December 28, 2009
#681: Gravity Wells
((A schematic of the depths of the gravity wells of each planet in the solar system and several moons. At extreme left, an arrow pointing down and to the left, labeled “To Sun, very very far down”. From left to right the gravity wells depicted are: Mercury; Venus; Earth, 5,478 km; Moon, 288 km; Mars, 1,286 km; Ganymede; Io; Jupiter; Europa; Titan, with two small bumps captioned “WEEOOOEEOOOEEEOOO”; Saturn, with its rings depicted as various-colored horizontal bands; Uranus; and Neptune, with a figure exclaiming, “An even more glorious dawn awaits!”
Inset below Earth, the Moon, and Mars are three panels depicting Mars’, Deimos’s, and Phobos’s gravity wells. The Mars inset shows Mars’ gravity well, 1,286 km deep, in relation to its moons, Deimos and Phobos, and a NASA Mars Exploration Rover. The Deimos inset shows Deimos’ gravity well and a person, labeled “to scale”; the gravity well is approximately two thirds the height of the person, and the caption reads, “You could escape Deimos with a bike and a ramp.” The Phobos inset is similar, except that the gravity well is approximately three times the height of the person included for scale, and reads, “A thrown baseball could escape Phobos.”
To the right of Jupiter’s gravity well is a diagram of a well. The height of the well is labeled “very deep”; at the bottom is a figure labeled “your mom”; and three figures, labeled “local football team”, are shown falling in head first. Beneath that, the text reads, “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.”
At the right of the panel is an inset diagram detailing Earth’s gravity well, which is labeled as being 6,379 km deep. Also depicted are the altitudes of low Earth orbit, the ISS, the Space Shuttle, GPS satellites, geosynchronous orbit, and the Moon’s gravity well, 288 km deep. A figure standing on the Earth’s “surface” says, “This is why it took a huge rocket to get to the moon, but only a small one to get back.” Beneath that, the text, “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.”
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 x PlanetMass)
(g x PlanetRadius)
G = Newton’s constant
g = 9.81 meters per second squared