Pyramid Science

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Wednesday, November 25, 2009

Origin Of Earth's Moon


The following entry is speculative, but blends in with other (unexamined and untestable) argument that has been arrived at using properly reasoned logic. The Earth Moon is very large compared to other moons associated with their planets and the Earth Moon could be considered more like the Pluto and Charon double planet (Pluto is known as a dwarf planet). The origin could even be argued that it is an inner rocky planet, closer to the Sun than Venus or Mercury. The (known) physical properties of the Moon and its appearance are similar to Mercury and Venus. As an ejected object blasted into space by being hit with the force of a coronal mass ejection (CME) this would probably have happened billions of years ago. The object may have been captured by (a primordial) Earth gravity, it being the largest object in the vicinity. Venus would be large enough, but the proximity and velocity would both conspire against possible capture.

Sidereal time reflects the actual time where synodic time describes the apparent time. The relationship between the distance of a planet from the Sun (r =  radius of the orbit) and its orbital period (P) can be estimated using Keplar's Third Law of Planetary Motion.

Verification of values: r = million km and P = days, though as a proportionality, only the relative numbers are necessary and not the absolute magnitude.

Mercury
  • P = 88, r = 57.9

    • P^2/r^3 = 0.0399
Venus
  • P = 224.7, r = 108.2
    • P^2/r^3 = 0.0399
Earth
  • P = 365.25, r =  149.6

    •   P^2/r^3 = 0.0398
Mars
  • P = 687, r = 227.9

    • P^2/r^3 = 0.0399
Jupiter
  • P = 4332.8, r = 778.3

    • P^2/r^3 = 0.0398
Saturn
  • P =10755.7, r = 1427

    • P^2/r^3 = 0.0398
Uranus
  • P =30687.1, r = 2870

    • P^2/r^3 = 0.0398
Neptune
  • P = 60190, r = 4497

    • P^2/r^3 = 0.0398 
The modified Titius-Bode value for Neptune gives:
  • P = 88025.3, r = 5800

    • P^2/r^3 = 0.0397
Within acceptable error limits, these value support Keplar's Third Law of Planetary Motion.

Simplistically, the radius is inversely proportional to the square of the velocity or v^2 * r = constant (k). The nearer one object is to another, the faster it will travel around it. This can be demonstrated by the velocity of each of the eight planets in the solar system and the four inner moons orbiting around Jupiter (Io, Europa, Ganymede and Callisto).
  • Mercury 
    • 47.9 km/s * 47.9 km/s * 57.9m km = 132,846
  • Venus 
    • 35.03 km/s * 35.03 km/s * 108.2m km = 132,772
  • Earth 
    • 29.8 km/s * 29.8 km/s * 149.6m km = 132,850
  • Mars 
    • 24.1 km/s * 24.1 km/s * 227.9m km = 132,366
  • Jupiter 
    • 13.1 km/s * 13.1 km/s * 778.3m km = 133,564
  • Saturn 
    • 9.6 km/s * 9.6 km/s * 1427m km = 131,512
  • Uranus 
    • 6.8 km/s * 6.8 km/s * 2870m km = 132,709
  • Neptune 
    • 5.45 km/s * 5.45 km/s * 4497m km = 133,572
    Average = 132,774

    Facts relating to the major planets
    • Io 17.334 km/s * 17.334 km/s * 421,700 km = 126,707,168
    • Europa 13.744 km/s * 13.744 km/s * 670,900 km = 126,731,357
    • Ganymede 10.88 km/s * 10.88 km/s * 1,070,400 km = 126,707,958
    • Callisto 8.204 km/s * 8.204 km/s * 1,882,700 km = 126,716,283
      Average = 126,715,692

      Moons of Saturn (inner 7 of 61)
      • Mimas 14 km/s * 14 km/s * 182520 km = 35,773,920
      • Enceledus 12.6 km/s * 12.6 km/s * 237948 km = 37,776,624
      • Tethys 11.35 km/s * 11.35 km/s * 294619 km = 37,953,556
      • Dione 10 km/s * 10 km/s * 377396 km = 37773960
      • Rhea 8.50 km/s * 8.50 km/s * 527000 km = 38,075,750
      • Titan 5.55 km/s * 5.55 km/s * 1221870 km = 37,636,651
      • Iapetus 3.28 km/s * 3.28 km/s * 3560000 km = 38,299,904
      Average = 37,612,909

      Moons of Uranus (inner 5 of 27)
      • Miranda 6.66 km/s * 6.66 km/s * 12390 km = 5,739,171
      • Ariel 5.5 km/s * 5.5 km/s * 191020 km = 5,778,355
      • Umbriel 4.67 km/s * 4.67 km/s * 266000 km = 5,801,167
      • Titania 3.64 km/s * 3.64 km/s * 435910 km = 5,775,633
      • Oberon 3.15 km/s * 3.15 km/s * 583520 km = 5,789,977 
      Average = 5,776,861

