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## Escape Velocity

by | Nov 9, 2018

Staying with the gravity themes of recent Physics Friday IFODs (Gravitational Waves and General Relativity), today’s IFOD is about Escape Velocity.

Escape velocity is the minimum speed that an object needs to be traveling to break free of a celestial object’s gravity well and leave it without further propulsion.

To escape Earth’s gravity, an object needs to be traveling about 11.2 km/s (about 7 miles per second or 25,000 miles per hour). Escape velocity is constant for anywhere on the earth’s surface at average planet radius as escape velocity only depends on the mass of earth and the distance the escaping object is from the center of the Earth as escape velocity is inversely proportional to the square root of the distance from the center of earth.

However, the Earth is not a perfect sphere – it is actually an “oblate spheroid—a sphere that is squashed at its poles and swollen at the equator” which results in the the distance to the center of the earth being about 13 miles farther away at the equator than at the poles. Thus, escape velocity is slightly less at the equator than the poles.

Additionally, because of the spin of the Earth, about 0.46 km/s is added to an object’s initial velocity as it takes off from earth traveling east at the equator. As you move from the equator towards the poles the benefit of the Earth’s spin is reduced and at the poles there is no benefit to be had from the spin.

Thus, for those two reasons (greater radius from the center of Earth and added velocity from Earth’s spin) rocket launches generally take place closer to the equator. Thus, U.S. rockets generally lift off from Florida. SpaceX’s first few launches were from an atoll called Kwajalein in in the Pacific near the equator. Note, however, that a slight drawback launching near the equator is that the atmosphere also bulges at the equator so there is more air drag to fight through.

Satellites and other objects that orbit the Earth do not need to achieve escape velocity – rather they merely need to travel at orbital velocity speeds. Orbital velocity is how fast an object must travel to achieve orbit – which is not completely escaping the Earth’s gravitational pull. To achieve an orbit at about 150 miles an object would need to travel at about 17,000 mph – quite a bit less than the 25,000 mph escape velocity.

Related IFOD on Why Astronauts Float in Space

1. Interestingly — In many disease -cure efforts we often use the “moon shot” analogy without really understanding what it really means — we did not get to the moon by aiming our rockets at it and going for broke. neither did we just lift off in an “hail mary pass” attempt. A major challenge was overcoming gravity — and the solution was the “slingshot” — using gravity to overcome gravity. So what would a real “moonshot” for cancer or alzheimer’s or any other complex problem look like? It might mean really looking at the problem from a new perspective, working hard to really understand the problem to be solved and considering solutions that are seemingly counter-intuitive. THANKS John for a thought provoking post!

2. Oblate Spheroid….wasn’t that the name of a musical group in the early 70s?
They were a progressive experimental rock jazz fusion group…the Oblate Spheroids…..yeah that’s the ticket!
Good article John.

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