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- Physicists made many exotic predictions using general relativity. The bending of light around the Sun is small, but researchers realized the effect would be much larger for galaxies, to the point where gravity would form images of more distant objects — the phenomenon now called gravitational lensing.
www.cfa.harvard.edu/research/science-field/einsteins-theory-gravitationEinstein's Theory of Gravitation | Center for Astrophysics ...
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The theory explained the anomalous orbit of Mercury, but the first major triumph came in 1919 when Arthur Eddington and his colleagues measured the influence of the Sun’s gravity on light from stars during a total solar eclipse. Physicists made many exotic predictions using general relativity.
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Stated in modern language, Newton’s universal law of gravitation states that every particle in the universe attracts every other particle with a force along a line joining them. The force is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
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- Newton’s law of gravity
Newton discovered the relationship between the motion of the Moon and the motion of a body falling freely on Earth. By his dynamical and gravitational theories, he explained Kepler’s laws and established the modern quantitative science of gravitation. Newton assumed the existence of an attractive force between all massive bodies, one that does not require bodily contact and that acts at a distance. By invoking his law of inertia (bodies not acted upon by a force move at constant speed in a straight line), Newton concluded that a force exerted by Earth on the Moon is needed to keep it in a circular motion about Earth rather than moving in a straight line. He realized that this force could be, at long range, the same as the force with which Earth pulls objects on its surface downward. When Newton discovered that the acceleration of the Moon is 1/3,600 smaller than the acceleration at the surface of Earth, he related the number 3,600 to the square of the radius of Earth. He calculated that the circular orbital motion of radius R and period T requires a constant inward acceleration A equal to the product of 4π2 and the ratio of the radius to the square of the time:
The Moon’s orbit has a radius of about 384,000 km (239,000 miles; approximately 60 Earth radii), and its period is 27.3 days (its synodic period, or period measured in terms of lunar phases, is about 29.5 days). Newton found the Moon’s inward acceleration in its orbit to be 0.0027 metre per second per second, the same as (1/60)2 of the acceleration of a falling object at the surface of Earth.
In Newton’s theory every least particle of matter attracts every other particle gravitationally, and on that basis he showed that the attraction of a finite body with spherical symmetry is the same as that of the whole mass at the centre of the body. More generally, the attraction of any body at a sufficiently great distance is equal to that of the whole mass at the centre of mass. He could thus relate the two accelerations, that of the Moon and that of a body falling freely on Earth, to a common interaction, a gravitational force between bodies that diminishes as the inverse square of the distance between them. Thus, if the distance between the bodies is doubled, the force on them is reduced to a fourth of the original.
Newton saw that the gravitational force between bodies must depend on the masses of the bodies. Since a body of mass M experiencing a force F accelerates at a rate F/M, a force of gravity proportional to M would be consistent with Galileo’s observation that all bodies accelerate under gravity toward Earth at the same rate, a fact that Newton also tested experimentally. In Newton’s equation F12 is the magnitude of the gravitational force acting between masses M1 and M2 separated by distance r12. The force equals the product of these masses and of G, a universal constant, divided by the square of the distance.
The constant G is a quantity with the physical dimensions (length)3/(mass)(time)2; its numerical value depends on the physical units of length, mass, and time used. (G is discussed more fully in subsequent sections.)
The force acts in the direction of the line joining the two bodies and so is represented naturally as a vector, F. If r is the vector separation of the bodies, then In this expression the factor r/r3 acts in the direction of r and is numerically equal to 1/r2.
Newton discovered the relationship between the motion of the Moon and the motion of a body falling freely on Earth. By his dynamical and gravitational theories, he explained Kepler’s laws and established the modern quantitative science of gravitation. Newton assumed the existence of an attractive force between all massive bodies, one that does not require bodily contact and that acts at a distance. By invoking his law of inertia (bodies not acted upon by a force move at constant speed in a straight line), Newton concluded that a force exerted by Earth on the Moon is needed to keep it in a circular motion about Earth rather than moving in a straight line. He realized that this force could be, at long range, the same as the force with which Earth pulls objects on its surface downward. When Newton discovered that the acceleration of the Moon is 1/3,600 smaller than the acceleration at the surface of Earth, he related the number 3,600 to the square of the radius of Earth. He calculated that the circular orbital motion of radius R and period T requires a constant inward acceleration A equal to the product of 4π2 and the ratio of the radius to the square of the time:
The Moon’s orbit has a radius of about 384,000 km (239,000 miles; approximately 60 Earth radii), and its period is 27.3 days (its synodic period, or period measured in terms of lunar phases, is about 29.5 days). Newton found the Moon’s inward acceleration in its orbit to be 0.0027 metre per second per second, the same as (1/60)2 of the acceleration of a falling object at the surface of Earth.
In Newton’s theory every least particle of matter attracts every other particle gravitationally, and on that basis he showed that the attraction of a finite body with spherical symmetry is the same as that of the whole mass at the centre of the body. More generally, the attraction of any body at a sufficiently great distance is equal to that of the whole mass at the centre of mass. He could thus relate the two accelerations, that of the Moon and that of a body falling freely on Earth, to a common interaction, a gravitational force between bodies that diminishes as the inverse square of the distance between them. Thus, if the distance between the bodies is doubled, the force on them is reduced to a fourth of the original.
Newton saw that the gravitational force between bodies must depend on the masses of the bodies. Since a body of mass M experiencing a force F accelerates at a rate F/M, a force of gravity proportional to M would be consistent with Galileo’s observation that all bodies accelerate under gravity toward Earth at the same rate, a fact that Newton also tested experimentally. In Newton’s equation F12 is the magnitude of the gravitational force acting between masses M1 and M2 separated by distance r12. The force equals the product of these masses and of G, a universal constant, divided by the square of the distance.
The constant G is a quantity with the physical dimensions (length)3/(mass)(time)2; its numerical value depends on the physical units of length, mass, and time used. (G is discussed more fully in subsequent sections.)
The force acts in the direction of the line joining the two bodies and so is represented naturally as a vector, F. If r is the vector separation of the bodies, then In this expression the factor r/r3 acts in the direction of r and is numerically equal to 1/r2.
Kepler’s laws describe the orbits of the objects whose motions are described by Newton’s laws of motion and the law of gravity. Knowing that gravity is the force that attracts planets toward the Sun, however, allowed Newton to rethink Kepler’s third law.
Gravity and Orbits. Move the sun, Earth, moon and space station in this simulation to see how it affects their gravitational forces and orbital paths. Visualize the sizes and distances between different heavenly bodies. Turn off gravity to see what would happen without it!
How did Newton establish that it was the force of gravity between the sun and the planets was the force responsible for keeping the planets in motion along their elliptical path? Click to see.
Orbital Motion and Mass. Kepler’s laws describe the orbits of the objects whose motions are described by Newton’s laws of motion and the law of gravity. Knowing that gravity is the force that attracts planets toward the Sun, however, allowed Newton to rethink Kepler’s third law.
