Gravitation keeps the planets in orbit about the Sun.
Gravitation, or
gravity, is a
natural phenomenon by which
objects with
mass attract one another. In
everyday life, gravitation is most familiar as the agent that lends
weight to objects with mass and causes them
to fall to the ground when dropped. Gravitation causes dispersed
matter to coalesce, thus accounting for the existence of the
Earth, the
Sun, and most of
the macroscopic objects in the
universe. It
is responsible for keeping the Earth and the other planets in their
orbits around the Sun; for keeping the
Moon in its orbit around the Earth; for the
formation of
tides; for
convection, by which fluid flow occurs under the
influence of a density gradient and gravity; for heating the
interiors of forming stars and planets to very high temperatures;
and for various other phenomena observed on Earth.
Modern
physics describes gravitation using
the
general theory of
relativity, in which gravitation is a consequence of the
curvature of
spacetime which governs the
motion of inertial objects. The simpler
Newton's law of universal
gravitation provides an accurate approximation for most
calculations.
History of gravitational theory
Scientific revolution
Modern work on gravitational theory began with the work of
Galileo Galilei in the late 16th and early
17th centuries.
In his famous (though possibly apocryphal)
experiment dropping balls from the Tower of Pisa, and later with careful measurements of balls
rolling down inclines, Galileo showed
that gravitation accelerates all objects at the same rate.
This was a major departure from Aristotle's belief that heavier
objects are accelerated faster. Galileo correctly postulated air
resistance as the reason that lighter objects may fall more slowly
in an atmosphere. Galileo's work set the stage for the formulation
of Newton's theory of gravity.
Newton's theory of gravitation
In 1687, English mathematician Sir
Isaac
Newton published
Principia,
which hypothesizes the
inverse-square
law of universal gravitation. In his own words, “I deduced that
the forces which keep the planets in their orbs must [be]
reciprocally as the squares of their distances from the centers
about which they revolve: and thereby compared the force requisite
to keep the Moon in her Orb with the force of gravity at the
surface of the Earth; and found them answer pretty nearly.”
Newton's theory enjoyed its greatest success when it was used to
predict the existence of
Neptune based on
motions of
Uranus that could not be accounted
by the actions of the other planets. Calculations by
John Couch Adams and
Urbain Le Verrier both predicted the
general position of the planet, and Le Verrier's calculations are
what led
Johann Gottfried
Galle to the discovery of Neptune.
Ironically, it was another discrepancy in a planet's orbit that
helped to point out flaws in Newton's theory. By the end of the
19th century, it was known that the orbit of
Mercury showed slight perturbations that
could not be accounted for entirely under Newton's theory, but all
searches for another perturbing body (such as a planet orbiting the
Sun even closer than Mercury) had been
fruitless. The issue was resolved in 1915 by
Albert Einstein's new
General Theory of Relativity, which
accounted for the small discrepancy in Mercury's orbit.
Although Newton's theory has been superseded, most modern
non-relativistic gravitational calculations are still made using
Newton's theory because it is a much simpler theory to work with
than
General relativity, and
gives sufficiently accurate results for most applications.
Gravitational torsion, weak equivalence principle and
gravitational gradient
Loránd Eötvös published
on surface tension between 1876 and 1886.The Torsion or Eötvös
balance, designed by Hungarian Baron
Loránd Eötvös, is a sensitive
instrument for measuring the density of underlying rock strata. The
device measures not only the direction of force of gravity, but the
change in the force of gravity's extent in horizontal plane. It
determines the distribution of masses in the Earth's crust. The
Eötvös torsion balance, an important instrument of geodesy and
geophysics throughout the whole world, studies the Earth's physical
properties. It is used for mine exploration, and also in the search
for minerals, such as oil, coal and ores.
Eötvös' law of capillarity (
weak equivalence principle)
served as a basis for Einstein's theory of relativity.(Capillarity:
the property or exertion of capillary attraction of repulsion, a
force that is the resultant of adhesion, cohesion, and surface
tension in liquids which are in contact with solids, causing the
liquid surface to rise - or be depressed...)
