What is the escape velocity of Earth?

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Discussion Overview

The discussion revolves around the concept of escape velocity from Earth, exploring its definition, implications, and the conditions under which a projectile can escape Earth's gravitational influence. Participants examine whether the direction of launch affects the escape velocity and discuss theoretical scenarios involving the absence of atmospheric resistance.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant questions the definition of escape velocity and whether it must be fired perpendicular to the ground, suggesting that it might be more accurately termed escape speed since it is independent of direction.
  • Another participant asserts that as long as the projectile's trajectory does not intersect the Earth's surface, it can escape regardless of the launch direction, provided it reaches or exceeds the escape velocity.
  • A participant proposes a hypothetical scenario where a projectile is fired horizontally from 1000m above the ground at the escape speed and questions whether it would successfully travel into space, acknowledging uncertainties about the calculations involved.
  • Further clarification is provided that a projectile could be aimed slightly downwards and still escape, indicating that the direction of travel changes but the escape condition remains satisfied.

Areas of Agreement / Disagreement

Participants generally agree on the concept that escape velocity is independent of launch direction, but there are nuances in the scenarios discussed, particularly regarding the conditions of launch and the effects of Earth's shape and atmosphere. The discussion remains unresolved regarding the specifics of the calculations and assumptions involved.

Contextual Notes

Participants express uncertainty about the mathematical implications of launching from a height and the effects of Earth's shape, noting that Earth is not a perfect sphere but rather a bolate shape. There are also assumptions about the absence of atmospheric resistance that are not fully explored.

Stephanus
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What is escape velocity?
According to Wikipedia
http://en.wikipedia.org/wiki/Earth
Earth:
Escape velocity: 11.186km/s?
What does that mean?
Does the projectile should be fired perpendicular with respect to the ground angle?

According to this:
http://en.wikipedia.org/wiki/Escape_velocity
The term escape velocity is a misnomer, and it is referred to as escape speed since it is independent of direction.
According to this, can the projectile be fired in any direction (because it is speed not velocity) as long as its speed is 11.186 Km/s to escape earth?If (supposed Earth has no atmosphere) the projectile is fired parallely to the ground (tangent), what is its escape velocity?

Thanks for any explanation.
 
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The wikipedia article has it right. As long as the trajectory doesn't intersect the surface of the Earth and go "boom!", if it is launched at or above escape velocity the projectile will escape no matter what direction it is aimed. Escape velocity tangent to the surface of an airless non-rotating body is the same as escape velocity vertical to the surface.

There are many ways of showing this, but the easiest is to look at the sum of the projectile's potential and kinetic energy, which must remain constant throughout its trajectory.
 
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Nugatory said:
...as long as the trajectory doesn't intersect the surface of the Earth and go "boom...".
Yes, yes, I understand now. So if the projectile is placed, say..., 1000m above ground (earth).
And it's fired horizontally and 10 to the ground, supposed the Earth has no atmosphere and no mountain (and skyscraper for that matter), I don't know if the math is correct for 10; 1000 m above the ground; and Earth radius. After all Earth is bolate not sphere.
Just supposed in that height and direction the projectile is fired 11.186 km/s, and doesn't go boom, it will travel to space, Right?
 
Stephanus said:
Yes, yes, I understand now. So if the projectile is placed, say..., 1000m above ground (earth).
And it's fired horizontally and 10 to the ground, supposed the Earth has no atmosphere and no mountain (and skyscraper for that matter), I don't know if the math is correct for 10; 1000 m above the ground; and Earth radius. After all Earth is bolate not sphere.
Just supposed in that height and direction the projectile is fired 11.186 km/s, and doesn't go boom, it will travel to space, Right?

Yes. In fact, you could aim the thing slightly downwards so that it just barely missed grazing the surface of the earth, and it would still escape.

All that will change is the direction that it's traveling as it heads away from earth.
 
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