Mass versus weight - Wikipedia
And insofar as gravity is concerned, it is the total mass-energy (which includes . When we state this relation by a mathematical equation like Effect = function of. The weight of an object is the force of gravity on the object and may be defined as the mass times the acceleration of gravity, w = mg. Since the weight is a force. Gravity or gravitation, is a natural phenomenon by which all things with mass or energy—including planets, stars, galaxies, and even light—are brought toward.
So as the mass of either object increases, the force of gravitational attraction between them also increases. If the mass of one of the objects is doubled, then the force of gravity between them is doubled. If the mass of one of the objects is tripled, then the force of gravity between them is tripled. If the mass of both of the objects is doubled, then the force of gravity between them is quadrupled; and so on. Since gravitational force is inversely proportional to the square of the separation distance between the two interacting objects, more separation distance will result in weaker gravitational forces.
So as two objects are separated from each other, the force of gravitational attraction between them also decreases. If the separation distance between two objects is doubled increased by a factor of 2then the force of gravitational attraction is decreased by a factor of 4 2 raised to the second power.
If the separation distance between any two objects is tripled increased by a factor of 3then the force of gravitational attraction is decreased by a factor of 9 3 raised to the second power. Thinking Proportionally About Newton's Equation The proportionalities expressed by Newton's universal law of gravitation are represented graphically by the following illustration.
Observe how the force of gravity is directly proportional to the product of the two masses and inversely proportional to the square of the distance of separation. Another means of representing the proportionalities is to express the relationships in the form of an equation using a constant of proportionality.
This equation is shown below. The constant of proportionality G in the above equation is known as the universal gravitation constant. The precise value of G was determined experimentally by Henry Cavendish in the century after Newton's death. This experiment will be discussed later in Lesson 3. Using Newton's Gravitation Equation to Solve Problems Knowing the value of G allows us to calculate the force of gravitational attraction between any two objects of known mass and known separation distance.
As a first example, consider the following problem. The solution of the problem involves substituting known values of G 6. The solution is as follows: This would place the student a distance of 6. Two general conceptual comments can be made about the results of the two sample calculations above.
First, observe that the force of gravity acting upon the student a. This illustrates the inverse relationship between separation distance and the force of gravity or in this case, the weight of the student. The student weighs less at the higher altitude. The solutions of the field equations are the components of the metric tensor of spacetime.
A metric tensor describes a geometry of spacetime.
Mass, Weight, Density
The geodesic paths for a spacetime are calculated from the metric tensor. Solutions Notable solutions of the Einstein field equations include: The Schwarzschild solutionwhich describes spacetime surrounding a spherically symmetric non- rotating uncharged massive object. For compact enough objects, this solution generated a black hole with a central singularity. For radial distances from the center which are much greater than the Schwarzschild radiusthe accelerations predicted by the Schwarzschild solution are practically identical to those predicted by Newton's theory of gravity.
For charges with a geometrized length which are less than the geometrized length of the mass of the object, this solution produces black holes with double event horizons. The Kerr solution for rotating massive objects. This solution also produces black holes with multiple event horizons. The Kerr-Newman solution for charged, rotating massive objects.
Tests General relativity accounts for the anomalous perihelion precession of Mercury.
Newton's Law of Universal Gravitation
The prediction of the deflection of light was first confirmed by Arthur Stanley Eddington from his observations during the Solar eclipse of 29 May However, his interpretation of the results was later disputed.
The time delay of light passing close to a massive object was first identified by Irwin I. Shapiro in in interplanetary spacecraft signals. Gravitational radiation has been indirectly confirmed through studies of binary pulsars. Alexander Friedmann in found that Einstein equations have non-stationary solutions even in the presence of the cosmological constant.
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 confirmed this prediction.
This was verified on earth and in the solar system around Gravity and quantum mechanics Main articles: Graviton and Quantum gravity In the decades after the publication of the theory of general relativity, it was realized that general relativity is incompatible with quantum mechanics.
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.
Gravity - Wikipedia
Specifics Earth's gravity An initially-stationary object that is allowed to fall freely under gravity drops a distance that is proportional to the square of the elapsed time. This image spans half a second and was captured at 20 flashes per second. Earth's gravity Every planetary body including the Earth is surrounded by its own gravitational field, which can be conceptualized with Newtonian physics as exerting an attractive force on all objects.