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. 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. | ||
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+ | 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. 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. In reality, the strength of gravity decreases the further you get from the planet. However, a comparison of energy expended to escape the gravitational pull allows for a simpler comparison between the objects. | ||
− | The | + | The moons shown in the chart are at the appropriate distance from their respective planets' gravity wells for their orbits. 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. |
− | 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 ==== | ||
− | * {{w| | + | |
− | * {{w| | + | * {{w|Mercury_(planet)|Mercury}} — no facts listed |
− | * {{w|Earth}} | + | |
− | * {{w|Mars}} | + | * {{w|Venus_(planet)|Venus}} — no facts listed |
+ | |||
+ | * {{w|Earth}} & {{w|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. | ||
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+ | * {{w|Mars}} — listed with the depth of gravity well of 1286 km | ||
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+ | ==== Cut outs ==== | ||
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+ | * 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 its gravity well and 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, 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 the football team being attracted to, and falling into, her gravity well. A "Yo Mama" joke also appears in comic [[89: Gravitational Mass]]. | ||
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+ | * The Earth/Moon cut out shows the significant difference in strength between the {{w|gravity well}} of the Earth and the Moon. Cueball comments on how the {{w|Apollo Lunar Module|Apollo Lunar Module}} could be so small and still return to Earth while the {{w|Saturn V}} rocket used to get the moon had to be so huge since it was escaping Earth's well while the Lunar Module only needed to escape the pull of the Moon. 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. | ||
==== Outer Planets ==== | ==== Outer Planets ==== | ||
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− | * {{w| | + | * {{w|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. Strong gravitational pull is a significant factor in igniting fusion. As gravity pulls matter together the pressure and temperature increase. With sufficient increase in pressure and temperature {{w|Nuclear fusion|nuclear fusion}} begins. Had that happen during creation of our solar system, i.e. had a few dozen times the mass of gasses contained in Jupiter condensed in that location, then we would had two {{w|Sun|Suns}} and our solar system would have been a {{w|Binary system (astronomy)|Binary system}}. |
− | ** {{w| | + | ** {{w|Ganymede_(moon)|Ganymede}} -- (Moon of jupiter) -- no facts given. |
+ | ** {{w|Io_(moon)|Io}} -- (Moon of jupiter) -- no facts given. | ||
+ | ** {{w|Europa_(moon)|Europa}} -- (Moon of jupiter) -- no facts given. | ||
− | * {{w| | + | * {{w|Saturn}} & its rings — The "Rings" in Saturn's gravity well are {{w|Rings of Saturn|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 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. |
− | + | ** {{w|Titan (moon)|Titan}} — (Moon of Saturn) 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. | |
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− | + | * {{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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− | + | ==== How to interpret gravity wells ==== | |
− | + | To escape a planet's or moon'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. | |
− | + | 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 text | ||
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). |
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− | The size of the gravity-well as described in this comic is not accounting for these factors | + | The Title Text refers to that the planet motions can affect the actual amount of energy for escape velocity {{w|Gravity_assist|to gain (or loose) speed by using the planets orbital speed to gravity assist}} the speed of vehicle -- this is know as doing sling-shoot around planets to gain speed (or to break when needed, breaking is just doing the same in reverse) -- on earth the same principle is used slightly differently when launching rockets -- rockets are always launched in a eastward direction to make maximum use of the rotational energy -- launching rockets in a westward direction would require a significant additional energy, and hence most satellites are flying from west to east as turning them in a different orbit would be requiring more fuel. The {{w|Oberth effect}} is an extension of the same principle, where the use of rocket engines are more effective when used at the high speed phase of the slingshot. |
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+ | The size of the gravity-well as described in this comic is not accounting for these factors and hence leaving the solar system (or any of the gravity wells of the planets) may require less energy than described by the size of each well if the launch and slingshots are carefully planned 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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