Planet Uranus, is the mass underestimated?
James Wood
March 03, 2009
When I was seriously into my seeking the mechanics of the Solar System I found that Uranus was somewhat strange when considered in the light of the other planets. Uranus and Venus are the only known planets that are in retrograde rotation; meaning that as to the Sun´s counter clockwise rotation these planets rotate clockwise. There is no doubt in my mind that they were not born that way but the possible cause for their condition is not germane to the purpose of this article.
Venus has no satellites so we cannot delve fully into its mechanics.
Uranus has satellites and some of them are also a bit strange due to their retrograde revolution. Note that revolution is the path a planet or a satellite travels in its orbit around another object. Rotation is the physical spinning on a planets axis as that planet revolves around some other object. Just about all objects in orbit around the Sun follow a path; revolve, in a counter clockwise manner. These motions were almost certainly instilled in the system as a part of its formation. This means that when we have objects that do not conform we should take note of them and try to decide what is going on. If you think of a ball rotating counter clockwise and tip that ball over on its side towards the Sun it will still be rotating counter clockwise while on its side. Uranus equator is inclined 97.9 degrees to its orbit. To change the rotation to clockwise you must flip Uranus over on its side facing away from the Sun or flip it 270 degrees. That is 3/4ths of the distance around the planet to put what was the North Pole facing directly away from the Sun. No small feat considering the size of Uranus.
My intent for this article is to check the facts to see if there is a reason why astronomers measure Uranus as less massive than Neptune even though Uranus is larger than Neptune. While working on the planets rotations seeking a formula to predict potential rotation speed I found that it was uniformly true that the larger planets always rotate faster than smaller planets. At first I thought it was probably due to the mass of the orbiting object. This prospect was quickly put aside because while Neptune was "more massive" than Uranus, Neptune´s rotation was slower. This narrowed down the item in common to be limited to size without regard to mass. Curious.
The mass of the objects in space is determined by using Sir Isaac Newton´s Universal Laws of Gravitation. The basic formula looks something like this:
F = G m1 m2 / r^2
F= force, G= Newton´s constant, m1 & m2 masses, Orbit radius ^2.
The point here is that the orbits of objects are an important factor when using this formula to determine an objects mass. Suppose we did not have Newton´s formula to measure an objects mass or we can suppose that Uranus had no satellites by which to apply the formula. Lets further assume that Neptune does have satellites so we can use Newton´s formula to weigh Neptune. Now our goal is to reason the mass of Uranus based upon all the other criteria we have gathered about the two planets and then equate the data by how it would project a potential mass for Uranus.
The published oblate ness for Uranus is .03 and Neptune is .026. I will deduct that difference from Uranus (31764.43*.004) = 127.05 miles.
Uranus equatorial diameter is 31,637.37 miles = 1.028 times Neptune.
Neptune equatorial diameter 30,775.21 miles.
Uranus volume 1.678119E+13 cubic miles = 1.099 times Neptune.
Neptune volume 1.526170E+13 cubic miles.
So, there is no doubt that Uranus is larger than Neptune. The next published statistical data is the density of each planet. Neptune is shown as 1660 kg/m^3 and Uranus is shown as 1300 kg/m^3. This appears to confirm that Neptune is made of heavier stuff than our Uranus. Before we can make that conclusion we must consider how density is determined. It is simply by dividing a planets mass, as derived from Newton´s formulas, by the same planets volume that we get what is determined to be the density. This is simple enough. More stuff in a smaller package means it is denser. If we believe the data then Neptune would be about (1660/1300) 1.277 times as dense as Uranus. However if the original determination of the mass of Uranus were faulty then that poor result would carry over into the other calculations that we must rely upon.
Other than the size the other distinctions between Uranus and Neptune are:
A. Uranus is in retrograde rotation and Neptune is not.
B. Uranus has satellites in retrograde revolution.
C. Uranus has satellites in retrograde rotation.
D. Uranus is inclined 97.9 degrees to its orbit, Neptune 29.6.
I have contended that the gravitation of the Sun. planets and satellites is like a large disk, the extent of which is determined by the mass of the object at the center of the disk. As a planet rotates all of the space subject to the planets gravitation moves with the disk and sweeps along the objects, such as satellites, along with it, causing the continued revolution of the other objects. The Sun is the initial cause of the momentum that carries over to all the objects within the Sun´s gravitational control. This momentum is shared with all objects in orbit around the Sun. Each object, in its turn, makes a contribution of its gravitation that would be somewhat less with out the contribution of the Sun to the final effect.
