Planet Rotations, my theory
James Wood
September 26, 2008
I have been seeking a mathematical formula to provide a means to calculate in advance how fast a planet or satellite will rotate just by using the common data that we have obtained about the objects. The task has not received much if any attention by academics that I am aware of and it may be that there is simply no interest in the subject. There is much information telling us the data and the details of the days in the years of the planets, mostly in terms of Earth comparisons but not much talk about the why of it. An excellent Web Site for comparison of days and rotations will be found at www.cseligman.com. http://cseligman.com/text/sky/rotationvsday.htm by an astronomy professor.
My efforts are basic and comparatively humble. I am somewhat ashamed to admit that after years of effort I have not completely solved the issue so that I can predict with accuracy the exact speed of rotation any particular planet will display based on its orbit and its size. I have approached the problem in many different ways. In my book, Surfing the Solar System, I went into fine points on the orbits of the planets to get what I called a position number for each known planet, including Pluto. Before that I approached the orbits of the planets as fixed roads with the planet going like a rolling ball around the orbit. That is Earth´s mean orbit radius of 92961440*6.2832 = 584,095,319.8 miles circumference. If the Earth was simply rolling around the orbit it could, at 24,902.2 miles circumference rotate 23,455.56 times but we know it rotates only about 365.25 times. There is a lot swish involved and that, it turns out, is due to the orbital velocity of the planet. If we divide 23,455.56 by 365.25 we get 64.218. Divide the 64.218 by the orbital velocity of 18.505 miles per second and get 3.47. It so happens that 3.47 or 3.469 are the precise number of seconds it takes for the Earth´s equator to rotate 1 mile. 1/3.47 = .2882 miles a second. This does little more than show that the size of the planet and the orbital velocity are important factors in the planets rotation. If I did not include the known number of Earth days in the orbit I would not get an accurate result.
The orbits lengths and the orbit velocities as well as the size of every planet have their own unique factors. The only common denominator of note is that large planets rotate faster than small planets. That observation tends to suggest that the pull of the Sun on the planet provides a drag sufficient to cause a large planet to turn more often and doing so to turn faster. However I have found no reason to believe that the mass of the planet plays any part in the character of the orbit or of the planets rotations.
My position number was useful in providing the specific equatorial velocity of each planet but that also included in the formula the actual days of the orbit. The number had other qualities providing useful information but it did not serve to further my rotation inquires. I developed my Miles-Mass measure as an alternative to the Weight-Mass provided by Isaac Newton´s formula. I was hopeful that approaching the issue from a different vantage point would open a new door into my quest. It opened a number of doors and created a number of issues but nothing I have found so far adds to the rotation solution.
I tried a simple chart layout using the planets radius divided by the equatorial surface velocity to seek some uniformity. The chart below is the result of that particular effort. Remember everything is in miles and seconds.
Planet======Radius=====/===Miles PS==========Relationship
Mercury====1515.5==========. 1102============13752.26860254
Venus======3759.5==========. 2732============13760.98096632
Earth======3963.3==========. 2882============13751.90839694
Mars=======2111.5==========. 1497============14104.87641950
Jupiter======44678.7========7.962=============5611.49208741
Saturn======37284. ==========6.36=============5862.26415094
Uranus======16246.5========1.829=============8882.72279934
Neptune=====15379.6=========1.689============9105.74304322
I have no idea why I did not do this simple comparison at the beginning of my efforts. The relationship between size and surface velocity is very pronounced for the first three planets. Then we have Mars a little bit off the trend. The difference of Mars could be due to a slightly slower rotation compared to the first three or a small overestimate of the size of the Mars radius. If Mars was rotating at .154 mps then the relationship would be 13711.03896. You can see how easy it is to manipulate the figures to have Mars fall in line with Earth. If we assume that the radius is probably correct then we must decide why Mars rotates a little slower than other planets of a similar size. As we know Mars is on the edge of the Asteroid belt that covers a large area as you head toward Jupiter. As I wonder at the cause for the Asteroid belt my intuition wants to tell me that this is all due to the strong gravitation of Jupiter. If Mars was rotating at .1534 mps the relationship would be 13764.66 or close enough. .1534-.1497 = .00037 miles per second difference that is so small that I cannot form a decision about it. We do not know what was present in the Asteroid belt area before it disintegrated, if that is what actually happened; or before the stuff ever managed to form a sphere, if that is what happened. Informed academics tell us that all the stuff in the Asteroid belt put together would not make a ball the size of out moon. I do not doubt the conclusion but I doubt that any object that was there was that small. My guess about 20000 M radius.
This little chart shows some other detail worth noting. Jupiter and Saturn and Uranus and Neptune pair into groups based on their relationship. That results, I think, from two special combinations. First they are a similar size radius and second they are in similar orbits that might be considered connected in some way. If I was willing to satisfy my curiosity by just doing some rounding of numbers with no desire for accuracy I could take the first four relationships divided by for and then using that result make a conclusion on all objects in the radius range to estimate their equatorial velocity. The same thing could be done for the pairs like Jupiter and Saturn and Uranus and Neptune but I do not suggest it for anything but the grossest results.
