Gravity Wells
Gravity Wells
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/s 2

Planetary Descriptions To Sun, very very far down Mercury Venus Earth - 6379 km [originally 5,478 km] Moon - 288 km Mars - 1,286 km Ganymede Io Jupiter [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. Europa Titan Two alarms: Weeoooeeoooeeooo Saturn Rings Uranus Neptune Megan: An even more glorious dawn awaits!

Mars Inset [Mars gravity well, with one of the Mars rovers 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/s 2 Earth gravity.
Hence, Earth's well is 6,000 km deep.

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.
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 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.
The following items are listed from top to bottom and left to right.
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:
depth = (G * Planet-mass ) / (9.81 m/s 2 * Planet-radius) where G is Newton 's gravitational constant , and 9.81 m/s 2 is the acceleration rate of a 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 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 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.
The following table was adapted from the table in Escape velocity , using h = V_e ^2 / 2 g :
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/s 2

Planetary Descriptions To Sun, very very far down Mercury Venus Earth - 6379 km [originally 5,478 km] Moon - 288 km Mars - 1,286 km Ganymede Io Jupiter [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. Europa Titan Two alarms: Weeoooeeoooeeooo Saturn Rings Uranus Neptune Megan: An even more glorious dawn awaits!

Mars Inset [Mars gravity well, with one of the Mars rovers 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/s 2 Earth gravity.
Hence, Earth's well is 6,000 km deep.
