I wish to now give a non-rigorous proof of the Idea that the earth must be moving around in space. I will try as much as possible to use as little actual mathematics as possible. relying instead on logic and deductive reasoning when I can.(there will still be math though).
as pertaining to this motion of the earth, there are many possiblities.
1. Earth is moving in a straight line.
2. Earth is moving in a circle.
3. Earth is moving in bizarre fashion. similar to brownian motion of small bodies. this cannot be considered.
4. Earth is not moving at all.
we can find which is the case by figuring out what possible Force could guide motion of such a massive body, like the earth. If we consider that the earth is moving in a straight line, then we must realize that there is no force on the earth. as constant velocity requires no force. however, from experiment, this is quickly dismissed. because a motion of earth in a straight line will cause redshift of light from distant galaxies behind it and blueshift of light from galaxies in front of it. and our night sky would have been quite a peculiar one. also, parallax would occur over the ears as the stars would definitely shift their positions, the consistency of light from the universe points to a stationary earth. therefore, we can safely conclude the earth is not moving.
another theory is to assume the stars are in fact, very far away, and that the earth is moving in a confined space. in order to account for the lack of parallax
hence, we are reduced to two options.
1. the earth is in fact stationary.
2. the earth moves in a confined space.
to choose, we will study the moon.
studying the moon, one realizes that it moves around the earth every . . . 28 days or so. it possesses centripetal acceleration towards the earth. this can be explained by newton's equation.
F = ma
this shows us that earth must possess some kind of center seeking force that pulls the moon towards it. causing the moon to curve around the earth. near the earth, it is found also that objects dropped fall towards the earth with a constant acceleration, irrespective of the mass. this is very interesting.
A constant acceleration, irrespective of mass means that the force itself must be based on mass. for it to cancel out inertia so perfectly. so we have a relationship for this unknown force. which the earth possesses.
F α m
which means, this force is directly proportional to the mass of the object that was falling. of course, we immediately realize our obnoxiousness and realize we have to account for symmetry by including the mass of the earth of the earth itself. so we revise the equation.
F α Mm
which means, this force is directly proportional to the mass of the object that was falling, as well as the object it was falling onto. which in this case is the earth. we must not kid ourselves. our equation is obviously not complete yet. the moon does not experience the same amount of acceleration that objects on the earth do. it is far smaller. as can be found by calculating the centripetal acceleration of the moon with v2/r . Hence,
F α Mm x f(r)
where f(r) is a function of the distance. as we have seen that this force relies on distance. and upon calculation of the moon's acceleration and comparing it with the acceleration of objects on earth, we can deduce that this function is 1/r2
so we revise our equation.
F α Mm/r2
we can keep testing for other factors, such as heat, or brightness, but eventually, we realize that no other factor is involved. this force seems only to care about the masses of objects and the distances between them.
the final Job is now to find the proportionality constant. which can only be found by experiment, so we shall not do that here. however, if you are interested in finding it yourself, you may quote me and ask for a procedure. anyway, I will tell you, it is 6.67 x 10-10 and is denoted by G hence,
F = GMm/r2
and this force is called Gravity.
Gravity is an inverse square force. objects which move under the influence of inverse square forces will move in an elliptical path if they try to move perpendicular to to the direction of the force. this is what happens when you tie a stone around a string and you try to spin it. the stone is trying to leave but just ends up going round in a circle due to the inverse square force that the string is exerting on it.
coming back to the earth, we can generalize that any object that has mass will possess gravity. and the entirety of the rest of this post will survive on that fact. if you can succeed that there are some objects that have mass but do not possess gravity, then this proof is considered null and void.
seeing as this is true, we can put earth in the center of the universe and have everything else rotate around it. the moon, the sun, the planets, the galaxy, and the superclusters, all rotating around the the earth. in this scenario, the earth is not moving. instead, it is perfectly stationary, and everything else is moving around it. then we can do two body problems for each object in space, rotating around the earth. we can find how far they are. but first, we have to derive some more equations.
first, we know that gravity causes objects to fall down to the earth, near the surface. hence, it gives objects weight. mathematically, this means,
GMm/r2 = mg
where mg is weight.(not milligrams, guys. damn it.) with this, we can do some cancellations. bring out your books. small m cancels the other small m.
