Editing 681: Gravity Wells

* The xkcd page links to [http://xkcd.com/681_large/ a much larger version].

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 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.

* {{w|Mercury (planet)|Mercury}} — no facts listed

* {{w|Venus (planet)|Venus}} — 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.

* {{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;

** {{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|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;

* 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.

* 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.

::where G is {{w|Isaac Newton|Newton}}'s {{w|gravitational constant}}, and

::9.81 m/s² is the {{w|acceleration}} rate of a {{w|Gravity of Earth|free falling body on earth}} at sea level (g).

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.

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.

:[Mars gravity well, with one of the Mars rovers on its surface, with its moons Deimos and Phobos as smaller gravity wells.]