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| | | titletext = This doesn't take into account the energy imparted by orbital motion (or gravity assists or the Oberth effect), all of which can make it easier to reach outer planets. | | | titletext = This doesn't take into account the energy imparted by orbital motion (or gravity assists or the Oberth effect), all of which can make it easier to reach outer planets. |
| | }} | | }} |
| − | {{TOC}}
| + | |
| − | * The xkcd page links to [http://xkcd.com/681_large/ a much larger version].
| + | The xkcd page links to [http://xkcd.com/681_large/ a much larger version]. |
| | | | |
| | ==Explanation== | | ==Explanation== |
| − | The comic shows the gravitational potential (energy transferred per unit mass due to gravity) for the positions of each planet in the solar system — including some moons and Saturn's rings. An object traveling along an upward slope loses energy, while an object traveling along a downward slope gains energy. Escaping a planet or moon's orbit requires enough energy (e.g. by walking, jumping, or rocket) to reach the top of either peak that defines the edge of the well. The peak to the left indicates the minimum energy required to exit orbit. The peak to the right indicates the maximum energy required to exit orbit. In order to exit orbit with the minimum amount of energy, you would have to travel towards the center of the solar system; to exit orbit with the maximum amount of energy, you would have to travel away from the center of the solar system (the Sun). In reality, the strength of gravity decreases with distance from the planet. However, a comparison of energy expended to escape the gravitational pull allows for a simpler comparison between the objects.
| + | {{incomplete|Fix Grammar}} |
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| − | The height of the graph is scaled to kilometers via the gravitational potential an object has at the given height assuming at a constant acceleration due to Earth's surface gravity. The {{w|Sun|Sun's}} gravity well is not shown in its entirety, but is just indicated on the far left as ''"Very very far down"''. Had it been shown in its full extent it would have made the rest of the drawing so small in comparison that it would have been unreadable. As the gravitational potential increases with distance from the sun, the graph has a general upward slope. To rise out of each well on the diagram, and therefore escape the planet's gravity, it would require the same energy required to rise out of a physical well of that depth at Earth's surface gravity. | + | The comic shows the solar system gravity field of each planet and some of their satellites, in a simplified form. Each well is scaled such that rising out of a physical well of that depth in constant Earth surface gravity would take the same energy as escaping from that planet's gravity in reality. Each planet is shown cut in half at the bottom of its well, with the depth of the well measured down to the planet's flat surface. |
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| − | The length of each gravity well is scaled to the diameter of the planet and the spacing between the planets is not to scale with distance from the sun. This is necessary to make the graph readable. Because the distances between the planets are condensed, the gravitational potential - from the gravity pulling toward the sun - accumulates quicker. This is the reason for the large peaks between the planets. The moons shown in the chart are at the appropriate distance from their respective planets' gravity wells for their orbits. Each planet is shown cut in half at the bottom of its well, with the depth of the well measured down to the planet's flat surface.
| + | This is a simplified method of comparing the escape velocities of the various planets and satellites: since, in reality, the strength of gravity decreases the further you get from the planet, it's harder to do a direct comparison when seen in a more realistic format. |
| | + | |
| | + | Besides the eight planets, several moons are also included: Earth's moon is included; Mars' tiny moons Phobos and Deimos are shown in an inset panel (at the appropriate distance up Mars' gravity well for their orbits). Jupiter's moons Ganymede, Io, and Europa are included, as well as Saturn's moon Titan. |
| | + | |
| | + | The {{w|Sun}} gravity well is not shown in it entirety, but is just indicated on the far left as ''"Very very far down"'' -- had it been shown in its full extent it would have made the rest of the drawing so small in comparison that it would have been unreadable. |
| | | | |
| | ==== Inner Planets ==== | | ==== Inner Planets ==== |
| − | * {{w|Mercury (planet)|Mercury}} — no facts listed | + | |
| − | * {{w|Venus (planet)|Venus}} — no facts listed | + | * Mercury -- no facts listed |
| − | * {{w|Earth}} and {{w|Moon}}: The listed depth of the gravity well at Earth was originally listed at 5478 km rather than the correct value of 6379 km seen in the cutout. Randall has since corrected it. The Moon's is 288 km. | + | |
| − | * {{w|Mars}}: The listed depth of the gravity well of Mars is 1286 km.
