A ball is thrown under influence of gravity. Suppose observer a films this motion and play the tape
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This article was part of a project we ran to celebrate the International Year of Astronomy 2009. The project asked you to nominate the questions about the Universe you'd most like to have answered, and this is one of them. We took it to Professor Bangalore Sathyaprakash of the School of Physics and Astronomy at Cardiff
University, and here is his answer. This interview is also available as a podcast.
Gravity according to Newton
"According to Newton's relatively simply picture, gravity is a force that works between two objects," says Sathyaprakash. "So if you have the Earth and the Sun, for example, then the Earth feels a force that is exerted by the Sun, and in turn the Sun feels the same force, exerted by the Earth." The magnitude $F$ of this force is given by the familar inverse square law
\[ F=G\frac{m_1 m_2}{r^2}, \]
where $G$ is the gravitational constant, $r$ is the distance between the centres of the Earth and the Sun, and $m_1$ and $m_2$ are their respective masses.
Newtonian gravity diagram
The gravitational interaction of two spherical bodies according to Newton. Image: Dennis Nilsson.
The forces experienced by Earth and Sun may be equal in magnitude, but the resulting motion is not the same for the two bodies. According to Newton's second law of motion, the magnitude of the acceleration a body experiences when it is subjected to a force is equal to the magnitude of the force divided by the body's mass. Since the Sun's mass is large, the acceleration it experiences due to the Earth's gravitational pull is negligible compared to that experienced by the much less massive Earth. That's why the Sun remains more or less stationary, while the Earth is forced on an orbit around it.
Newton's theory of gravity, published in 1687, is remarkably accurate when it comes to most practical purposes, and went unchallenged for over 300 years. Problems arose, however, when Einstein developed his special theory of relativity in 1905. "According to Newton's theory, gravitational interaction is instantaneous. Suppose the Sun were to vanish from the horizon today. We would not notice its disappearance immediately just by looking at the Sun, because light takes some time to travel. But according to Newton's gravity, the effect of the Sun's vanishing would be felt immediately, as the Earth would fly away in a tangential direction to its original path." Einstein's special theory of relativity, however, states that nothing, not even information, can travel faster than the speed of light. "It's possible to use the vanishing Sun analogy to construct [theoretical] gravitational telegraphs which would transmit information instantaneously — and that, according to Einstein, is impossible. That's the reason why Einstein had to reformulate the theory of gravity." Einstein published his reformulation in 1916, under the name of general relativity.
Gravity according to Einstein
"Einstein's theory of general relativity doesn't really look at gravity as a force anymore, rather it replaces the concept of force by that of geometry," says Sathyaprakash. According to general relativity, massive objects curve the geometry of space, and the paths that moving objects take through space are a result of this curvature. An analogy often used is that of a bowling ball placed on a trampoline: the ball will create a dip in the trampoline, curving its surface, so a marble placed nearby will roll into the dip towards the ball. The marble's motion isn't a result of some attractive force exerted by the ball, but a result of the curvature of the surface it's moving on. The analogy is slightly wonky, since it is the Earth's gravity, and not that of the bowling ball, which creates the dip in the trampoline as the bowling ball is drawn to the floor. "We should really move out of this analogy and try and picture the full three-dimensional space, as well as time, as being curved," says Sathyaprakash. "It's because of this curvature that planets move along curved orbits, rather than straight lines."
Einstein's gravity
give me brainlesst
Gravity according to Newton
"According to Newton's relatively simply picture, gravity is a force that works between two objects," says Sathyaprakash. "So if you have the Earth and the Sun, for example, then the Earth feels a force that is exerted by the Sun, and in turn the Sun feels the same force, exerted by the Earth." The magnitude $F$ of this force is given by the familar inverse square law
\[ F=G\frac{m_1 m_2}{r^2}, \]
where $G$ is the gravitational constant, $r$ is the distance between the centres of the Earth and the Sun, and $m_1$ and $m_2$ are their respective masses.
Newtonian gravity diagram
The gravitational interaction of two spherical bodies according to Newton. Image: Dennis Nilsson.
The forces experienced by Earth and Sun may be equal in magnitude, but the resulting motion is not the same for the two bodies. According to Newton's second law of motion, the magnitude of the acceleration a body experiences when it is subjected to a force is equal to the magnitude of the force divided by the body's mass. Since the Sun's mass is large, the acceleration it experiences due to the Earth's gravitational pull is negligible compared to that experienced by the much less massive Earth. That's why the Sun remains more or less stationary, while the Earth is forced on an orbit around it.
Newton's theory of gravity, published in 1687, is remarkably accurate when it comes to most practical purposes, and went unchallenged for over 300 years. Problems arose, however, when Einstein developed his special theory of relativity in 1905. "According to Newton's theory, gravitational interaction is instantaneous. Suppose the Sun were to vanish from the horizon today. We would not notice its disappearance immediately just by looking at the Sun, because light takes some time to travel. But according to Newton's gravity, the effect of the Sun's vanishing would be felt immediately, as the Earth would fly away in a tangential direction to its original path." Einstein's special theory of relativity, however, states that nothing, not even information, can travel faster than the speed of light. "It's possible to use the vanishing Sun analogy to construct [theoretical] gravitational telegraphs which would transmit information instantaneously — and that, according to Einstein, is impossible. That's the reason why Einstein had to reformulate the theory of gravity." Einstein published his reformulation in 1916, under the name of general relativity.
Gravity according to Einstein
"Einstein's theory of general relativity doesn't really look at gravity as a force anymore, rather it replaces the concept of force by that of geometry," says Sathyaprakash. According to general relativity, massive objects curve the geometry of space, and the paths that moving objects take through space are a result of this curvature. An analogy often used is that of a bowling ball placed on a trampoline: the ball will create a dip in the trampoline, curving its surface, so a marble placed nearby will roll into the dip towards the ball. The marble's motion isn't a result of some attractive force exerted by the ball, but a result of the curvature of the surface it's moving on. The analogy is slightly wonky, since it is the Earth's gravity, and not that of the bowling ball, which creates the dip in the trampoline as the bowling ball is drawn to the floor. "We should really move out of this analogy and try and picture the full three-dimensional space, as well as time, as being curved," says Sathyaprakash. "It's because of this curvature that planets move along curved orbits, rather than straight lines."
Einstein's gravity
give me brainlesst
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