GM/r2 = g
and the mass of the earth, would be
M = gr2/G --------- 1
where g is acceleration due to gravity, r is the radius of the earth, and G is of course, the proportionality constant.
and then, for cases where the earth's gravity is causing objects in space to move in a circle, where it causes centripetal acceleration. that can be given by
GMm/r2 = mv2/r
cancelling what needs to be canceled. we get
GM = v2r
continuing, we replace v with 2πr/T
what that means was that we replaced velocity by distance traveled,(which is a circumference,) over the time taken to travel that distance. in this case, the distance around the earth, over the time taken for these bodies to travel around. for the sun, it travels around the earth every twenty four hours, for the moon, this occurs every 28 days.
doing the math, we get,
GM = 4π2r2/T2 * r
which means
GM/4π2 = r3/T2 --------- 2
we are done.
we have found a method to find the mass of the earth, we have also found a way to find the relationship for the objects that orbit the earth in our stationary earth scenario, which include the sun, the moon, the planets, the galaxy, and everything else. the relationship between how far they are, and how fast they travel around the earth. hence, if you give me the speed of a planet as it goes around the earth, I will tell you how far away it is.
great. now, I will find the mass of the earth and use it to find out how far away the sun is because that is the next most conspicuous thing in the sky. and if the earth was not moving, the only way to account for night and day is that the sun is revolving around the earth.
in the equation I labeled one, g is easily verified by experimentation, 9.8m/s squared, the radius of the earth as well can be easily deduced. 6,400,000 meters. and G, we all know to be 6.67 x 10-11.
substituting these values, we get an approximate value of 6.00 x 1024kg.
hence, for the second equation, big M = mass of the earth already found above, the gravitational constant, already established severally, and the amount of time it takes the sun to circle the earth, 86400 seconds, and pi, 3.14.
doing the rather tedious calculation, I have arrived at a value of around 42200 kilometers away. that's far closer than the moon is. this does not agree with experimental observation. at this close proximity, the sun must be very light in order to be that big and still not rip the earth to pieces. but if the sun is that light, then how is it a circle? this violates our formulas. the sun, if light, cannot possess enough gravitaional energy to collapse into a ball. and more importantly, the the question of using fusion to power it's light is out of the question as it will be too light. also, why doesn't it come between the moon and the earth? why don't we have sun eclipses? also, using a triangular method to find this distance fails because the sun exhibits almost no parallax. all of these point to the sun being incredibly far away.
when the calculation is carried out for the other planets, a similar result is acheived. their distances according to the equation disagrees with what is observed. so the equation must be wrong. right?
so we must consider one other contradiction before we accept that the earth cannot be the unmoving center of the observable universe.
spectral analysis of light from planets, as well as viewing them, allow us to deduce that they are infact made of matter. which contains mass. if they are rotating around the earth, then the earth must be supermassive in comparison to them, or the earth must be a pivot point, such that the center of mass of the solar system and of the galaxy must lie in the center of the earth. since the center of mass of any system of objects must remain stationary or move in a straight line upon the absence of some external force.
the first option is easily debunked. several planets have been observed with dense elements. which means they are heavy. and if this is so, their total mass can be found to be more than that of the earth. so earth cannot be a supermassive body.
the second option is also debunked because if earth were a pivot point, then we would observe pairs of bodies forming a centrifugal pair. so, for each planetary body we observe at a distance x, moving to the right, on the opposite side of the earth, we must observe another body, distance y from the earth, moving in the opposite direction. in essence, we would find the rotation of bodies around the earth be in pairs. and constant. this has never been observed.
because of this, we must consider the scenario where the sun resides at the center. then the equations are reapplied, and this time the correspond perfectly with observations. the sun has been found to be a supermassive body with 99% mass of the enter solar system, and the time period of the earth corresponds with its Goldilocks status, and the predictions of the equation are valid for situations in which they are applied.