| + | * Venus -- no facts listed |
| | + | |
| | + | * Earth & Moon -- listed with the depth of the gravity well of 5,478 km for Earth and 288 km for the Moon. Calculations of depth is explained in the Saturn insert. |
| | + | |
| | + | * Mars -- listed with the depth of gravity well of 1286 km |
| | + | |
| | + | ==== Cut outs ==== |
| | + | |
| | + | * The Mars cutout shows how small mars moons really are, specifically in terms of gravity -- {{w|Deimos_(moon)|Deimos}} is so small that a bike jump would be sufficient to escape and on {{w|Phobos_(moon)|Phobos}} you could launch a baseball into space simply by throwing... |
| | + | |
| | + | * The drawing next to Jupiter is playing on the classic "Yo Mama" joke, combining the aspects of your mom being very fat (having a huge gravitational pull) and very slutty (having sex with the entire football team), represented by them being attracted to, and falling into, her gravity well. A "Yo Mama" joke also appears in comic [[89:_Gravitational_Mass|89: Gravitational Mass]]. |
| | + | |
| | + | * The Earth/Moon cutout shows the significant difference in the {{w|gravity well}} between the two and explain why the moon landing needed such a {{w|Apollo_Lunar_Module|small vehicle}} to return to earth. The drawing shows that most space explanation like the {{w|International_Space_Station|space shuttle}}, {{w|GPS_satellite|GPS satellites}} and {{w|Geostationary_orbit|geo-stationary satellites}} are in fact still within the {{w|Gravity_well|gravity well}} of earth and has not really escaped. |
| | | | |
| | ==== Outer Planets ==== | | ==== Outer Planets ==== |
| − | * {{w|Jupiter}}: Jupiter is so massive and dense that it is one thirteenth the mass of a small {{w|Brown dwarf}} which is the smallest kind of star. Saturn, while similar in size, is composed of much lighter gas material. Hence Saturn's mass and therefore its gravitational pull are much smaller. If a few dozen times the mass of gasses contained in Jupiter had condensed in that location, the gravitational pull would cause the pressure and temperature to increase to a level that is sufficient to ignite {{w|Nuclear fusion|nuclear fusion}}. Had that happened during the creation of our solar system, we would have two {{w|Sun|Suns}} and our solar system would be a {{w|Binary system (astronomy)|Binary system}}. Jupiter has {{w|Moons of Jupiter|67 moons}} of which 3 are shown;
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| − | ** {{w|Ganymede (moon)|Ganymede}} — moon of Jupiter, no facts given
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| − | ** {{w|Io (moon)|Io}} — moon of Jupiter, no facts given
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| − | ** {{w|Europa (moon)|Europa}} — moon of Jupiter, no facts given
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| − | * {{w|Saturn}}: The diagram shows the position of the {{w|rings of Saturn}} in Saturn's gravity well. Saturn's rings start fairly near the planet and extend out quite far, therefore multiple stripes are shown in the figure. The rings are also shown in multiple colors and roughly match the observed colors from photos take by the {{w|Cassini–Huygens|Cassini spacecraft}} expedition as it passed Saturn. All of the colors of the planets and moons represent the predominant color of that object as observed from earth. Saturn has {{w|Moons of Saturn|62 moons}} of which one is shown;
| + | The fascinating fact about {{w|Jupiter}}'s mass is that it is border line in mass to have ignited as a {{w|Brown dwarf}} which is the smallest kind of star. Saturn, while similar in size, is composed of much lighter gas material and hence the mass is much smaller and the gravitational pull is smaller. Large gravity is a significant factor in igniting fusion, as the gravity pull the matter together to increase the pressure and temperature to the degree where the {{w|Nuclear_fusion|nuclear reactions}} can start. Had that happen at the creation of our solar system, i.e. had a few more Saturns dropped into Jupiter, then we would had two {{w|Sun}}'s and our solar system would have been a {{w|Binary star}}. |
| − | ** {{w|Titan (moon)|Titan}}, a moon of Saturn. The figures on Titan are sirens, a reference to Kurt Vonnegut's ''{{w|The Sirens of Titan}}''.
