681: Gravity Wells
Title text: 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.
The xkcd page links to a much larger version.
| This explanation may be incomplete or incorrect: Fix Grammar and explain title text|
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The comic shows the relative strengths of the gravitational fields of each planet in the solar system as well as some of their satellites. 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.
This is a simplified method of comparing the escape velocities of the various planets and satellites. 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.
Moons shown in the chart are at the appropriate distance from their respective planets' gravity wells for their orbits. Those moons featured are: Earth's moon, Mars' tiny moons Phobos and Deimos (in an inset panel), Jupiter's moons Ganymede, Io, and Europa, and Saturn's moon Titan.
The 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.
 Inner Planets
- Mercury -- no facts listed
- 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. Deimos is so small that a bike jump would be sufficient to escape its gravity well and on Phobos you could launch a baseball into space simply by throwing it.
- 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.
- The Earth/Moon cut out shows the significant difference in strength between the gravity well of the Earth and the Moon. Cueball comments on how the Apollo Lunar Module could be so small and still return to Earth while the 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 International Space Station, the space shuttle, GPS satellites and geo-stationary satellites at their respective positions within Earth's gravity well.
 Outer Planets
- Jupiter -- is so massive and dense that it is comparable in mass to a 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 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 Suns and our solar system would have been a Binary system.
- Saturn & its rings -- The "Rings" in 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 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 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.
- Uranus -- notably absent is any "your-anus" jokes.
- Neptune -- Megan's quote is a paraphrase of 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." [Video here]
 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 calculation for a gravity well is:
- depth = (G * Planet-mass ) / (9.81 m/s2 * Planet-radius)
 Escape Velocities
The following table was adapted from the table in Escape velocity, using h = V_e^2 / 2g:
|Location||with respect to||Ve (km/s)||Well depth (km)||Location||with respect to||Ve (km/s)||Solar well (Mm)||Total depth (Mm)|
|on the Sun,||the Sun's gravity:||617.5||19,435,000||19,435|
|on Mercury,||Mercury's gravity:||4.3||942||at Mercury,||the Sun's gravity:||67.7||233.6||235|
|on Venus,||Venus' gravity:||10.3||5,407||at Venus,||the Sun's gravity:||49.5||124.9||130|
|on Earth,||the Earth's gravity:||11.2||6,393||at the Earth/Moon,||the Sun's gravity:||42.1||90.3||97|
|on the Moon,||the Moon's gravity:||2.4||294||at the Moon,||the Earth's gravity:||1.4||91|
|on Mars,||Mars' gravity:||5||1,274||at Mars,||the Sun's gravity:||34.1||59.3||61|
|on Jupiter,||Jupiter's gravity:||59.5||180,400||at Jupiter,||the Sun's gravity:||18.5||17.4||198|
|on Ganymede,||Ganymede's gravity:||2.7||372|
|on Saturn,||Saturn's gravity:||35.6||64,600||at Saturn,||the Sun's gravity:||13.6||9.43||74|
|on Uranus,||Uranus' gravity:||21.2||22,907||at Uranus,||the Sun's gravity:||9.6||4.7||28|
|on Neptune,||Neptune's gravity:||23.6||28,400||at Neptune,||the Sun's gravity:||7.7||3.02||31|
|on Pluto,||Pluto's gravity:||1.2||73|
|at Solar System
|the Milky Way's gravity:||525||14,000|
- Main Text
- Gravity Wells scaled to Earth surface gravity
- This chart shows the "depth" of various solar system gravity wells.
- 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.
- The planet sizes are to the same scale as the wells. Interplanetary distances are not to scale.
- Depth = (G × PlanetMass) / (g × PlanetRadius)
- G = Newton's constant
- g = 9.81 m/s2
- Planetary Descriptions
- To Sun, very very far down
- Earth - 5,478 km
- Moon - 288 km
- Mars - 1,286 km
- [A drawing of a "very deep" gravity well, "Your mom" at the bottom, several member of "local football team" falling down towards her.]
- Jupiter is not much larger than Saturn, but much more massive. At its size, adding more mass just makes it denser due to the extra squeezing of gravity.
- If you dropped a few dozen more Jupiters into it, the pressure would ignite fusion and make it a star.
- Two figures: Weeoooeeoooeeooo
- Megan: An even more glorious dawn awaits!
- Mars Inset
- [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.]
- You could escape Deimos with a bike and a ramp.
- [Figure of a man (to scale) in Phobos's gravity well.]
- A thrown baseball could escape Phobos.
- Earth Inset
- [Zoomed-in view of Earth/moon gravity well, featuring the relative locations of the atmosphere, Low Earth Orbit, the International Space Station, the Space Shuttle, GPS satellites, and satellites in geosynchronous orbit.]
- Cueball: This is why it took a huge rocket to get to the moon but only a small one to get back.
- It takes the same amount of energy to launch something on an escape trajectory away from Earth as it would to launch it 6,000 km upward under constant 9.81 m/s2 Earth gravity.
- Hence, Earth's well is 6,000 km deep.