Energy = mass x speed of light squared.
Energy is not equal to the momentum alone.
Energy = the mass of a particle, not its momentum.
Isaac Newton's
First Law of Motion states, "A body at rest will remain at rest, and a body in motion will remain in motion unless it is acted upon by an external force." What, then, happens to a body when an external force is applied to it? That situation is described by Newton's Second Law of Motion.
According to NASA, this law states, "Force is equal to the change in momentum per change in time. For a constant mass, force equals mass times acceleration." This is written in mathematical form as
F =
ma
F is force,
m is mass and
a is acceleration. The math behind this is quite simple. If you double the force, you double the acceleration, but if you double the mass, you cut the acceleration in half.
Newton's second law of motion states that F = ma, or net force is equal to mass times acceleration. A larger net force acting on an object causes a larger acceleration, and objects with larger mass require more force to accelerate. Both the net force acting on an object and the object's mass determine how the object will accelerate. Created by Sal Khan.
In physics, you perform work when you apply force to an object and move it over a distance. No work happens if the object does not move, no matter how much force you apply. When you perform work, it generates kinetic energy. The mass and velocity of an object impact how much kinetic energy it has. Equating work and kinetic energy allows you to determine velocity from force and distance. You cannot use force and distance alone, however; since kinetic energy relies on mass, you must determine the mass of the moving object as well.
Einstein’s theory of gravity, the
general theory of relativity, differs in many ways from Newton’s earlier theory of gravity.
One of the most important is that Einstein’s theory incorporates the cosmic speed limit: the speed of light.
Newton had assumed that gravity is felt everywhere in the Universe instantaneously, in other words that it travels at infinite speed.
Newton would therefore have predicted that, if the Sun vanished at this moment, the Earth would notice the lack of gravitational pull immediately and fly off out of the Solar System.
Einstein recognized that since nothing, not even gravity, can travel faster than the speed of light, the Earth would not notice the absence of gravity for 8.5 minutes, the time it takes gravity to travel (at 300,000km/s or 6.7 million mph) from the Sun to the Earth.
Another difference between Newton and Einstein is that Einstein’s theory recognises that the source of gravity is not mass, as Newton believed, but energy, one form of which is mass.
This means that all forms of energy have gravity: sound energy, heat energy and so on.
Crucially, gravity itself is a form of energy, so gravity creates more gravity.
What this means is that close to the Sun where solar gravity is at its most powerful, gravity is slightly stronger than Newton predicted.
In Newtonian gravity, a planet can only follow an elliptical orbit, but Mercury’s orbit continually shifts so that it traces out a pattern like a rosette.
The prediction of this ‘precession’ of the perihelion of Mercury was one of the key triumphs of Einstein’s theory of gravity.
See:
https://www.skyatnightmagazine.com/space-science/newton-einstein-gravity
See:
https://www.nbcnews.com/mach/scienc...-about-gravity-now-scientists-are-ncna1038671
See:
https://www.popularmechanics.com/sp...y-contradicts-newton-einstein-theory-gravity/
A
new study brings them closer to the answer.
The
study, published Aug. 16 in the journal Science, shows that
gravity works just as Einstein predicted even at the very edge of a black hole — in this case Sagittarius A*, the supermassive black hole at the center of our Milky Way galaxy. But the study is just the opening salvo in a far-ranging effort to find the point where Einstein’s model falls apart.
"We now have the technological capacity to test gravitational theories in ways we've never been able to before,” study co-author Jessica Lu, an astrophysicist at the University of California, Berkeley, said. “Einstein's theory of gravity is definitely in our crosshairs."
That means we may be closer to the day when Einstein’s relativity is supplanted by some as-yet-undescribed new theory of gravity.
“Newton had a great time for a long time with his description [of gravity], and then at some point it was clear that that description was fraying at the edges, and then Einstein offered a more complete version,” said Andrea Ghez, an astrophysicist at UCLA and a co-leader of the new research. “And so today, we're at that point again where we understand there has to be something that is more comprehensive that allows us to describe gravity in the context of black holes.”
In Newton’s view, all objects — from his
not-so-apocryphal apple to planets and stars — exert a force that attracts other objects. That universal law of gravitation worked pretty well for predicting the motion of planets as well as objects on Earth — and it's still used, for example, when making the calculations for a
rocket launch.