The farther objects are from the central disk the slower their revolutions will be. That fact is common knowledge and I have been able to elaborate on that with simple formulas that carry the orbits mile for mile throughout the Solar System. The details have been discussed in my other articles. For the purpose of this discussion I would like you to accept my view. If I am correct what effect will the planet have on its companions if its equator is not inclined in any way to its orbit? Will that effect vary in any way from other planets that have moderate to severe inclination of their equators to their orbits?
It seems quite clear that a planet rotating the same way that the Sun rotates, counter clockwise, will benefit from whatever incentives the Sun´s gravitation provides. Revolution of the planets is not involved here because all of the known planets revolve around the Sun counter clockwise. However if the retrograde rotation of Uranus reduces the gravitational push on Uranus satellites we should reasonably expect that the objects in orbit around Uranus would have shorter mean orbit radii than they would if Uranus rotated like the Sun. Because the size of the mean orbit radius of orbiting objects is a major factor in the determination of the mass of a planet you can see how it can occur that the orientation of the planet, as related to the system, could have an effect on the measurement process. I cannot start out by stating exactly what the orbits of Uranus satellites should be if all of their behavior was in line with the orbits of the other planet´s satellites. It may be possible however, to relate some comparative data to Uranus data and see if we will discover anything. We are in luck here because I have demonstrated in other published workups that the mass of the orbiting object has nothing to do with the orbit size or the velocity of the orbit. This means we can look for data to compare without being concerned that the satellite may be contributing to the orbit. If you check my other articles in the www.americanchronicle.com you will see how I arrived at the Miles-Mass values for determining the relative mass of objects without using Newton´s formulas.
My MM value for Uranus is 1,372,202.
My MM value for Neptune is 1,663,774
You can divide the mean orbit radius of a satellite of Uranus into the Uranus MM# and you will get the orbital velocity of that satellite squared. The square root of that are the actual miles per second. The same thing works for Neptune.
Uranus has a satellite Titania with a mean orbit radius of about 270,930 miles. (1372202/270930)= 5.064784. The sqr. root is 2.250508.
Neptune MM / 270930= 6.140974. The sqr, root is 2.478099 mps.
This shows that if Uranus Titania was in the same orbit distance from Neptune it would be traveling faster around Neptune than it does around Uranus. Also note that Neptune MM divided by Uranus MM (1663774/1372202)=1.212485 confirming here that Neptune measures
more massive than Uranus. Note 1.212485^(1/2)= 1.101129. While I am at it Saturn MM of 9117035.8 divided by Uranus MM of 1372202.7 gives me 6.644. The square root is 2.5776.
If we multiply the orbital velocity of Titania, 2.250508 by 1.101129 we will get 2.4781 which is the exact orbital velocity Titania would have if the orbit was the same, but around Neptune. If we multiply the orbital velocity of Titania, 2.250588, by 2.5776 we have 5.8. 5.8 mps is the exact velocity Titania would have in the same orbit if that orbit was around Saturn. 9117035/270930.4 = 33.65 the ^(1/2) of which is 5.8.
I wanted to include this to make one more dramatization of the exact mechanics of the Solar System. This, so far, only shows that both Newton´s formula and my formula will provide results that show Neptune is more massive than Uranus. However the progression from planet mass to other planets mass was a surprise to me. I have not yet ran the numbers on all the planets using Titania or some other satellite to see if it applies to all but I am very confident it will. This is also one more confirmation of the accuracy of my Miles-Mass ratio for using it to compare mass values with this new ratio result being a new breakthrough of sorts. When properly worked up this new discovery may be very important in our comparisons of the planets. However, I must find another way to test Uranus if I want to show that the planet Uranus mass may be underestimated.
In my book, Surfing the Solar System, I show how I arrived at the Miles-Mass value for the planets, including Uranus. Uranus was a little unique because of the five largest satellites four were in retrograde revolution. The main balance of 10 small satellites was in orbits closer to Uranus. The average MM obtained using the 5 largest of the satellites was 1,372,022. The MM average obtained using the 10 small satellites was 1,398,507. So, 1398507/1372022 = 1.019. On this finding I can argue that Uranus may be at least 1.02 times more massive than we thought but that is a trivial difference. Measuring the orbits of the Uranus family will not by itself reveal anything of help. My source of additional data will, of necessity, relate to the planets tilt and possibly the planets attitude in relation to the ecliptic plane.
The sketch that was here did not upload. Sorry!