| + | |
| | + | The figures on {{w|Titan_(moon)|Titan}} are sirens, a reference to Kurt Vonnegut's ''{{w|The Sirens of Titan}}''. |
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| − | * {{w|Uranus}}: Notably absent is any "your-anus" jokes.
| + | The "Rings" in {{w|Saturn}}'s gravity well are Saturn's rings: The farther you get from a planet, the weaker the effect of its gravity on you, so, at some point, when climbing out of Saturn's gravity well, you've reached the point equivalent to starting your climb from the rings of Saturn, or, in fact, from specific rings of Saturn: Saturn's rings start fairly near the planet and extend out fairly far, hence why there's several stripes.. |
| − | * {{w|Neptune}}: Megan's quote is a paraphrase of {{w|Carl Sagan|Carl Sagan's}} quote, "...but from a planet orbiting a star in a distant globular cluster, a still more glorious dawn awaits, not a sun-rise, but a galaxy rise." [http://www.youtube.com/watch?v=zSgiXGELjbc Video here]
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| | | | |
| − | ==== Cut outs and sketches====
| + | {{w|Uranus}} -- notably absent is any "your-anus" jokes. |
| − | The following items are listed from top to bottom and left to right.
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| | | | |
| − | * Mars moons: The Mars cutout shows the Mars moon system, including the moons Deimos and Phobos. The depth of the Mars gravity well is listed at 1286 km.
| + | {{w|Neptune}} -- Megan's quote is a paraphrase of {{w|Carl_Sagan|Carl Sagan}}'s quote, "...but from a planet orbiting a star in a distant globular cluster, a still more glorious dawn awaits, not a sun-rise, but a galaxy rise." [[http://www.youtube.com/watch?v=zSgiXGELjbc Video here]] |
| − | ** {{w|Deimos (moon)|Deimos}}: The gravity on Deimos, a moon of Mars, is so weak that a bike jump would be sufficient to escape its gravity.
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| − | ** {{w|Phobos (moon)|Phobos}}: The gravity on Phobos, a moon of Mars, is so weak that you could launch a baseball into space simply by throwing it.
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| | | | |
| − | * Your mom and a local football team: The sketch next to Jupiter is playing on the classic "Yo Mama" joke. It combines "Yo Mama is so fat" and "Yo Mama is so horny". The sketch implies that she has a huge gravitational pull because she is very fat, and has sex with an entire football team by demonstrating a football team falling into her very deep gravity well. A "Yo Mama" joke also appears in comic [[89: Gravitational Mass]].
| + | ==== How to interpret gravity wells ==== |
| | | | |
| − | * Earth's Moon: The cut out shows the significant difference in strength between the {{w|gravity well}} of the Earth and the Moon. Cueball comments that the {{w|Apollo Lunar Module|Apollo Lunar Module}} was very small and the {{w|Saturn V}} rocket was very large because escaping the Earth's gravity well takes much more energy than escaping the Moon's. The cut out also shows objects like the {{w|International_Space_Station|International Space Station}}, the {{w|Space shuttle|space shuttle}}, {{w|GPS satellite|GPS satellites}} and {{w|Geostationary orbit|geo-stationary satellites}} at their respective positions within Earth's gravity well. The depth of Earth's gravity well is listed correctly at 6 379 km (note the difference from the non-cutout number). The depth of the Moon's gravity well is listed at 288 km.
