Can anyone help mess around with escape velocities?

  • Context: Graduate 
  • Thread starter Thread starter autisticmoose
  • Start date Start date
  • Tags Tags
    Escape
Click For Summary

Discussion Overview

The discussion revolves around the concept of escape velocities and their relationship to radius in celestial bodies. Participants explore mathematical relationships and seek to understand under what conditions the escape velocity can equal the radius as integers, focusing on theoretical implications and calculations related to various planets in the solar system.

Discussion Character

  • Exploratory
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant proposes a mathematical relationship where escape velocity (v) could equal radius (r) as integers under certain conditions, suggesting a specific formula derived from gravitational principles.
  • Another participant argues that by choosing suitable units, one can make v equal r, but questions the physical validity of equating quantities with different dimensions.
  • A third participant emphasizes that there exists a specific point where escape velocity and radius could be equal integers, suggesting that this is not universally applicable but rather conditional based on the radius from the center of a celestial body.
  • Participants discuss specific numerical examples from Earth and other celestial bodies, noting variances in escape velocities and their relationships to radius.

Areas of Agreement / Disagreement

There is disagreement regarding the validity of equating escape velocity and radius as integers. Some participants believe it is possible under certain conditions, while others assert that it is not physically meaningful due to differing dimensions.

Contextual Notes

The discussion includes assumptions about the mathematical relationships and the physical interpretations of escape velocity and radius. The validity of the proposed relationships may depend on the definitions and units used, which remain unresolved.

autisticmoose
Messages
5
Reaction score
0
v=(gr2)^.5
i assume that g is directly related to r as g = Gm/r^2

in such I started to wonder when, if ever, will v = r as an INTEGER ONLY NOT DIMENSIONS?

v = ( 2 * g * r )^.5
v = ( 2 * G * ( m / r^2 ) * r )^.5
v = ( 2 * G * m / r )^.5
v * r^.5 = ( 2 * G * m )^.5
REMEMBER! v=r at some point NATURALLY
r^1.5 = ( 2 * G * m )^.5
(r^1.5)^(2/3) = ( 2 * G * m )^.5
r^1 = ( ( 2 * G * m )^.5 )^(2/3)
r = ( 2 * G * m )^(1/3)

then r =(G*m*2)^(1/3) ---- NOT IN DIMENSIONS ONLY TO FIND NUMERICAL VALUE!

now re-calc based on new r with previous calculations and for every planet in out solar system (including the sun) your v should be an equal integer as r. meaning with the above r = you then put that number in for r in the equation v=(2gr)^.5. by doing so you will result in the same numerical value for v as you have for r.

earth statistics:
m = 5.9742e24 mass of earth
r = ( 2 * G * m )^(1/3) NUMERICAL distance from center
G = 6.673e-11 gravitational constant
g = Gm/r^2 acceleration of gravity
v = (2gr)^.5 escape velocity

r = ( 2 * 6.673e-11 * 5.9742e24 )^(1/3) = 9.2728e4
v = ( 2 * (6.673e-11 * 5.9742e24 / 9.2728e4^2) * 9.2728e4 )^.5 = ?

whats your answer? I bet it's 9.2728e4

the premise is how can you relate this nifty radius-escape-velocity thing to something else celestially bound. first thing i noticed was the 11 km/s of escape velocity required for the surface of Earth was about 10 times less than the radius-escape-velocity (when v=r) of Earth (9.27278718604467680471147551902e4). actually 8.30. then i tested on the rest of our solar system and received a similar variance. about 10ish off from the Sun to Pluto and every planet in between.

(Radius-Escape-Velocity) / ~10 = (Surface-Escape-Velocity)

Sun's surface escape velocity times 10.4 = (Radius-Escape-Velocity)
Mercury's surface escape velocity times 8.31 = (Radius-Escape-Velocity)
Venus' surface escape velocity times 8.36 = (Radius-Escape-Velocity)
Earth's surface escape velocity times 8.29 = (Radius-Escape-Velocity)
our Moon's surface escape velocity times 9.01 = (Radius-Escape-Velocity)
Mars' surface escape velocity times 8.74 = (Radius-Escape-Velocity)
Jupiter's surface escape velocity times 10.6 = (Radius-Escape-Velocity)
Saturn's surface escape velocity times 11.8 = (Radius-Escape-Velocity)
Uranus' surface escape velocity times 10.6 = (Radius-Escape-Velocity)
Neptune's surface escape velocity times 10.2 = (Radius-Escape-Velocity)
and Pluto's surface escape velocity times 11.0 = (Radius-Escape-Velocity)

can others assist with any other patterns or relations? I'm just messing around and enjoy math and space. also can someone make sure i didn't fat finger it, please double check my work. I am wishing to define any parameters about this radius-escape-velocity. For instance if this is true then the radius-escape-velocity ALWAYS happens below the surface of a planet/star.

i am really hoping for an intelligent discussion as i am getting a lot of people on other sites that can't even begin to comprehend this. and please don't say... r doesn't equal (2gr)^.5. i know! but if you actually read what i posted then you'll find that is NOT what i am stating. sorry and thanks, i just like messing around with math and space so... is this a waste of time? probably, but its fun for me and I'm looking to see if someone else can have fun with me.

Thank you,

other men who seek one thing
often search to find it
but a man who seeks most anything
leaves other men behind him
-AutisticMoose
 
Last edited:
Astronomy news on Phys.org
autisticmoose said:
in such my question is when, if ever, will v = r as an INTEGER ONLY NOT DIMENSIONS?

Whenever you want. Since the dimensions don't match, by suitable choice of units you can make this happen whenever you like. Simple example - if v is in units of escape velocities, and r is in units of radii, it happens automatically.
 
really? really? did you even read my post?

look we have 1.1e4 km/s of escape velocity on Earth at surface. the surface is at a radius of 6.378e6. one is smaller than the other! well... the closer to the center of the planet with less radius then the more escape velocity you get. THERE IS A POINT NATURALLY THAT THEY WILL BE EQUAL INTEGERS! it is not all the time only at a certain radius from the center! people! come on! the math is up there, didn't you do the Earth example? what was your answer?!
 
Yes, I read it. It's not physics, since in physics you cannot equate two quantities with different dimensions. I was trying to explain why.
 

Similar threads

Undergrad Atmospheric escape parametre statistics
  • · Replies 1 ·
Replies
1
Views
2K
High School 'A Brief History of Time' question on gravity
  • · Replies 4 ·
Replies
4
Views
2K
Variation of escape velocity with equal surface gravity
  • · Replies 7 ·
Replies
7
Views
1K
Undergrad Sun gravitational lensing forces
  • · Replies 11 ·
Replies
11
Views
2K
Undergrad Escape velocity near a black hole: Newtonian or Special Relativity?
  • · Replies 17 ·
Replies
17
Views
2K
Finding r of a Jovian-synchronous orbit and escape velocity
  • · Replies 7 ·
Replies
7
Views
2K
Velocity required to escape the solar system
  • · Replies 15 ·
Replies
15
Views
2K
Escape velocity of solar system
  • · Replies 11 ·
Replies
11
Views
3K
High School An exercise related to the mass of the Milky Way, sort of.
  • · Replies 2 ·
Replies
2
Views
2K
Graduate N-Body inputs from Keplerian Orbits
  • · Replies 6 ·
Replies
6
Views
2K