The above is my rough sketch showing what I believe happened to Uranus in the distant past, there is no scale involved. The normal Uranus was in counterclockwise revolution and counterclockwise rotation and was given about a 260-degree flip reversing the rotation to clockwise and tilting the original equator off of the ecliptic. What is a little weird is that the major satellites of Uranus apparently managed to tag along with Uranus causing, Ariel, Umbriel Titania and Oberon to remain in orbits that are now retrograde.
We know that Uranus travels in its orbit around the Sun at 4.22 miles per second and that speed is correct based on the formula that I use for all of the planets so I cannot use the orbit velocity as a measure for comparison with Neptune. Also the retrograde rotation of Uranus does not appear to affect the orbit data in any way.
The only thing left it seems is the extreme tilt of Uranus to the ecliptic. Suppose I was standing on a platform that was turning 360 degrees at 10 miles per second. In my hand I have a string about 6 feet long at the end of which there is a ball that I am swinging independently at 20 miles per second. If I did not swing the ball at all it would revolve around the center at 10 miles per second. When I activate the ball the total speed, when related to every one outside looking in could be 30 miles per second or something else. Actually the apparent speed of the ball will be 20 miles per second. The initial 10 miles per second is absorbed in the balls travels providing a net apparent speed of 20 miles per second.
Now if we relate that hypothetical to Uranus travel around the Sun we know that the Sun at Uranus location is pushing things along at 4.22 miles per second. The speed would be the same if Neptune was in Uranus spot or if the Earth was in Uranus spot. We now have two contributors to the momentum of objects in orbit around Uranus, the Sun and Uranus. I have already tested Uranus for proper momentum. To evaluate the calculated mass of Uranus we must test, if possible, the proper momentum for the satellites that we will use to determine the mass of Uranus. The remaining question is will a planet in retrograde rotation lying on its side provide less momentum to its satellites than a proper upright planet rotating in the same direction as the Sun? My intuition told me it would not. In theory the actual mass of Uranus would be the same without regard to its orientation but in practice the method we use to calculate that mass depends on the orbits of the satellites. We do not think about it but the orbital speed of a satellite remains fairy constant even though at times it is in front of the planet, or behind it or along the side parallel to the orbit of the planet. The Sun appears to have no effect of note on the satellites.
The end result of this effort is that I cannot show there is any prospect that Uranus may be more massive than Neptune at this time. I continue to work on this project and seek solutions.
www.surfingthesolarsystem.com
www.thesolarsimplicity.com
Venus has no satellites so we cannot delve fully into its mechanics.
Uranus has satellites and some of them are also a bit strange due to their retrograde revolution. Note that revolution is the path a planet or a satellite travels in its orbit around another object. Rotation is the physical spinning on a planets axis as that planet revolves around some other object. Just about all objects in orbit around the Sun follow a path; revolve, in a counter clockwise manner. These motions were almost certainly instilled in the system as a part of its formation. This means that when we have objects that do not conform we should take note of them and try to decide what is going on. If you think of a ball rotating counter clockwise and tip that ball over on its side towards the Sun it will still be rotating counter clockwise while on its side. Uranus equator is inclined 97.9 degrees to its orbit. To change the rotation to clockwise you must flip Uranus over on its side facing away from the Sun or flip it 270 degrees. That is 3/4ths of the distance around the planet to put what was the North Pole facing directly away from the Sun. No small feat considering the size of Uranus.
My intent for this article is to check the facts to see if there is a reason why astronomers measure Uranus as less massive than Neptune even though Uranus is larger than Neptune. While working on the planets rotations seeking a formula to predict potential rotation speed I found that it was uniformly true that the larger planets always rotate faster than smaller planets. At first I thought it was probably due to the mass of the orbiting object. This prospect was quickly put aside because while Neptune was "more massive" than Uranus, Neptune´s rotation was slower. This narrowed down the item in common to be limited to size without regard to mass. Curious.
The mass of the objects in space is determined by using Sir Isaac Newton´s Universal Laws of Gravitation. The basic formula looks something like this:
F = G m1 m2 / r^2
F= force, G= Newton´s constant, m1 & m2 masses, Orbit radius ^2.
The point here is that the orbits of objects are an important factor when using this formula to determine an objects mass. Suppose we did not have Newton´s formula to measure an objects mass or we can suppose that Uranus had no satellites by which to apply the formula. Lets further assume that Neptune does have satellites so we can use Newton´s formula to weigh Neptune. Now our goal is to reason the mass of Uranus based upon all the other criteria we have gathered about the two planets and then equate the data by how it would project a potential mass for Uranus.