| + | To escape a planet or satellite's orbit, you need merely climb to the highest of the two peaks to ''either''the left or right of the object. So, for example, to escape Venus, you need merely reach the peak left of it, the slope right of it is part of the Sun's gravity well, and shows how much further you'd need to climb out of the Sun's gravity well to get from Venus to Earth. Likewise, the peak left of Jupiter is slightly lower than the one to the right; this is because the rightmost peak includes the difficulty of moving away from the sun to get to Saturn, the next planet along. |
| | | | |
| − | === How to calculate gravity wells ===
| + | The text explains that the depth of the well is mass-of-planet over radius-of-planet with newtons constant and 9.81 m/s² as constants, where 9.81 m/s² is the {{w|Gravity_of_Earth|acceleration of a free falling body at earths gravity}}. |
| − | The text near the bottom of Jupiter's gravity well explains that the depth of the well is mass-of-planet over radius-of-planet with Newton's constant and 9.81 m/s² as constants, where 9.81 m/s² is the acceleration of a free falling body at Earth's gravity. | |
| | | | |
| | The calculation for a gravity well is: | | The calculation for a gravity well is: |
| | :depth = (G * Planet-mass ) / (9.81 m/s<sup>2</sup> * Planet-radius) | | :depth = (G * Planet-mass ) / (9.81 m/s<sup>2</sup> * Planet-radius) |
| − | ::where G is {{w|Isaac Newton|Newton}}'s {{w|gravitational constant}}, and | + | ::where G is {{w|Isaac_Newton|Newton}}'s {{w|Gravitational_constant|gravitational constant}}, and |
| − | ::9.81 m/s<sup>2</sup> is the {{w|acceleration}} rate of a {{w|Gravity of Earth|free falling body on earth}} at sea level (g). | + | ::9.81 m/s<sup>2</sup> is the {{w|Acceleration|acceleration}} rate of a {{w|Gravity_of_Earth|free falling body on earth}} at sea level (g). |
| − | | |
| − | ====Title text====
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| − | The title text indicates that the planets motion can affect the amount of energy for escape velocity. It is possible to change speed by using the planets orbital speed and gravity. This is known as a performing a slingshot or a {{w|gravity assist}}, and is done to gain speed or to brake when needed. The use of rocket engines are more effective when used at a high speed slingshot maneuver, which is known as the {{w|Oberth effect}}, where most energy is going into moving the rocket as opposed to moving the exhaust — conserving the maximum useful energy. On earth the same principle is used when launching rockets. Rockets are always launched in an eastward direction to make maximum use of the rotational energy of the earth. Launching rockets in a westward direction would require significant additional energy. Because of this most artificial satellites are flying east around the globe.
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| − | | |
| − | The size of the gravity-well as described in this comic is not accounting for these factors. Therefore, leaving the solar system (or any of the gravity wells of the planets) could require less energy than described by the graph, assuming that the launch and slingshots are properly designed and executed.