But Newton's view of gravity didn't work for some things, like Mercury’s peculiar orbit around the sun. The orbits of planets shift over time, and Mercury’s orbit shifted faster than Newton predicted.
Einstein offered a different view of gravity, one that made sense of Mercury. Instead of exerting an attractive force, he reasoned that each object curves the fabric of space and time around them, forming a sort of well that other objects — and even beams of light — fall into. Think of the sun as a bowling ball on a mattress. It creates a depression that draws the planets close.
This new model solved the Mercury problem. It showed that the sun so curves space that it distorts the orbits of nearby bodies, including Mercury. In Einstein’s view, Mercury might look like a marble forever circling the bottom of a drain.
Einstein’s theory has been confirmed by more than a century of experiments, starting with
one involving a 1919 solar eclipse in which the path of light from distant stars was shifted by the sun’s intense gravitation — by just the amount Einstein had predicted.
But Ghez and her colleagues wanted to subject Einstein to a more rigorous test. So they watched what happened when light from the star S0-2 passed Sagittarius A*, which is four million times more massive than the sun.
For the new research, Lu, Ghez and their collaborators used a trio of giant telescopes in Hawaii to watch as a bluish star named S0-2 made its closest approach to Sagittarius A* in its 16-year orbit around the black hole.
If Einstein was right, the black hole would warp space and time in a way that extended the wavelength of light from S0-2. In short, the waves would stretch out as the intense gravity from the black hole drained their energy, causing the starlight's color to shift from blue to red. If the star continued to glow blue, it would give credence to Newton's model of gravity, which doesn't account for the curvature of space and time. If it turned a different color, it would have hinted at some other model of gravity altogether.
Just as Einstein would have predicted, the star
glowed red.
“You might say, ‘Who cares?’ But in fact, no one has looked there,” Ghez, from UCLA, said. “So we've been able to take a big step forward in terms of exploring a regime that's not been explored before … You know there's a cliff, and you want to get close to that cliff, but you don't know where the drop-off is.”
Scientists know that at some point in a black hole, Einstein's theory stops working. “The curvature of spacetime is so extreme that Einstein's general relativity fails," said Kip Thorne, a Nobel Prize-winning theoretical physicist at the California Institute of Technology, who wasn't involved in the new research. "We don't understand how it works when the thing you're dealing with is extreme.”
This experiment brings scientists a little closer to understanding.
"It's definitely exciting," said Zoltan Haiman, a Columbia University astrophysicist who wasn't involved in the new research. "It's pushing the envelope. This is how we get to some place where we discover [Einstein's] theory no longer works."
Haimain said he was "in awe" of the work researchers had done, likening tracking S0-2 from an observatory on Earth to studying a tree in Paris from a balcony in New York City.
"This test is just the beginning," Lu said. Researchers plan to use a new generation of
high-powered instruments to conduct more tests of gravity around black holes. For example, they'll keep an eye on SO-2, to see if its orbit proceeds as Einstein would have expected, or if it takes a different path around Sagittarius A*, suggesting an alternate model of gravity.
In the next 10 years, Lu said, "we should be able to push Einstein's theory of gravity to its limits and hopefully start to see cracks."
What would that mean for science?
“It’s very hard to predict how new discoveries in fundamental physics will impact our day-to-day lives,” Lu said. “But a new theory of gravity might help us understand how our own universe was born, and how we got to where we are today 13½ billion years later.”
Space is a big place, and even Einsteins sometimes meet their limit. One of the most well-known of these limits is a
black hole’s center, or singularity, where Einstein’s famous theory appears to break down completely. Now, a new study from scientists at South Korea’s Sejong University
suggests that another limit to Newton and Einstein’s conception of gravity can be found in the orbital motions of long-period, widely separated, binary stars—also known simply as “wide binaries.” The results of this study
were published in
The Astrophysical Journal.
The main difference between Einstein and Newton gravity is that Einstein described gravity as a curvature in a 4D space-time fabric proportional to the
masses of objects, whereas Newton described gravity as a force between two objects based on their masses. Gravity is a fundamental interaction (a force of attraction) that causes mutual attraction between all things with mass or energy. Gravity is a universal force, meaning it acts on all objects with mass, no matter how large or small the object is. However, compared to other fundamental forces, gravity is a relatively weak force.
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