The simplest way to test the weak equivalence principle is to drop
two objects of different masses or compositions in a vacuum, and
see if they hit the ground at the same time. These experiments
demonstrate that all objects fall at the same rate with negligible
friction (including air resistance). More sophisticated tests use a
torsion balance of a type invented by
Loránd Eötvös. Satellite
experiments are planned for more accurate experiments in
space.
General relativity
In
general
relativity, the effects of gravitation are ascribed to
spacetime curvature instead of a force. The starting point
for general relativity is the
equivalence principle, which equates
free fall with inertial motion, and describes free-falling inertial
objects as being accelerated relative to non-inertial observers on
the ground. In
Newtonian physics,
however, no such acceleration can occur unless at least one of the
objects is being operated on by a force.
Einstein proposed that spacetime is curved by matter, and that
free-falling objects are moving along locally straight paths in
curved spacetime. These straight lines are called
geodesics. Like Newton's First
Law, Einstein's theory stated that if there is a force applied to
an object, it would deviate from the geodesics in spacetime. For
example, we are no longer following the geodesics while standing
because the mechanical resistance of the Earth exerts an upward
force on us. Thus, we are non-inertial on the ground. This explains
why moving along the geodesics in spacetime is considered
inertial.
Einstein discovered the
field
equations of general relativity, which relate the presence of
matter and the curvature of spacetime and are named after him. The
Einstein field equations
are a set of 10
simultaneous,
non-linear,
differential equations. The solutions
of the field equations are the components of the
metric tensor of
spacetime. A metric tensor describes a geometry of spacetime. The
geodesic paths for a spacetime are calculated from the metric
tensor.
Notable solutions of the Einstein field equations include:
The
tests of general
relativity included:
- General relativity accounts for the anomalous perihelion precession of
Mercury.
- The prediction that time runs slower at lower potentials has
been confirmed by the Pound–Rebka experiment, the
Hafele–Keating
experiment, and the GPS.
- The prediction of the deflection of light was first confirmed
by Arthur Stanley Eddington
in 1919. . Quote, p. 192: "About a dozen stars in all were studied,
and yielded values 1.98 ± 0.11" and 1.61 ± 0.31", in substantial
agreement with Einstein's prediction θ_{ʘ} = 1.75"." The
Newtonian corpuscular theory also predicted a lesser deflection of
light, but Eddington found that the results of the expedition
confirmed the predictions of general relativity over those of the
Newtonian theory. However this interpretation of the results was
later disputed. More recent tests using radio interferometric
measurements of quasars passing behind the
Sun have more accurately and consistently
confirmed the deflection of light to the degree predicted by
general relativity. See also gravitational lens.
- The time delay of light
passing close to a massive object was first identified by Irwin I. Shapiro in 1964 in interplanetary
spacecraft signals.
- Gravitational radiation
has been indirectly confirmed through studies of binary pulsars.
- Alexander Friedmann in 1922
found that Einstein equations have non-stationary solutions (even
in the presence of the cosmological constant). In 1927
Georges Lemaître showed that
static solutions of the Einstein equations, which are possible in
the presence of the cosmological constant, are unstable, and
therefore the static universe envisioned by Einstein could not
exist. Later, in 1931, Einstein himself agreed with the results of
Friedmann and Lemaître. Thus general relativity predicted that the
Universe had to be non-static—it had to either expand or contract.
The expansion of the universe discovered by Edwin Hubble in 1929 confirmed this
prediction.
Gravity and quantum mechanics
Several decades after the discovery of general relativity it was
realized that general relativity is incompatible with
quantum mechanics. It is possible to
describe gravity in the framework of
quantum field theory like the other
fundamental forces, such that the
attractive force of gravity arises due to exchange of
virtual gravitons,
in the same way as the electromagnetic force arises from exchange
of virtual
photons. This reproduces general
relativity in the
classical limit.
However, this approach fails at short distances of the order of the
Planck length, where a more complete
theory of
quantum gravity (or a new
approach to quantum mechanics) is required. Many believe the
complete theory to be
string theory,
or more currently
M-theory, and, on the
other hand, it may be a
background independent theory such as
loop quantum gravity or
causal dynamical
triangulation.
