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Tides and Leap Seconds

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• The Gravitational force between two objects depends inversely upon their separation.

• The greater the distance between two objects the weaker the gravitational attraction between them.
• Different points on the surface of the Earth feel differing amounts of pull from the Moon's gravity.
• The portion of the Earth closest to the Moon is tugged more strongly by the Moon than the far side of the Earth.

• There is an excess of gravity on the near side. What is not so obvious is that there is a deficit of gravity on the far side.
  

  

  • As the Moon and Earth orbit each other the side of the Earth opposite the Moon is flung away from the center of the system (as is the side of the Moon opposite the Earth).
• This differing tug between the two sides of the Earth stretches the Earth and the water on its surface toward and away from the Moon.

• The solid Earth resists stretching more than the liquid water on its surface, thus the oceans are stretched more than the land.

• These "tidal bulges" remain aligned with the Moon which orbits the Earth slowly. As the Earth rotates rapidly compared with the slow motion of the Moon, a spot on the Earth's surface is carried through two of these "tidal bulges" every day.
• The Sun raises tides on the Earth in a similar fashion -- though not as strongly as the Moon.

  • When the Sun and Moon line up (i.e. Full Moon and New Moon) larger than usual tides are produced.

  
  

• The rotation of the Earth actually carries the tidal bulges slightly away from the point directly beneath the Moon.

• This "dragging" of the tidal bulges produces a force which slows the rotation of the Earth.



• The day is getting LONGER.

  • The day lengthens by about 1 second every 50,000 years. A couple of hundred million years ago the day was only 22 hours long!

  • The day will be 25 hours long in about 150 million years.

  • Since the second has been precisely defined by international agreement, clocks run fast relative to the slowing rotation rate of the Earth

  • Currently 1 "leap second" is added to the time every 18 months or so.

• The tidal bulges also pull back on the Moon providing a force which pulls the Moon along in its orbit. This pull accelerates the Moon and causes it to slowly move away from the Earth.

  • The Moon moves about 4 centimeters per year away from the Earth. This effect is actually measured.

  • At the time of the Moon's formation it was almost 20 times closer than it is now!
• The Earth raises even larger tides in the solid body of the Moon, slowing the rotation of the Moon even more effectively.

  • The Moon may once have rotated rapidly, but now rotates only once every 27.3 days.

    • One rotation every 27.3 days is just the right rate to keep the same face toward the Earth all of the time (almost)

    • There is a side of the Moon we never see from Earth.

  • In this configuration the Moon's rotation is no longer slowed by tidal drag. Why?

    • Eventually (if the evolving Sun does not destroy it first) the Earth's rotation will be slowed until it, too, keeps the same face toward the Moon. At that point the "day" will be about 50 days long (and so will the lunar month)!

  • This effect, which slows a moon's rotation down so that it rotates at the same rate as it revolves around its planet is called tidal locking.

    • The rotation of nearly every moon in the solar system is tidally locked to its planet.