Quick question about Escape velocity

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Discussion Overview

The discussion revolves around the concept of escape velocity, specifically in the context of calculating the escape velocity of a person at a distance of 3 meters. Participants explore the implications of the calculated escape velocity and the factors affecting it, including unit conversions and gravitational effects.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant questions the escape velocity calculation and expresses confusion about the implications of a very low escape velocity, suggesting that it feels counterintuitive.
  • Another participant points out a potential error in the mass calculation, indicating that the weight should be divided by 9.8 to find mass, but notes the escape velocity is indeed small.
  • There is a clarification regarding the distinction between weight and mass, emphasizing the need for consistent units in calculations.
  • Some participants discuss the theoretical scenario where an object would return if tossed with less than escape velocity, while also noting that real-world factors complicate this ideal scenario.
  • One participant reiterates the importance of unit consistency and provides a conversion from pounds to kilograms, while also confirming the escape speed calculation.
  • There is acknowledgment that the escape velocity formula assumes a spherical mass distribution, which may not apply in all cases.

Areas of Agreement / Disagreement

Participants generally agree on the calculations and the implications of escape velocity, but there are differing views on the interpretation of the results and the importance of unit consistency. The discussion remains unresolved regarding the broader implications of the escape velocity in practical scenarios.

Contextual Notes

Limitations include potential errors in arithmetic, assumptions about mass distribution, and the impact of external gravitational forces not being accounted for in the calculations.

zeromodz
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Okay this equation is giving me some trouble, I just have a question

vescape = √(2GM)/R

Say I wanted to find the escape velocity of myself 3 meters away
So I would use
vescape = √(2)(6.674*10^-11)((145*4.44)/9.8)/(3)
= 5.419003598 *10^-5

So does this mean something that moves that slow cannot escape me farther than 3 meters away?

It doesn't seem right. My gravitational field feels so ephemeral. Is this correct?
 
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I don't know why your mass is 145/9.8 (you weigh only 15 kg?), but yes, your escape velocity is tiny, and yes, something moving slower than your escape velocity can't escape from you in an ideal world. In the real world, turbulence, Brownian motion, and the gravity of other objects make that conclusion moot.
 
Weight is a force.
F = MA
Therefore
M = F/A or F/G

So I could take my weight in ibs and divide it by 9.8 to get my mass.
 
zeromodz said:
So I could take my weight in ibs and divide it by 9.8 to get my mass.
Careful! If you knew your weight in Newtons (not pounds), then you could divide by g = 9.8 m/s2 to get your mass in kg. When using equations such as W = mg, you need to use consistent units: in this case, Newtons, kilograms, and m/s2.

If you weigh 145 pounds, your mass is about 66 kg.
 
Doc Al said:
Careful! If you knew your weight in Newtons (not pounds), then you could divide by g = 9.8 m/s2 to get your mass in kg. When using equations such as W = mg, you need to use consistent units: in this case, Newtons, kilograms, and m/s2.

If you weigh 145 pounds, your mass is about 66 kg.

Okay, thanks a lot. That really messed me up. I changed it, but back to my point. Was my calculations and logic correct?
 
In theory, if you were isolated in a big region of empty space, and tried to toss say a marble away, it would return to you if the initial velocity were less than escape velocity, or it would go into orbit around you if it had a correct satellite velocity. I think ...

http://en.wikipedia.org/wiki/Escape_velocity

The proper unit for mass in British enegineering is slugs, that is, your weight in pounds force divided by standard gravity 32.174 ft/s/s. Always work in some consistent set of units.
 
zeromodz said:
Was my calculations and logic correct?
Using your numbers, I get an escape speed of about 5.4 x 10-5 m/s. (So double check your arithmetic.) Which basically says that it doesn't take all that much energy to escape your gravitational field. So if you were in outer space--away from any other masses--and some small object was 3 meters away and moving at less than that speed it could not escape your gravitational field. (But give it the merest push and it's gone!)

Of course, this calculation assumes that you are a spherical ball! (That's how the escape velocity formula is derived.) So I wouldn't take it too seriously.
 
Doc Al said:
Using your numbers, I get an escape speed of about 5.4 x 10-5 m/s. (So double check your arithmetic.) Which basically says that it doesn't take all that much energy to escape your gravitational field. So if you were in outer space--away from any other masses--and some small object was 3 meters away and moving at less than that speed it could not escape your gravitational field. (But give it the merest push and it's gone!)

Of course, this calculation assumes that you are a spherical ball! (That's how the escape velocity formula is derived.) So I wouldn't take it too seriously.


Thanks, the weight thing in Newtons messed me up. Thank you so much anyways. I understand now.
 

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