In other articles I offered my opinion for the revolution of the planets around the Sun and the satellites around the planets.
These efforts arise from my view of the Solar System as a mechanical object. Newton saw it that way and his work has been the most reliable. I want to break it down to even finer details if I can and I see that as a worthwhile goal even if not every one sees it the way I do.
Happy days.
My efforts are basic and comparatively humble. I am somewhat ashamed to admit that after years of effort I have not completely solved the issue so that I can predict with accuracy the exact speed of rotation any particular planet will display based on its orbit and its size. I have approached the problem in many different ways. In my book, Surfing the Solar System, I went into fine points on the orbits of the planets to get what I called a position number for each known planet, including Pluto. Before that I approached the orbits of the planets as fixed roads with the planet going like a rolling ball around the orbit. That is Earth´s mean orbit radius of 92961440*6.2832 = 584,095,319.8 miles circumference. If the Earth was simply rolling around the orbit it could, at 24,902.2 miles circumference rotate 23,455.56 times but we know it rotates only about 365.25 times. There is a lot swish involved and that, it turns out, is due to the orbital velocity of the planet. If we divide 23,455.56 by 365.25 we get 64.218. Divide the 64.218 by the orbital velocity of 18.505 miles per second and get 3.47. It so happens that 3.47 or 3.469 are the precise number of seconds it takes for the Earth´s equator to rotate 1 mile. 1/3.47 = .2882 miles a second. This does little more than show that the size of the planet and the orbital velocity are important factors in the planets rotation. If I did not include the known number of Earth days in the orbit I would not get an accurate result.
The orbits lengths and the orbit velocities as well as the size of every planet have their own unique factors. The only common denominator of note is that large planets rotate faster than small planets. That observation tends to suggest that the pull of the Sun on the planet provides a drag sufficient to cause a large planet to turn more often and doing so to turn faster. However I have found no reason to believe that the mass of the planet plays any part in the character of the orbit or of the planets rotations.
My position number was useful in providing the specific equatorial velocity of each planet but that also included in the formula the actual days of the orbit. The number had other qualities providing useful information but it did not serve to further my rotation inquires. I developed my Miles-Mass measure as an alternative to the Weight-Mass provided by Isaac Newton´s formula. I was hopeful that approaching the issue from a different vantage point would open a new door into my quest. It opened a number of doors and created a number of issues but nothing I have found so far adds to the rotation solution.
I tried a simple chart layout using the planets radius divided by the equatorial surface velocity to seek some uniformity. The chart below is the result of that particular effort. Remember everything is in miles and seconds.
Planet======Radius=====/===Miles PS==========Relationship
Mercury====1515.5==========. 1102============13752.26860254
Venus======3759.5==========. 2732============13760.98096632
Earth======3963.3==========. 2882============13751.90839694
Mars=======2111.5==========. 1497============14104.87641950
Jupiter======44678.7========7.962=============5611.49208741
Saturn======37284. ==========6.36=============5862.26415094
Uranus======16246.5========1.829=============8882.72279934
Neptune=====15379.6=========1.689============9105.74304322
I have no idea why I did not do this simple comparison at the beginning of my efforts. The relationship between size and surface velocity is very pronounced for the first three planets. Then we have Mars a little bit off the trend. The difference of Mars could be due to a slightly slower rotation compared to the first three or a small overestimate of the size of the Mars radius. If Mars was rotating at .154 mps then the relationship would be 13711.03896. You can see how easy it is to manipulate the figures to have Mars fall in line with Earth. If we assume that the radius is probably correct then we must decide why Mars rotates a little slower than other planets of a similar size. As we know Mars is on the edge of the Asteroid belt that covers a large area as you head toward Jupiter. As I wonder at the cause for the Asteroid belt my intuition wants to tell me that this is all due to the strong gravitation of Jupiter. If Mars was rotating at .1534 mps the relationship would be 13764.66 or close enough. .1534-.1497 = .00037 miles per second difference that is so small that I cannot form a decision about it. We do not know what was present in the Asteroid belt area before it disintegrated, if that is what actually happened; or before the stuff ever managed to form a sphere, if that is what happened. Informed academics tell us that all the stuff in the Asteroid belt put together would not make a ball the size of out moon. I do not doubt the conclusion but I doubt that any object that was there was that small. My guess about 20000 M radius.
This little chart shows some other detail worth noting. Jupiter and Saturn and Uranus and Neptune pair into groups based on their relationship. That results, I think, from two special combinations. First they are a similar size radius and second they are in similar orbits that might be considered connected in some way. If I was willing to satisfy my curiosity by just doing some rounding of numbers with no desire for accuracy I could take the first four relationships divided by for and then using that result make a conclusion on all objects in the radius range to estimate their equatorial velocity. The same thing could be done for the pairs like Jupiter and Saturn and Uranus and Neptune but I do not suggest it for anything but the grossest results.
In other articles I offered my opinion for the revolution of the planets around the Sun and the satellites around the planets.
These efforts arise from my view of the Solar System as a mechanical object. Newton saw it that way and his work has been the most reliable. I want to break it down to even finer details if I can and I see that as a worthwhile goal even if not every one sees it the way I do.
Happy days.