The published oblate ness for Uranus is .03 and Neptune is .026. I will deduct that difference from Uranus (31764.43*.004) = 127.05 miles.
Uranus equatorial diameter is 31,637.37 miles = 1.028 times Neptune.
Neptune equatorial diameter 30,775.21 miles.
Uranus volume 1.678119E+13 cubic miles = 1.099 times Neptune.
Neptune volume 1.526170E+13 cubic miles.
So, there is no doubt that Uranus is larger than Neptune. The next published statistical data is the density of each planet. Neptune is shown as 1660 kg/m^3 and Uranus is shown as 1300 kg/m^3. This appears to confirm that Neptune is made of heavier stuff than our Uranus. Before we can make that conclusion we must consider how density is determined. It is simply by dividing a planets mass, as derived from Newton´s formulas, by the same planets volume that we get what is determined to be the density. This is simple enough. More stuff in a smaller package means it is denser. If we believe the data then Neptune would be about (1660/1300) 1.277 times as dense as Uranus. However if the original determination of the mass of Uranus were faulty then that poor result would carry over into the other calculations that we must rely upon.
Other than the size the other distinctions between Uranus and Neptune are:
A. Uranus is in retrograde rotation and Neptune is not.
B. Uranus has satellites in retrograde revolution.
C. Uranus has satellites in retrograde rotation.
D. Uranus is inclined 97.9 degrees to its orbit, Neptune 29.6.
I have contended that the gravitation of the Sun. planets and satellites is like a large disk, the extent of which is determined by the mass of the object at the center of the disk. As a planet rotates all of the space subject to the planets gravitation moves with the disk and sweeps along the objects, such as satellites, along with it, causing the continued revolution of the other objects. The Sun is the initial cause of the momentum that carries over to all the objects within the Sun´s gravitational control. This momentum is shared with all objects in orbit around the Sun. Each object, in its turn, makes a contribution of its gravitation that would be somewhat less with out the contribution of the Sun to the final effect.
The farther objects are from the central disk the slower their revolutions will be. That fact is common knowledge and I have been able to elaborate on that with simple formulas that carry the orbits mile for mile throughout the Solar System. The details have been discussed in my other articles. For the purpose of this discussion I would like you to accept my view. If I am correct what effect will the planet have on its companions if its equator is not inclined in any way to its orbit? Will that effect vary in any way from other planets that have moderate to severe inclination of their equators to their orbits?
It seems quite clear that a planet rotating the same way that the Sun rotates, counter clockwise, will benefit from whatever incentives the Sun´s gravitation provides. Revolution of the planets is not involved here because all of the known planets revolve around the Sun counter clockwise. However if the retrograde rotation of Uranus reduces the gravitational push on Uranus satellites we should reasonably expect that the objects in orbit around Uranus would have shorter mean orbit radii than they would if Uranus rotated like the Sun. Because the size of the mean orbit radius of orbiting objects is a major factor in the determination of the mass of a planet you can see how it can occur that the orientation of the planet, as related to the system, could have an effect on the measurement process. I cannot start out by stating exactly what the orbits of Uranus satellites should be if all of their behavior was in line with the orbits of the other planet´s satellites. It may be possible however, to relate some comparative data to Uranus data and see if we will discover anything. We are in luck here because I have demonstrated in other published workups that the mass of the orbiting object has nothing to do with the orbit size or the velocity of the orbit. This means we can look for data to compare without being concerned that the satellite may be contributing to the orbit. If you check my other articles in the www.americanchronicle.com you will see how I arrived at the Miles-Mass values for determining the relative mass of objects without using Newton´s formulas.
My MM value for Uranus is 1,372,202.
My MM value for Neptune is 1,663,774
You can divide the mean orbit radius of a satellite of Uranus into the Uranus MM# and you will get the orbital velocity of that satellite squared. The square root of that are the actual miles per second. The same thing works for Neptune.
Uranus has a satellite Titania with a mean orbit radius of about 270,930 miles. (1372202/270930)= 5.064784. The sqr. root is 2.250508.
Neptune MM / 270930= 6.140974. The sqr, root is 2.478099 mps.
This shows that if Uranus Titania was in the same orbit distance from Neptune it would be traveling faster around Neptune than it does around Uranus. Also note that Neptune MM divided by Uranus MM (1663774/1372202)=1.212485 confirming here that Neptune measures
more massive than Uranus. Note 1.212485^(1/2)= 1.101129. While I am at it Saturn MM of 9117035.8 divided by Uranus MM of 1372202.7 gives me 6.644. The square root is 2.5776.
