LAB – Why Is There a Tidal Bulge Opposite the Moon?
By: Stephen J Edberg, Jet Propulsion Laboratory, California Institute of Technology,, Stephen.J.Edberg@jpl.nasa.gov
The PUMAS Collection http://pumas.jpl.nasa.gov
©2011, Jet Propulsion Laboratory, California Institute of Technology (R)
Why does this happen?
The force of gravity diminishes with distance. Because of this, the force of gravity is different, and measurably so, from the first floor of a building (stronger) to the top floor of the building (weaker, because it is farther from the center of the Earth).
Tides may be defined as the difference of the gravitational attraction of an outside object through another (nearby) object.
In the Earth-Moon system, the strength of the Moon’s attraction is:
• Greatest on Earth’s surface directly “below” the Moon (Moon at the zenith), called the sub-Moon point
• Weaker at Earth’s center and
• Weakest at the antipode, the point on Earth’s surface on the line from the Moon, through Earth’s center, to the far surface.
If one now thinks of the Earth as falling towards the Moon – due to the Moon’s gravitational attraction – then the sub-Moon point has a greater force on it than the center, which has a greater force on it than the antipode.
So water (and the solid-earth surface) on the Moon-side falls towards the Moon faster than the center which falls faster than the antipode water (and solid-earth surface there).
The antipode water is being left behind by the center, which is being left behind by sub-Moon water. Back on Earth, we see these as two bulges of water which we call tides (and we can measure solid-earth tides as well).
It is important to understand that in this demonstration, although Earth’s gravity is stretching the slinky down, the important analogy is that the restoration force of the spring acting through the hook is the equivalent of the Moon’s gravity acting upon Earth. (Between the top and bottom flags, the spring represents Earth’s self-gravity combined with some lunar gravity).
The restoration force along the hanging slinky changes (decreases closer to the floor) because the coil near the hook has more coils below it, and their weight exerts a greater force than do the smaller number of coils that pull downward on an individual coil lower down.
Sketches of the gravitational force vectors involved (lunar and Earth self-gravity) at the sub-Moon point, Earth center, and antipode may help illuminate the forces individually and their sums.
– Advanced –
By studying tide tables for various places, you can see that the behavior of lunar tides is not nearly as simple as the analogy and the physical/mathematical calculations in the DISCUSSION section demonstrate. Additional complications include:
(1) Solar tides, which can sum with the lunar tide to increase or reduce the bulges of water, creating a spring tide (Sun, Earth, Moon aligned) or a neap tide (Sun, Earth, Moon make 90 degree angle).
(2) The varying physical distances of the Moon and Sun, demonstrated by higher tides in December-January. Earth is closest to the Sun in early January.
(3) The varying angular distances of the sub-Moon and sub-Sun points above and below Earth’s equator, varying the position of the bulge over the year.
(4) The topography of the ocean floor near shoreline monitoring stations.
(5) The effects of wind and weather systems on the ocean’s surface (for example, a hurricane storm surge may add to the astronomical tide, causing a “storm tide”).
2016 Massachusetts Science and Technology/Engineering Curriculum Framework
8.MS-ESS1-2. Explain the role of gravity in ocean tides, the orbital motions of planets, their moons, and asteroids in the solar system.
HS-ESS1-4. Use Kepler’s laws to predict the motion of orbiting objects in the solar system.
Describe how orbits may change due to the gravitational effects from, or collisions
with, other objects in the solar system.
HS-PS2-4. Use mathematical representations of Newton’s law of gravitation and Coulomb’s law to both qualitatively and quantitatively describe and pre
HS-PS2-10(MA). Use free-body force diagrams, algebraic expressions, and Newton’s laws of motion to predict changes to velocity and acceleration for an object moving in one
dimension in various situations.
A Framework for K-12 Science Education: Practices, Crosscutting Concepts, and Core Ideas (2012)
PS2.B: TYPES OF INTERACTIONS
Gravitational, electric, and magnetic forces between a pair of objects do not require that they be in contact. These forces are explained by force fields that contain energy and can transfer energy through space. These fields can be mapped by their effect on a test object (mass, charge, or magnet, respectively). Objects with mass are sources of gravitational fields and are affected by the gravitational fields of all other objects with mass. Gravitational forces are always attractive. For two human-scale objects, these forces are too small to observe without sensitive instrumentation. Gravitational interactions are non-negligible, however, when very massive objects are involved. Thus the gravitational force due to Earth, acting on an object near Earth’s surface, pulls that object toward the planet’s center. Newton’s law of universal gravitation provides the mathematical model to describe and predict the effects of gravitational forces between distant objects. These long-range gravitational interactions govern the evolution and maintenance of large-scale structures in the universe (e.g., the solar system, galaxies) and the patterns of motion within them… Newton’s law of universal gravitation and Coulomb’s law provide the mathematical models to describe and predict the effects of gravitational and electrostatic forces between distant objects.