The correlation of the theory with the observation is the proof that the theory is correct. and if the consequence of the theory is that the earth is moving around the sun, then that is also proven correct by induction.
as pertaining to this motion of the earth, there are many possiblities.
1. Earth is moving in a straight line.
2. Earth is moving in a circle.
3. Earth is moving in bizarre fashion. similar to brownian motion of small bodies. this cannot be considered.
4. Earth is not moving at all.
we can find which is the case by figuring out what possible Force could guide motion of such a massive body, like the earth. If we consider that the earth is moving in a straight line, then we must realize that there is no force on the earth. as constant velocity requires no force. however, from experiment, this is quickly dismissed. because a motion of earth in a straight line will cause redshift of light from distant galaxies behind it and blueshift of light from galaxies in front of it. and our night sky would have been quite a peculiar one. also, parallax would occur over the ears as the stars would definitely shift their positions, the consistency of light from the universe points to a stationary earth. therefore, we can safely conclude the earth is not moving.
another theory is to assume the stars are in fact, very far away, and that the earth is moving in a confined space. in order to account for the lack of parallax
hence, we are reduced to two options.
1. the earth is in fact stationary.
2. the earth moves in a confined space.
to choose, we will study the moon.
studying the moon, one realizes that it moves around the earth every . . . 28 days or so. it possesses centripetal acceleration towards the earth. this can be explained by newton's equation.
F = ma
this shows us that earth must possess some kind of center seeking force that pulls the moon towards it. causing the moon to curve around the earth. near the earth, it is found also that objects dropped fall towards the earth with a constant acceleration, irrespective of the mass. this is very interesting.
A constant acceleration, irrespective of mass means that the force itself must be based on mass. for it to cancel out inertia so perfectly. so we have a relationship for this unknown force. which the earth possesses.
F α m
which means, this force is directly proportional to the mass of the object that was falling. of course, we immediately realize our obnoxiousness and realize we have to account for symmetry by including the mass of the earth of the earth itself. so we revise the equation.
F α Mm
which means, this force is directly proportional to the mass of the object that was falling, as well as the object it was falling onto. which in this case is the earth. we must not kid ourselves. our equation is obviously not complete yet. the moon does not experience the same amount of acceleration that objects on the earth do. it is far smaller. as can be found by calculating the centripetal acceleration of the moon with v2/r . Hence,
F α Mm x f(r)
where f(r) is a function of the distance. as we have seen that this force relies on distance. and upon calculation of the moon's acceleration and comparing it with the acceleration of objects on earth, we can deduce that this function is 1/r2
so we revise our equation.
F α Mm/r2
we can keep testing for other factors, such as heat, or brightness, but eventually, we realize that no other factor is involved. this force seems only to care about the masses of objects and the distances between them.
the final Job is now to find the proportionality constant. which can only be found by experiment, so we shall not do that here. however, if you are interested in finding it yourself, you may quote me and ask for a procedure. anyway, I will tell you, it is 6.67 x 10-10 and is denoted by G hence,
F = GMm/r2
and this force is called Gravity.
Gravity is an inverse square force. objects which move under the influence of inverse square forces will move in an elliptical path if they try to move perpendicular to to the direction of the force. this is what happens when you tie a stone around a string and you try to spin it. the stone is trying to leave but just ends up going round in a circle due to the inverse square force that the string is exerting on it.
coming back to the earth, we can generalize that any object that has mass will possess gravity. and the entirety of the rest of this post will survive on that fact. if you can succeed that there are some objects that have mass but do not possess gravity, then this proof is considered null and void.
seeing as this is true, we can put earth in the center of the universe and have everything else rotate around it. the moon, the sun, the planets, the galaxy, and the superclusters, all rotating around the the earth. in this scenario, the earth is not moving. instead, it is perfectly stationary, and everything else is moving around it. then we can do two body problems for each object in space, rotating around the earth. we can find how far they are. but first, we have to derive some more equations.
first, we know that gravity causes objects to fall down to the earth, near the surface. hence, it gives objects weight. mathematically, this means,
GMm/r2 = mg
where mg is weight.(not milligrams, guys. damn it.) with this, we can do some cancellations. bring out your books. small m cancels the other small m.