If we multiply the orbital velocity of Titania, 2.250508 by 1.101129 we will get 2.4781 which is the exact orbital velocity Titania would have if the orbit was the same, but around Neptune. If we multiply the orbital velocity of Titania, 2.250588, by 2.5776 we have 5.8. 5.8 mps is the exact velocity Titania would have in the same orbit if that orbit was around Saturn. 9117035/270930.4 = 33.65 the ^(1/2) of which is 5.8.
I wanted to include this to make one more dramatization of the exact mechanics of the Solar System. This, so far, only shows that both Newton´s formula and my formula will provide results that show Neptune is more massive than Uranus. However the progression from planet mass to other planets mass was a surprise to me. I have not yet ran the numbers on all the planets using Titania or some other satellite to see if it applies to all but I am very confident it will. This is also one more confirmation of the accuracy of my Miles-Mass ratio for using it to compare mass values with this new ratio result being a new breakthrough of sorts. When properly worked up this new discovery may be very important in our comparisons of the planets. However, I must find another way to test Uranus if I want to show that the planet Uranus mass may be underestimated.
In my book, Surfing the Solar System, I show how I arrived at the Miles-Mass value for the planets, including Uranus. Uranus was a little unique because of the five largest satellites four were in retrograde revolution. The main balance of 10 small satellites was in orbits closer to Uranus. The average MM obtained using the 5 largest of the satellites was 1,372,022. The MM average obtained using the 10 small satellites was 1,398,507. So, 1398507/1372022 = 1.019. On this finding I can argue that Uranus may be at least 1.02 times more massive than we thought but that is a trivial difference. Measuring the orbits of the Uranus family will not by itself reveal anything of help. My source of additional data will, of necessity, relate to the planets tilt and possibly the planets attitude in relation to the ecliptic plane.
The sketch that was here did not upload. Sorry!
The above is my rough sketch showing what I believe happened to Uranus in the distant past, there is no scale involved. The normal Uranus was in counterclockwise revolution and counterclockwise rotation and was given about a 260-degree flip reversing the rotation to clockwise and tilting the original equator off of the ecliptic. What is a little weird is that the major satellites of Uranus apparently managed to tag along with Uranus causing, Ariel, Umbriel Titania and Oberon to remain in orbits that are now retrograde.
We know that Uranus travels in its orbit around the Sun at 4.22 miles per second and that speed is correct based on the formula that I use for all of the planets so I cannot use the orbit velocity as a measure for comparison with Neptune. Also the retrograde rotation of Uranus does not appear to affect the orbit data in any way.
The only thing left it seems is the extreme tilt of Uranus to the ecliptic. Suppose I was standing on a platform that was turning 360 degrees at 10 miles per second. In my hand I have a string about 6 feet long at the end of which there is a ball that I am swinging independently at 20 miles per second. If I did not swing the ball at all it would revolve around the center at 10 miles per second. When I activate the ball the total speed, when related to every one outside looking in could be 30 miles per second or something else. Actually the apparent speed of the ball will be 20 miles per second. The initial 10 miles per second is absorbed in the balls travels providing a net apparent speed of 20 miles per second.
Now if we relate that hypothetical to Uranus travel around the Sun we know that the Sun at Uranus location is pushing things along at 4.22 miles per second. The speed would be the same if Neptune was in Uranus spot or if the Earth was in Uranus spot. We now have two contributors to the momentum of objects in orbit around Uranus, the Sun and Uranus. I have already tested Uranus for proper momentum. To evaluate the calculated mass of Uranus we must test, if possible, the proper momentum for the satellites that we will use to determine the mass of Uranus. The remaining question is will a planet in retrograde rotation lying on its side provide less momentum to its satellites than a proper upright planet rotating in the same direction as the Sun? My intuition told me it would not. In theory the actual mass of Uranus would be the same without regard to its orientation but in practice the method we use to calculate that mass depends on the orbits of the satellites. We do not think about it but the orbital speed of a satellite remains fairy constant even though at times it is in front of the planet, or behind it or along the side parallel to the orbit of the planet. The Sun appears to have no effect of note on the satellites.
The end result of this effort is that I cannot show there is any prospect that Uranus may be more massive than Neptune at this time. I continue to work on this project and seek solutions.
www.surfingthesolarsystem.com
www.thesolarsimplicity.com