Specifics
Earth's gravity
Every planetary body (including the Earth) is surrounded by its own
gravitational field, which exerts an attractive force on all
objects. Assuming a spherically symmetrical planet (a reasonable
approximation), the strength of this field at any given point is
proportional to the planetary body's mass and inversely
proportional to the square of the distance from the center of the
body.
The strength of the gravitational field is numerically equal to the
acceleration of objects under its influence, and its value at the
Earth's surface, denoted
g, is approximately expressed
below as the
standard
average.
g = 9.81 m/s
^{2} = 32.2 ft/s
^{2}
This means that, ignoring air resistance, an object falling freely
near the Earth's surface increases its velocity with 9.81 m/s (32.2
ft/s or 22 mph) for each second of its descent. Thus, an object
starting from rest will attain a velocity of 9.81 m/s (32.2 ft/s)
after one second, 19.6 m/s (64.4 ft/s) after two seconds, and so
on, adding 9.81 m/s (32.2 ft/s) to each resulting velocity. Also,
again ignoring air resistance, any and all objects, when dropped
from the same height, will hit the ground at the same time.
According to
Newton's 3rd Law, the Earth itself experiences an equal [in
force] and opposite [in direction] force to
that acting on the falling object, meaning that the Earth also
accelerates towards the object (until the object hits the earth,
then the
Law of
Conservation of Energy states that it will move back with the
same acceleration with which it initially moved forward, canceling
out the two forces of gravity.). However, because the mass of the
Earth is huge, the acceleration of the Earth by this same force is
negligible, when measured relative to the system's
center of mass.
Equations for a falling body near the surface of the Earth
Ball falling freely under
gravity.
See text for description.
Under an assumption of constant gravity,
Newton's law of universal
gravitation simplifies to
F =
mg, where
m is the
mass of the body and
g is a constant vector with an average magnitude of
9.81 m/s². The acceleration due to gravity is equal to this
g. An initially-stationary object which is allowed to fall
freely under gravity drops a distance which is proportional to the
square of the elapsed time. The image on the right, spanning half a
second, was captured with a stroboscopic flash at 20 flashes per
second. During the first 1/20th of a second the ball drops one unit
of distance (here, a unit is about 12 mm); by 2/20ths it has
dropped at total of 4 units; by 3/20ths, 9 units and so on.
Under the same constant gravity assumptions, the
potential energy,
E_{p},
of a body at height
h is given by
E_{p} =
mgh (or
E_{p} =
Wh, with
W meaning weight). This expression is valid only over
small distances
h from the surface of the Earth.
Similarly, the expression h = \tfrac{v^2}{2g} for the maximum
height reached by a vertically projected body with velocity
v is useful for small heights and small initial velocities
only.
Gravity and astronomy
The discovery and application of Newton's law of gravity accounts
for the detailed information we have about the planets in our solar
system, the mass of the Sun, the distance to stars,
quasars and even the theory of
dark matter. Although we have not traveled to
all the planets nor to the Sun, we know their masses. These masses
are obtained by applying the laws of gravity to the measured
characteristics of the orbit. In space an object maintains its
orbit because of the force of gravity acting
upon it. Planets orbit stars, stars orbit
Galactic Centers,
galaxies orbit a center of mass in clusters, and
clusters orbit in
superclusters. The
force of gravity is proportional to the mass of an object and
inversely proportional to the square of the distance between the
objects.
Gravitational radiation
In general relativity, gravitational radiation is generated in
situations where the curvature of
spacetime is oscillating, such as is the case with
co-orbiting objects. The gravitational radiation emitted by the
Solar System is far too small to
measure. However, gravitational radiation has been indirectly
observed as an energy loss over time in binary pulsar systems such
as
PSR B1913+16. It is believed that
neutron star mergers and
black hole formation may create detectable
amounts of gravitational radiation.
Gravitational radiation observatories such
as LIGO have been created to study the problem. No
confirmed detections have been made of this hypothetical radiation,
but as the science behind LIGO is refined and as the instruments
themselves are endowed with greater sensitivity over the next
decade, this may change.