GM/r2 = g
and the mass of the earth, would be
M = gr2/G --------- 1
where g is acceleration due to gravity, r is the radius of the earth, and G is of course, the proportionality constant.
and then, for cases where the earth's gravity is causing objects in space to move in a circle, where it causes centripetal acceleration. that can be given by
GMm/r2 = mv2/r
cancelling what needs to be canceled. we get
GM = v2r
continuing, we replace v with 2πr/T
what that means was that we replaced velocity by distance traveled,(which is a circumference,) over the time taken to travel that distance. in this case, the distance around the earth, over the time taken for these bodies to travel around. for the sun, it travels around the earth every twenty four hours, for the moon, this occurs every 28 days.
doing the math, we get,
GM = 4π2r2/T2 * r
which means
GM/4π2 = r3/T2 --------- 2
we are done.
we have found a method to find the mass of the earth, we have also found a way to find the relationship for the objects that orbit the earth in our stationary earth scenario, which include the sun, the moon, the planets, the galaxy, and everything else. the relationship between how far they are, and how fast they travel around the earth. hence, if you give me the speed of a planet as it goes around the earth, I will tell you how far away it is.
great. now, I will find the mass of the earth and use it to find out how far away the sun is because that is the next most conspicuous thing in the sky. and if the earth was not moving, the only way to account for night and day is that the sun is revolving around the earth.
in the equation I labeled one, g is easily verified by experimentation, 9.8m/s squared, the radius of the earth as well can be easily deduced. 6,400,000 meters. and G, we all know to be 6.67 x 10-11.
substituting these values, we get an approximate value of 6.00 x 1024kg.
hence, for the second equation, big M = mass of the earth already found above, the gravitational constant, already established severally, and the amount of time it takes the sun to circle the earth, 86400 seconds, and pi, 3.14.
doing the rather tedious calculation, I have arrived at a value of around 42200 kilometers away. that's far closer than the moon is. this does not agree with experimental observation. at this close proximity, the sun must be very light in order to be that big and still not rip the earth to pieces. but if the sun is that light, then how is it a circle? this violates our formulas. the sun, if light, cannot possess enough gravitaional energy to collapse into a ball. and more importantly, the the question of using fusion to power it's light is out of the question as it will be too light. also, why doesn't it come between the moon and the earth? why don't we have sun eclipses? also, using a triangular method to find this distance fails because the sun exhibits almost no parallax. all of these point to the sun being incredibly far away.
when the calculation is carried out for the other planets, a similar result is acheived. their distances according to the equation disagrees with what is observed. so the equation must be wrong. right?
so we must consider one other contradiction before we accept that the earth cannot be the unmoving center of the observable universe.
spectral analysis of light from planets, as well as viewing them, allow us to deduce that they are infact made of matter. which contains mass. if they are rotating around the earth, then the earth must be supermassive in comparison to them, or the earth must be a pivot point, such that the center of mass of the solar system and of the galaxy must lie in the center of the earth. since the center of mass of any system of objects must remain stationary or move in a straight line upon the absence of some external force.
the first option is easily debunked. several planets have been observed with dense elements. which means they are heavy. and if this is so, their total mass can be found to be more than that of the earth. so earth cannot be a supermassive body.
the second option is also debunked because if earth were a pivot point, then we would observe pairs of bodies forming a centrifugal pair. so, for each planetary body we observe at a distance x, moving to the right, on the opposite side of the earth, we must observe another body, distance y from the earth, moving in the opposite direction. in essence, we would find the rotation of bodies around the earth be in pairs. and constant. this has never been observed.
because of this, we must consider the scenario where the sun resides at the center. then the equations are reapplied, and this time the correspond perfectly with observations. the sun has been found to be a supermassive body with 99% mass of the enter solar system, and the time period of the earth corresponds with its Goldilocks status, and the predictions of the equation are valid for situations in which they are applied.
The correlation of the theory with the observation is the proof that the theory is correct. and if the consequence of the theory is that the earth is moving around the sun, then that is also proven correct by induction.
No comments:
Post a Comment