Editing 681: Gravity Wells
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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. | ||
}} | }} | ||
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− | + | 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 | + | {{incomplete|Fix Grammar}} |
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+ | 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 would be giving up energy, while an object traveling along a downward one would be gaining energy. | ||
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+ | Escaping a planet's or moon's orbit requires enough energy to reach the top of either peak (e.g. by walking or jumping) that defines the edge of the well. The peak to the left indicates the minimum energy to exit orbit by traveling toward the center of the solar system. The peek to the right indicates the maximum energy to exit orbit by traveling directly away from 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. | ||
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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 earths 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 planets gravity, it would require the same energy required to rise out of a physical well of that depth at Earth's surface gravity. | ||
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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 distance between the planets are condensed the gravitational potential, from the gravity pulling toward the sun, accumulates quicker. This is the reason for the large peeks between the planet. 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. | |
− | The | + | The Earth's gravity well's depth in the inset and in the main part of the comic don't match. This is most likely a mistake by Randall. |
==== Inner Planets ==== | ==== Inner Planets ==== | ||
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− | + | * {{w|Mercury_(planet)|Mercury}} | |
− | * {{w| | + | |
− | + | * {{w|Venus_(planet)|Venus}} | |
− | * | + | |
− | + | * {{w|Earth}} & {{w|Moon}} - The listed depth of the gravity well of Earth is 5,478 km and the Moon's is 288 km. | |
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+ | * {{w|Mars}} - The listed depth of the gravity well of Mars is 1286 km | ||
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+ | ==== Cut outs ==== | ||
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+ | * The Mars cutout shows how weak the gravity of Mars' moons really are. {{w|Deimos (moon)|Deimos}} is so weak that a bike jump would be sufficient to escape its gravity. On {{w|Phobos (moon)|Phobos}} you could launch a baseball into space simply by throwing it. | ||
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+ | * The drawing 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 joke implies that she has a huge gravitational pull and has sex with the entire football team by demonstrating a football team being falling into her very deep gravity well. A "Yo Mama" joke also appears in comic [[89: Gravitational Mass]]. | ||
− | * {{w| | + | * The Earth/Moon 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 small and the {{w|Saturn V}} rocket was much larger because escaping the Earth's well takes much more energy than escaping the Moon's. The cut out also shows that 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. |
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− | + | ==== Outer Planets ==== | |
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− | + | * {{w|Jupiter}} — Jupiter is so massive and dense that it is comparable in mass to a {{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. Had a few dozen times the mass of gasses contained in Jupiter 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 happen during 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's moons | |
+ | ** {{w|Ganymede_(moon)|Ganymede}} | ||
+ | ** {{w|Io_(moon)|Io}} | ||
+ | ** {{w|Europa_(moon)|Europa}} | ||
− | * | + | * {{w|Saturn}} & its rings — The diagram shows the position of {{w|Rings of Saturn|Saturn's rings}} in its 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. |
− | + | *Moons of Saturn | |
− | ** {{w| | + | ** {{w|Titan (moon)|Titan}} — The figures on Titan are sirens, a reference to Kurt Vonnegut's ''{{w|The Sirens of Titan}}''. |
− | * | + | * {{w|Uranus}} — notably absent is any "your-anus" jokes. |
− | * | + | * {{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] |
=== How to calculate gravity wells === | === How to calculate gravity wells === | ||
− | The text | + | 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 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| | + | ::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| | + | ::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). |
− | ==== | + | ====Gravity assist==== |
− | 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 | + | 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 know as a performing a slingshot or a {{w|Gravity assist|gravity assist}}, and is done to gain speed or to break when needed. On earth the same principle is used when launching rockets. Rockets are always launched in a 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. Also, the use of rocket engines are more effective when used at a high speed. This is know as the {{w|Oberth effect}}. The use of engines are therefore more effective when used as part of a slingshot maneuver. |
− | The size of the gravity-well as described in this comic is not accounting for these factors. Therefore | + | 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. |
==== Escape Velocities ==== | ==== 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'': | 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'': | ||
{| class="wikitable" border="1" | {| class="wikitable" border="1" | ||
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:Mercury | :Mercury | ||
:Venus | :Venus | ||
− | :Earth - | + | :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 | + | ::Two figures: Weeoooeeoooeeooo |
:Saturn | :Saturn | ||
::Rings | ::Rings | ||
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:'''Mars Inset''' | :'''Mars Inset''' | ||
− | :[Mars gravity well, | + | :[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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{{comic discussion}} | {{comic discussion}} | ||
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[[Category:Comics with color]] | [[Category:Comics with color]] | ||
[[Category:Large drawings]] | [[Category:Large drawings]] | ||
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[[Category:Your Mom]] | [[Category:Your Mom]] | ||
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