Can anyone help mess around with escape velocities?

[autisticmoose]

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

 

[Vanadium 50]

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.

 

[autisticmoose]

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?!

 

[Vanadium 50]

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.

 

[pmacias]

I appreciate your curiosity and enthusiasm for math and space. Your calculations and observations are interesting and could potentially lead to further discoveries and understanding in the field. However, it is important to note that scientific theories and equations are based on empirical evidence and rigorous testing, and cannot be simply derived from mathematical manipulations or patterns.

In terms of escape velocities, it is true that they vary for different objects in our solar system due to differences in mass and radius. The pattern you have observed, where the surface escape velocity is roughly 10 times less than the radius-escape-velocity when v=r, is not a coincidence. It is a result of the fact that the escape velocity at the surface of an object is the minimum velocity required to escape its gravitational pull, while the radius-escape-velocity is the velocity required to escape from the object's surface when it has a radius equal to its gravitational radius.

As for your question about the radius-escape-velocity always happening below the surface of a planet or star, this is generally true. However, there are cases where the radius-escape-velocity can occur above the surface, such as with very low-density objects like gas giants. In these cases, the object's surface is not well-defined, and the radius-escape-velocity would be the velocity required to escape from its outermost layer.

In conclusion, while your observations and calculations are interesting and could potentially lead to further insights, it is important to remember that scientific theories and equations are based on rigorous testing and evidence, and cannot be simply derived from patterns or mathematical manipulations. Keep exploring and asking questions, and who knows what new discoveries you may make!