Joozu

How fast my “I love U” touches her hearts?

Friday, 5. October 2007, 16:40:50

It’s an emotional question and needs an emotional answer. But it is about “how fast” -- the phrase of mathematical question, so it needs a mathematical answer too. So we must count it “emotionally”. Like this:

Objectively, if I say “I love u” to someone who are in front of me, and we are in the same line with earth’s equator line, it means that:
first, my “I love U” is a sound wave which goes out of my mouth and then runs on atmosphere to reach her ears before touch her heart.
Second, this sound wave motion will be influenced by earth motion too hence of our relative position of the earth which orbit the sun and it causes this sound wave motion velocity is added by earth’s revolution velocity too. And then the equation that will determine the true velocity of this sound wave is:

Vsw = Vs + v

Where,
Vws = the velocity of my sound to reach her.
Vs = the velocity of all sound wave in the atmosphere medium.
v = the velocity of earth’s revolution

Ok, we know that the sound velocity, Vs, is equal to 0.344 Km/s, but we have not know about the velocity of earth, v!!! So we must count it before we count Vws.

$$$$ Oopss….sorry, do U can understand these? If u can’t, just leave this posting please…$$$$

There are two ways to count the velocity of earth's revolution.
First, by dividing its distance by time it needs. or, Second, by balancing it’s centripetal and centrifugal force effects.

First way.

We know that the earth’s orbital is an ellipse curve, but for simplicity, we can assume it as a circular orbital. We know, the distance between earth and sun are about 150 millions kilo meters. It means the distance earth travels is same with the perimeter of its orbital, 150 millions x 3.14 x 2 = 942 millions kilo meters.

And we know that earth spends 365 days per once circular motion. It means, our earth need 365 x 24 x 60 x 60 seconds or it is equal to 31536000 seconds.

And then, we can determine the velocity of earth'srevolution is 942000000 kilo meters divided by 31536000 seconds, is equal to 29.870624 Km/s, or we can make it simple: about 30 km/s .

now we get v = about 30 km/s. save this result.

Second way.

We know that the centrifugal force (Fcg) of the circular motion of earth is directly proportional with its mass (m) and velocity quadrate (v^2) and inversely proportional radius (R) circular motion. Symbolically in this equation:

Fcg = (m x v^2) / R

Where,
m = mass of the earth = about 5.98 x 10^24 Kg.
R = about 150000000 Km = 150 x 10^9 m.
And v = the velocity of earth, this is what we need to find guys!

Ok. Then, we know that the centripetal force (Fcp) which influences the earth circular orbital motion is because of sun’s gravitational force. So we use the general gravitational theory to determine this force influencing. Thoroughly, that centrifugal force equation is:

Fcp = G x (M x m) / (R^2)

Where,
G = about 6.67 x 10^ (-11) Kg^(-1). m^3/s^2
M = mass of the sun = about 1973400 x 10^24 kg

So we can balance between Fcp and Fcg as:

Fcp = Fcg

G x (M x m) / (R^2) = (m x v^2) / R

We must “throw out” the same symbols in both right and left equations (they are m and R) by multiplying the equation by R/(m) so that the equations become:

G x M / R = v^2

now, we can determine our earth revolution velocity (v) again:

v = (G x M / R)^(0.5)
= (6.67 x 10^ (-11) x 1973400 x 10^24/ 150 x 10^9)^(0.5)
= 29622.7 m/s = 2.96227 Km/s

2.96227 Km/s is the velocity of earth’s motion in its circular orbital, or we can make it simple: about 30 km/s.

Ok, now we know (for twice) that v = 30 km/s and we have known Vs = 0.344 Km/s, so my “I love U” sound wave will runs as fast as:

Vsw = Vs + v = 0.344 + 30 Km/s = 30.344 Km/s.

once again, we make it simple: about 30 km/s!

30 km/s! Cepat juga yak???