Anomalies and discrepancies
There are some observations that are not adequately accounted for,
which may point to the need for better theories of gravity or
perhaps be explained in other ways.
- Pioneer anomaly: The two Pioneer spacecraft seem to be slowing down
in a way which has yet to be explained.
- Flyby anomaly: Various spacecraft have
experienced greater accelerations during slingshot maneuvers than expected.
- Accelerating expansion: The metric expansion of space seems to
be speeding up. Dark energy has been
proposed to explain this. A recent alternative explanation is that
the geometry of space is not homogeneous (due to clusters of
galaxies) and that when the data are reinterpreted to take this
into account, the expansion is not speeding up after all, however
this conclusion is disputed.
- Anomalous increase of the AU: Recent
measurements indicate that planetary orbits are expanding
faster than if this was solely through the sun losing mass by
radiating energy.
- Extra energetic photons: Photons travelling
through galaxy clusters should gain energy and then lose it again
on the way out. The accelerating expansion of the universe should
stop the photons returning all the energy, but even taking this
into account photons from the cosmic microwave
background radiation gain twice as much energy as expected.
This may indicate that gravity falls off faster than
inverse-squared at certain distance scales.
- Dark flow: Surveys of galaxy motions have
detected a mystery dark flow towards an
unseen mass. Such a large mass is too large to have accumulated
since the Big Bang using current models and
may indicate that gravity falls off slower than
inverse-squared at certain distance scales.
- Extra massive hydrogen clouds: The spectral
lines of the Lyman-alpha forest
suggest that hydrogen clouds are more clumped together at certain
scales than expected and, like dark flow, may indicate that gravity
falls off slower than inverse-squared at certain distance
scales.
Alternative theories
Historical alternative theories
Recent alternative theories
See also
Notes
- Proposition 75, Theorem 35: p.956 - I.Bernard Cohen and Anne
Whitman, translators: Isaac Newton, The Principia:
Mathematical Principles of Natural Philosophy. Preceded by A
Guide to Newton's Principia, by I. Bernard Cohen. University
of California Press 1999 ISBN 0-520-08816-6 ISBN 0-520-08817-4
- Max Born (1924), Einstein's Theory
of Relativity (The 1962 Dover edition, page 348 lists a table
documenting the observed and calculated values for the precession
of the perihelion of Mercury, Venus, and Earth.)
Footnotes
- Does Gravity Travel at the Speed of Light?,
UCR Mathematics. 1998. Retrieved 3 July 2008
- Galileo (1638),
Two
New Sciences, First Day Salviati speaks: "If this were what
Aristotle meant you would burden him with another error which would
amount to a falsehood; because, since there is no such sheer height
available on earth, it is clear that Aristotle could not have made
the experiment; yet he wishes to give us the impression of his
having performed it when he speaks of such an effect as one which
we see."
- * (pp.1–2). The quotation comes from a memorandum thought to
have been written about 1714. As early as 1645 Ismaël
Bullialdus had argued that any force exerted by the Sun on
distant objects would have to follow an inverse-square law.
However, he also dismissed the idea that any such force did exist.
See, for example,
- http://www.gap-system.org/~history/Biographies/Eotvos.html
- http://zelmanov.ptep-online.com/papers/zj-2008-b2.pdf
- http://www.black-holes.org/relativity6.html
- http://laser.phys.ualberta.ca/~egerton/genrel.htm
- Law of Geodesic Motion
http://blog.sauliaus.info/temp/gravity.pdf
- . Quote, p. 332: "Thus the results of the expeditions to Sobral
and Principe can leave little doubt that a deflection of light
takes place in the neighbourhood of the sun and that it is of the
amount demanded by Einstein's generalised theory of relativity, as
attributable to the sun's gravitational field."
- .
- See W.Pauli, 1958, pp.219–220
- Wanted: Einstein Jr, The Economist,
6th March 2008.
- Dark energy may just be a cosmic illusion,
New Scientist, issue 2646, 7th March 2008.
- Swiss-cheese model of the cosmos is full of
holes, New Scientist, issue 2678, 18th October
2008.
- "Where Matter Fears to Tread", New Scientist issue 2669, 14
March 2009
References
Further reading
External links