      Moons of Neptune (inner 7 of 13)
      • Naiad 11.9 km/s * 11.9 km/s * 48277 km = 6,836,506
      • Thalassa 11.7 km/s * 11.7 km/s * 50075 km = 6,854,767
      • Despina 11.4 km/s * 11.4 km/s * 52526 km = 6,826,279
      • Galatea 10.5 km/s * 10.5 km/s * 61953 km = 6,830,318
      • Larissa 9.6 km/s * 9.6 km/s * 73548 km = 6,778,184
      • Proteus 7.63 km/s * 7.63 km/s * 117647 km = 6,849,044
      • Triton 4.39 km/s * 4.39 km/s * 354800 km = 6,837,741 
      Average = 6,830,406

      The values for each group do not relate to one another as the environments are greatly different and consequently the planetary distance or moon distance (millions of km and km, respectively from the object around which it orbits) is ignored, but they do illustrate the relationship within a group: the greater the distance from the central object the slower the orbital speed within the group and constancy is maintained within that group


      Orbits are elliptical and so the velocity is calculated from an average annual value. Smaller moons provide examples of captured objects. The Earth's Moon is similar, but being larger or approaching from a different direction, entered an orbit closer to the Sun. The Moon has currently an average distance from Earth of 384,600 km (the radius).The monthly (sidereal) distance travelled (animation) : 2 * 3.142 * 384,600 = 2,416,826 km. The time taken is 27.32 days so the velocity (in seconds) is given by distance/time: 2,416,826/27.32 * 24 * 60 *60 = 1.02388 km/sec. v^2 = 1.04834 km/sec and since, v^2 * r = k, the value of k = 1.04834 * 384,600 = 403,191.

      Values for the velocity at different values of radius (circular orbit) can be obtained:

      Radius (km) : velocity (km/sec)
      384,600 : 1.02388
      300,000 : 1.159
      200,000 : 1.42
      100,000 : 2.00
      50,000 : 2.84
      5,000 : 8.98
      500 : 28.4
      5 : 284
      1 : 635
      0.1 : 2008

      The closer an object gets, the faster it moves
      The greater the distance, the slower it moves

      Impact Earth!

      • According to this any impact or close encounter (50,000 - 5,000 km) between a moon 'object' and Earth would be in the region of 2000 km/s and with the Earth orbiting the Sun at almost 30 km/s, this represents a far from negligible difference. Such energy from an impact, would do immense damage and the total destruction of both objects is the most likely outcome. The kinetic energy is proportional to v^2 and for a mass the size of a 'moon object' travelling at 2000 km/s this equates to an enormous value. However, it is possible that a direct hit did not occur and Earth's gravitational attraction pulled the object towards itself, hijacking (partially) the gravitational influence of the Sun. This would have resulted in slowing the object (aerobraking) as it was moved out of a linear trajectory. The new arc angle would allow the slowed object to 'bump' into the Earth and a slingshot effect would have initiated the captured rotation around the Earth. This is likely when the velocity had slowed considerably so reducing the momentum. A 'moon object' would, in fact, not need to be particularly close to have been the cause of any subsequent effects and anywhere between 50,000 km (2.84 km/s) and 5000 km (8.98 km/s) is quite sufficient (before considerable acceleration began).
        • Various scenarios can be reasonably postulated including a fast moving object outside the solar system being pulled out of transit by the eight planets (especially Jupiter) and Sun. Upon entering the system of planets at an angle from below the ecliptic it would be dragged and consequently slowed to a velocity sufficient to effectively 'bump' into the Earth. The very hot early fireball of the cooling 'Earth' would heat the incoming object at its surface, so enabling a slick of molten material to deposit over the surface before being captured in an Earth orbit. Slowing further by gravitational attraction and moving into a close orbit around the planet with which it 'collided'.
          • Alternatively, transit near the Sun and travelling at high speed would prevent capture by the Sun yet melt its surface. Such an approach would then form a slick of molten material that then splashed over the surface of the Earth. A more likely solution to the origin of the Moon is a combination of factors and the effect of aerobraking. The outer planets (gas giants) would one by one reduce the velocity of any incoming object considerably from its initial value. The extent is totally unknowable, as would be the relative positions of the planets, and the associated composite gravitational influence could never be reliably established. The trajectory of such an object could encounter a close-enough approach to be affected by aerobraking. This is a realistic consideration regardless of the likelihood of such a scenario happening. Neither does the approach need to be in the same plane as the ecliptic. The resulting trajectory would be a spiral and the decreasing radius bringing the object closer to the Sun: the probable cause of the approach in the first place. An angular approach to the ecliptic could even result in 'leapfrogging' one or more of the inner planets.
          • The probability of this is no different to considering the chances of an object coming close enough to any specific planet within any solar system contained in the vastness of space. According to the empirical Titius-Bode law, Neptune should not be where it is, but much deeper in the solar system: 38.8AU not 30.1AU or roughly 1.3bn km. Even Saturn and Uranus should be moved further outward (10.0AU vs 9.5AU and 19.6AU vs 19.2AU, respectively). Aerobraking can account for this and represents a potentially huge energy exchange.


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