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What is the difference between inertial mass and gravitational mass? How gravitational mass related to Einstein's general theory of relativity


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Gravitational massis measured by comparing the force of gravity of an unknown mass to the force of gravity of a known mass. This is typically done with some sort of balance scale. The beauty of this method is that no matter where, or what planet, you are, the masses will always balance out because the gravitational acceleration on each object will be the same. This does break down near supermassive objects such as black holes and neutron stars due to the high gradient of the gravitational field around such objects. Inertial massis found by applying a known force to an unknown mass, measuring the acceleration, and applying Newton's Second Law, m = F/a. This gives as accurate a value for mass as the accuracy of your measurements. When the astronauts need to be weighed in outer space, they actually find their inertial mass in a special chair. The interesting thing is that, physically, no difference has been found between gravitational and inertial mass. Many experiments have been performed to check the values and the experiments always agree to within the margin of error for the experiment. Einstein used the fact that gravitational and inertial mass were equal to begin his Theory of General Relativity in which he postulated that gravitational mass was the same as inertial mass and that the acceleration of gravity is a result of a 'valley' or slope in the space-time continuum that masses 'fell down' much as pennies spiral around a hole in the common donation toy at your favorite chain store. To state the answer one more time, there is no difference between gravitational and inertial mass as far as we know. Inertial mass. This is mainly defined by Newton's law, the all-too-famous F = ma, which states that when a force F is applied to an object, it will accelerate proportionally, and that constant of proportion is the mass of that object. In very concrete terms, to determine the inertial mass, you apply a force of F Newtons to an object, measure the acceleration in m/s2, and F/a will give you the inertial mass m in kilograms. 2) Gravitational mass. This is defined by the force of gravitation, which states that there is a gravitational force between any pair of objects, which is given by F = G m1m2/r2 where G is the universal gravitational constant, m1and m2are the masses of the two objects, and r is the distance between them. This, in effect defines the gravitational mass of an object. As it turns out, these two masses are equal to each other as far as we can measure. Also, the equivalence of these two masses is why all objects fall at the same rate on earth.

Two objects exert a force of attraction on one another known as "gravity." Sir Isaac Newton quantified the gravity between two objects when he formulated his three laws of motion. The force tugging between two bodies depends on how massive each one is and how far apart the two lie. Even as the center of the Earth is pulling you toward it (keeping you firmly lodged on the ground), your center of mass is pulling back at the Earth. But the more massive body barely feels the tug from you, while with your much smaller mass you find yourself firmly rooted thanks to that same force. Yet Newton's laws assume that gravity is an innate force of an object that can act over a distance.

Albert Einstein in his theory of special relaxation determinedthat the laws of physics are the same for all non-accelerating observers, and he showed that the speed of lightwithin a vacuum is the same no matter the speed at which an observer travels. As a result, he found that space and time were interwoven into a single continuum known as space-time. Events that occur at the same time for one observer could occur at different times for another.

As he worked out the equations for his general theory of relativity, Einstein realized that massive objects caused a distortion in space-time. Imagine setting a large body in the center of a trampoline. The body would press down into the fabric, causing it to dimple. A marble rolled around the edge would spiral inward toward the body, pulled in much the same way that the gravity of a planet pulls at rocks in space.

​​​​ Experimental evidence

Gravitational lensing: Light around a massive object, such as a black hole, is bent, causing it to act as a lensfor the things that lie behind it. Astronomers routinely use this method to study stars and galaxies behind massive objects.

Einstein's Cross, a quasar in the pegasus constellationis an excellent example of gravitational lensing. The quasar is about 8 billion light-years from Earth, and sits behind a galaxy that is 400 million light-years away. Four images of the quasar appear around the galaxy because the intense gravity of the galaxy bends the light coming from the quasar.

Gravitational lensing can allow scientists to see some pretty cool things, but until recently, what they spotted around the lens has remained fairly static. However, since the light traveling around the lens takes a different path, each traveling over a different amount of time, scientists were able to observe a supernova occur four different typesas it was magnified by a massive galaxy.

In another interesting observation, NASA's Kepler telescope spotted a dead star, known as a white dwarf, orbiting a red dwarf in a binary system. Although the white dwarf is more massive, it has a far smaller radius than its companion.

"The technique is equivalent to spotting a flea on a light bulb 3,000 miles away, roughly the distance from Los Angeles to New York City," Avi Shporer of the California Institute of Technology said in a statement. Gravitational redshift: The electromagnetic radiation of an object is stretched out slightly inside a gravitational field. Think of the sound waves that emanate from a siren on an emergency vehicle; as the vehicle moves toward an observer, sound waves are compressed, but as it moves away, they are stretched out, or redshirt Knownas the Doppler Effect, the same phenomena occurs with waves of light at all frequencies. In 1959, two physicists, Robert Pound and Glen Rebka, shot gamma-rays of radioactive iron up the side of a tower at Harvard University and found them to be minutely less than their natural frequency due to distortions caused by gravity.

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