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| − | | |
| − | ==== Escape Velocities ====
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| − | The following table was adapted from the table in {{w|Escape velocity#List of escape velocities|Escape velocity}}, using ''h'' = ''V_e''^2 / 2''g'':
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| − | {| class="wikitable" border="1"
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| − | | Location || with respect to || Ve (km/s) || Well depth (km) ||
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| − | | Location || with respect to || Ve (km/s) || Solar well (Mm) || Total depth (Mm)
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| − | |-
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| − | | on the Sun, || the Sun's gravity: || 617.5 || 19,435,000 || || || || || || 19,435
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| − | |-
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| − | | on Mercury, || Mercury's gravity: || 4.3 || 942 ||
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| − | | at Mercury, || the Sun's gravity: || 67.7 || 233.6 || 235
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| − | |-
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| − | | on Venus, || Venus' gravity: || 10.3 || 5,407 ||
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| − | | at Venus, || the Sun's gravity: || 49.5 || 124.9 || 130
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| − | |-
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| − | | on Earth, || the Earth's gravity: || 11.2 || 6,393 ||
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| − | | at the Earth/Moon, || the Sun's gravity: || 42.1 || 90.3 || 97
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| − | |-
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| − | | on the Moon, || the Moon's gravity: || 2.4 || 294 ||
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| − | | at the Moon, || the Earth's gravity: || 1.4 || || 91
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| − | |-
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| − | | on Mars, || Mars' gravity: || 5 || 1,274 ||
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| − | | at Mars, || the Sun's gravity: || 34.1 || 59.3 || 61
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| − | |-
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| − | | on Jupiter, || Jupiter's gravity: || 59.5 || 180,400 ||
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| − | | at Jupiter, || the Sun's gravity: || 18.5 || 17.4 || 198
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| − | |-
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| − | | on Ganymede, || Ganymede's gravity: || 2.7 || 372 || || || || ||
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| − | |-
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| − | | on Saturn, || Saturn's gravity: || 35.6 || 64,600 ||
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| − | | at Saturn, || the Sun's gravity: || 13.6 || 9.43 || 74
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| − | |-
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| − | | on Uranus, || Uranus' gravity: || 21.2 || 22,907 ||
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| − | | at Uranus, || the Sun's gravity: || 9.6 || 4.7 || 28
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| − | |-
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| − | | on Neptune, || Neptune's gravity: || 23.6 || 28,400 ||
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| − | | at Neptune, || the Sun's gravity: || 7.7 || 3.02 || 31
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| − | |-
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| − | | on Pluto, || Pluto's gravity: || 1.2 || 73 || || || || ||
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| − | |-
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| − | |at Solar System <br/>galactic radius, || the Milky Way's gravity: || 525 || 14,000
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| − | |}
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| | ==Transcript== | | ==Transcript== |
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| | :Mercury | | :Mercury |
| | :Venus | | :Venus |
| − | :Earth - 6379 km [originally 5,478 km] | + | :Earth - 5,478 km |
| | :Moon - 288 km | | :Moon - 288 km |
| | :Mars - 1,286 km | | :Mars - 1,286 km |
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| | :Europa | | :Europa |
| | :Titan | | :Titan |
| − | ::Two alarms: Weeoooeeoooeeooo | + | ::Two figures: Weeoooeeoooeeooo |
| | :Saturn | | :Saturn |
| | ::Rings | | ::Rings |
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| | :'''Mars Inset''' | | :'''Mars Inset''' |
| − | :[Mars gravity well, with one of the Mars rovers on its surface, with its moons Deimos and Phobos as smaller gravity wells.] | + | :[Mars gravity well, the Pathfinder probe on its surface, with its moons Deimos and Phobos as smaller gravity wells.] |
| | | | |
| | :[Figure of a man (to scale) in Deimos's gravity well.] | | :[Figure of a man (to scale) in Deimos's gravity well.] |
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| | :Hence, Earth's well is 6,000 km deep. | | :Hence, Earth's well is 6,000 km deep. |
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| − | ==Trivia==
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| − | This comic used to be [https://web.archive.org/web/20211215032220/https://store.xkcd.com/products/gravity-wells-poster available as a poster] in the xkcd store before it was [[Store|shut down]].
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| | {{comic discussion}} | | {{comic discussion}} |
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| | [[Category:Comics with color]] | | [[Category:Comics with color]] |
| | [[Category:Large drawings]] | | [[Category:Large drawings]] |
| − | [[Category:Charts]]
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| − | [[Category:Illustrations of scale]]
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| − | [[Category:Comics featuring Cueball]]
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| − | [[Category:Comics featuring Megan]]
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| − | [[Category:American football]]
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| − | [[Category:Baseball]]
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| | [[Category:Your Mom]] | | [[Category:Your Mom]] |
| − | [[Category:Space]]
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| − | [[Category:Mars rovers]]
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| − | [[Category:Comics with xkcd store products]]
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