add_stop_color(offset=1, color='#ddc099')
lgrad = doc.defs.add(doc.linearGradient(id='lgrad', start=(0,0), end=(0,1), gradientUnits='objectBoundingBox'))
lgrad.add_stop_color(offset=0, color='#ddc099')
lgrad.add_stop_color(offset=1, color='#ffffff')

g = doc.add(doc.g(transform="translate({:.1f}, {:.1f})".format(cx, cy), fill="none"))
g.add(doc.rect(insert=(-cx, -R), size=(size[0], 0.07*R), fill="url(#lgrad)", stroke="none"))
g.add(doc.path(d="M {:.1f},{:.1f} h {:.1f}".format(-cx, -R, size[0]), stroke="black", stroke_width="3"))
g.add(doc.circle(r=str(R), center=(0,0), fill="url(#rgrad)", stroke="black", stroke_width="3"))

# trajectories
def parabola(x1, x2, abc): # using a quadratic Bezier curve
    a, b, c = abc
    y1 = a + b * x1 + c * x1**2
    y2 = a + b * x2 + c * x2**2
    txt = "M {:.1f},{:.1f} Q {:.1f},{:.1f} {:.1f},{:.1f}"
    return txt.format(x1, y1, (x1+x2)/2, (y1+y2)/2 - c/2*(x2-x1)**2, x2, y2)

def ellipse(p1, p2, abphi, l): # using arc
    a, b, phi = abphi
    c = 1
    if (pi/2-phi) % (2 * pi) > pi:
        c = 1 - c
    txt = "M {:.1f},{:.1f} A {:.1f},{:.1f} {:.1f} {:} {:} {:.1f},{:.1f}"
    return txt.format(p1[0], p1[1], a, b, degrees(phi), l, c, p2[0], p2[1])

p0 = (0, -R)
p1 = (2 * R * vx * vy, -R)
abc = -R, -vy / vx, 0.5 / R / vx**2
E2 = 2 - vx**2 - vy**2
a = R / E2
b = R * fabs(vx) / sqrt(E2)
phi = asin(vx / sqrt(E2) * sqrt((2 * a * R - b**2 - R**2) / (a**2 - b**2))) - pi/2
p2 = (-R * sin(2 * phi), R * cos(2 * phi))
abphi = a, b, phi
g.add(doc.path(d=ellipse(p2, p0, abphi, 1),
    stroke=c2, stroke_width=lw, stroke_dasharray=dash))
g.add(doc.path(d=parabola(-cx, 0, abc) + " " + parabola(2*R*vx*vy, size[0]-cx, abc),
    stroke=c1, stroke_width=lw, stroke_dasharray=dash))
g.add(doc.path(d=ellipse(p0, p2, abphi, 0), stroke=c2, stroke_width=lw))
g.add(doc.path(d=parabola(p0[0], p1[0], abc), stroke=c1, stroke_width=lw))

# arrows
arrowd = "M {:.1f},{:.1f} V {:.1f} M {:.1f},{:.1f} L {:.1f},{:.1f} L {:.1f},{:.1f}".format(
    0, 0, 110, -13, 88, 0, 110, 13, 88)
g.add(doc.path(transform="translate(0, {:.1f})".format(-R), d=arrowd,
    stroke="#777777", stroke_width="7", fill="none", stroke_linecap="butt"))
g.add(doc.path(transform="translate({:.1f}, {:.1f})".format(*p1), d=arrowd,
    stroke="#777777", stroke_width="7", fill="none", stroke_linecap="butt"))
g.add(doc.path(transform="rotate({:.2f}) translate(0, {:.1f})".format(degrees(2*phi-pi), -R), d=arrowd,
    stroke="#777777", stroke_width="7", fill="none", stroke_linecap="butt"))

g.add(doc.circle(r="6", center=(0,0), fill="black", stroke="none"))
g.add(doc.circle(r="6", center=p0, fill="black", stroke="none"))
g.add(doc.circle(r="6", center=p1, fill="black", stroke="none"))
g.add(doc.circle(r="6", center=p2, fill="black", stroke="none"))

# text
g.add(doc.text("g", font_size="30px", font_family="Bitstream Vera Sans",
    text_anchor="middle", transform="translate({:.1f}, {:.1f})".format(19, -0.955*R), stroke="none", fill="black"))
g.add(doc.text("g", font_size="30px", font_family="Bitstream Vera Sans",
    text_anchor="middle", transform="translate({:.1f}, {:.1f})".format(19+p1[0], -0.955*R), stroke="none", fill="black"))
g.add(doc.text("g'", font_size="30px", font_family="Bitstream Vera Sans",
    text_anchor="middle", transform="translate({:.1f}, {:.1f})".format(550, -1322), stroke="none", fill="black"))

legend = doc.add(doc.g(transform="translate({:.1f}, {:.1f})".format(510, 20), fill="none"))
legend.add(doc.rect(insert=(0, 0), size=(190, 100), fill="white", stroke="black", stroke_width="3"))
legend.add(doc.path(d="M {:.1f},{:.1f} h {:.1f}".format(20, 30, 40), stroke=c1, stroke_width=lw))
legend.add(doc.path(d="M {:.1f},{:.1f} h {:.1f}".format(20, 70, 40), stroke=c2, stroke_width=lw))
legend.add(doc.text("flat", font_size="30px", font_family="Bitstream Vera Sans",
    text_anchor="start", transform="translate({:.1f}, {:.1f})".format(76, 39), stroke="none", fill="black"))
legend.add(doc.text("planet", font_size="30px", font_family="Bitstream Vera Sans",
    text_anchor="start", transform="translate({:.1f}, {:.1f})".format(76, 79), stroke="none", fill="black"))

doc.save(pretty=True)

Licensing

I, the copyright holder of this work, hereby publish it under the following license:
w:en:Creative Commons
attribution share alike
This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.
You are free:
  • to share – to copy, distribute and transmit the work
  • to remix – to adapt the work
Under the following conditions:
  • attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
  • share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.

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3e29a2a78e43f1ad0e0653baf1aa9420e8390190

3,699 byte

440 pixel

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Date/TimeThumbnailDimensionsUserComment
current13:03, 13 October 2020Thumbnail for version as of 13:03, 13 October 2020720 × 440 (4 KB)Geek3Uploaded own work with UploadWizard

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