Gravitation
What Is Gravitation ?
Investigations in the field of physical science started with questions that people asked about the night sky.
- Why doesn’t the moon fall to earth?
- Why do the planets move across the sky?
- Why doesn’t the earth fly off into space rather than remaining in orbit around the sun?
The study of gravitation provides the answers to these and many related questions.
Gravitation is one of the four classes of interactions found in nature, and it was the earliest of the four to be studied extensively. Newton discovered in the 17th century that the same interaction that makes an apple fall out of a tree also keeps the planets in their orbits around the sun. This was the beginning of celestial mechanics, the study of the dynamics of objects in space. Today, our knowledge of celestial mechanics allows us to determine how to put a satellite into any desired orbit around the earth or to choose just the right trajectory to send a spacecraft to another planet.
The basic law that governs gravitational interactions : Gravity acts in the same fundamental way between the earth and your body, between the sun and a planet, and between a planet and one of its moons.
Frequently Asked Questions
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Ans: SUMMARY OF EVERY TOPIC OF FLUID MECHANISM. view more..
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Ans: When the speed of a flowing fluid exceeds a certain critical value, the flow is no
longer laminar. Instead, the flow pattern becomes extremely irregular and complex,
and it changes continuously with time; there is no steady-state pattern. This
irregular, chaotic flow is called turbulence view more..
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Ans: Viscosity is internal friction in a fluid. Viscous forces oppose the motion of one
portion of a fluid relative to another. Viscosity is the reason it takes effort to
paddle a canoe through calm water, but it is also the reason the paddle works.
Viscous effects are important in the flow of fluids in pipes, the flow of blood, the
lubrication of engine parts, and many other situations view more..
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Ans: Some of the earliest investigations in physical science started with questions
that people asked about the night sky. Why doesn’t the moon fall to earth?
Why do the planets move across the sky? Why doesn’t the earth fly off into
space rather than remaining in orbit around the sun? The study of gravitation
provides the answers to these and many related questions view more..
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Ans: Every particle of matter in the universe attracts every other particle with a force
that is directly proportional to the product of the masses of the particles and
inversely proportional to the square of the distance between them. view more..
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Ans: We have stated the law of gravitation in terms of the interaction between two
particles. It turns out that the gravitational interaction of any two bodies having
spherically symmetric mass distributions view more..
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Ans: To determine the value of the gravitational constant G, we have to measure the
gravitational force between two bodies of known masses m1 and m2 at a known
distance r. The force is extremely small for bodies that are small enough to be
brought into the laboratory, but it can be measured with an instrument called a
torsion balance, which Sir Henry Cavendish used in 1798 to determine G. view more..
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Ans: HERE ARE SOME SOLVED EXAMPLES TO CLEAR YOUR CONCEPTS view more..
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Ans: gravitational forces are negligible
between ordinary household-sized objects but very substantial between objects
that are the size of stars. Indeed, gravitation is the most important force on the
scale of planets, stars, and galaxies view more..
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Ans: We defined the weight of a body in Section 4.4 as the attractive gravitational
force exerted on it by the earth. We can now broaden our definition and say that
the weight of a body is the total gravitational force exerted on the body by all
other bodies in the universe view more..
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Ans: When we first introduced gravitational potential energy in Section 7.1, we
assumed that the earth’s gravitational force on a body of mass m doesn’t
depend on the body’s height. This led to the expression U = mgy view more..
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Ans: As a final note, let’s show that when we are close to the earth’s surface, Eq. (13.9)
reduces to the familiar U = mgy view more..
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Ans: Artificial satellites orbiting the earth are a familiar part of technology
But how do they stay in orbit, and what determines the properties of their orbits?
We can use Newton’s laws and the law of gravitation to provide the answers. In
the next section we’ll analyze the motion of planets in the same way. view more..
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Ans: A circular orbit, like trajectory 4 in Fig. 13.14, is the simplest case. It is also an
important case, since many artificial satellites have nearly circular orbits and the
orbits of the planets around the sun are also fairly circular view more..
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Ans: The name planet comes from a Greek word meaning “wanderer,” and indeed the
planets continuously change their positions in the sky relative to the background
of stars. One of the great intellectual accomplishments of the 16th and 17th centuries
was the threefold realization that the earth is also a planet, that all planets
orbit the sun, and that the apparent motions of the planets as seen from the earth
can be used to determine their orbits precisely view more..
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Ans: First consider the elliptical orbits described in Kepler’s first law. Figure 13.18 shows the geometry of an ellipse. The longest dimension is the major axis, with half-length a; this half-length is called the semi-major axis. view more..
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Ans: In a small time interval dt, the line
from the sun S to the planet P turns through an angle du. The area swept out is
the colored triangle with height r, base length r du, and area dA = 1
2 r2 du in
. The rate at which area is swept out, view more..
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Ans: We have already derived Kepler’s third law for the particular case of circular
orbits. Equation (13.12) shows that the period of a satellite or planet in a circular
orbit is proportional to the 3
2 power of the orbit radius. view more..
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