# 13.7 Einstein's theory of gravity

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By the end of this section, you will be able to:
• Describe how the theory of general relativity approaches gravitation
• Explain the principle of equivalence
• Calculate the Schwarzschild radius of an object
• Summarize the evidence for black holes

Newton’s law of universal gravitation accurately predicts much of what we see within our solar system. Indeed, only Newton’s laws have been needed to accurately send every space vehicle on its journey. The paths of Earth-crossing asteroids, and most other celestial objects, can be accurately determined solely with Newton’s laws. Nevertheless, many phenomena have shown a discrepancy from what Newton’s laws predict, including the orbit of Mercury and the effect that gravity has on light. In this section, we examine a different way of envisioning gravitation.

## A revolution in perspective

In 1905, Albert Einstein published his theory of special relativity. This theory is discussed in great detail in Relativity , so we say only a few words here. In this theory, no motion can exceed the speed of light—it is the speed limit of the Universe. This simple fact has been verified in countless experiments. However, it has incredible consequences—space and time are no longer absolute. Two people moving relative to one another do not agree on the length of objects or the passage of time. Almost all of the mechanics you learned in previous chapters, while remarkably accurate even for speeds of many thousands of miles per second, begin to fail when approaching the speed of light.

This speed limit on the Universe was also a challenge to the inherent assumption in Newton’s law of gravitation that gravity is an action-at-a-distance force    . That is, without physical contact, any change in the position of one mass is instantly communicated to all other masses. This assumption does not come from any first principle, as Newton’s theory simply does not address the question. (The same was believed of electromagnetic forces, as well. It is fair to say that most scientists were not completely comfortable with the action-at-a-distance concept.)

A second assumption also appears in Newton’s law of gravitation [link] . The masses are assumed to be exactly the same as those used in Newton’s second law, $\stackrel{\to }{F}=m\stackrel{\to }{a}$ . We made that assumption in many of our derivations in this chapter. Again, there is no underlying principle that this must be, but experimental results are consistent with this assumption. In Einstein’s subsequent theory of general relativity    (1916), both of these issues were addressed. His theory was a theory of space-time    geometry and how mass (and acceleration) distort and interact with that space-time. It was not a theory of gravitational forces. The mathematics of the general theory is beyond the scope of this text, but we can look at some underlying principles and their consequences.

## The principle of equivalence

Einstein came to his general theory in part by wondering why someone who was free falling did not feel his or her weight. Indeed, it is common to speak of astronauts orbiting Earth as being weightless, despite the fact that Earth’s gravity is still quite strong there. In Einstein’s general theory, there is no difference between free fall and being weightless. This is called the principle of equivalence    . The equally surprising corollary to this is that there is no difference between a uniform gravitational field and a uniform acceleration in the absence of gravity. Let’s focus on this last statement. Although a perfectly uniform gravitational field is not feasible, we can approximate it very well.

A central force is given as F vector (r),where a=2NM².Assuming the potential energy at infinity to be zero,calculate the potential energy of a particle located at the point (3,4)
what is a vector
A vector is any physical quantity which has a magnitude as well as a direction associated to it. Which means a vector is some physical quantity which has magnitude and direction.
malayala
what is matter
Seth
nice
Faith
What is the equation illustrating Williamsons ether synthesis
What is the equation illustrating Williamsons ether synthesis
Kingdom
what is simple harmonic motion
examples: vibrating prongs of a tuning fork and a guittar string.
Salman
It is a repetitive periodic motion of a system about an equilibrium position
Felix
SHM is the repitition process of to and fro motion.
Younus
SHM is the motion in which the restoring force is directly proportional to the displacement of body from its mean position and is opposite in direction to the displacement. From Hooke's law F=-kx
Kushal
SHM is the motion in which the restoring force is directly proportional to the displacement of body from its mean position and is opposite in direction to the displacement. From Hooke's law F=-kx
Kushal
what is a wave?
show that coefficient of friction of solid block inclined at an angle is equivalent to trignometric tangent of angle
DAVID
Wave is the transfer of energy due to the periodic vibration of the particles in the medium.
Kushal
wave is the transfer of energy
Vindora
Wave is the transfer of particles in a fluid or any way.
Younus
thanks for that definition.
Hi everyone please can dere be motion without force?
Lafon
no...
Enyia
Thanks
Lafon
hi
Omomaro
whats is schrodinger equation
Omomaro
l went spiral spring
Xalat
what is position?
position is simply where you are or where you were
Shii
position is the location of an object with respect to a two or three dimensional axes or space.
Bamidele
Can dere be motion without force?
Lafon
what is the law of homogeinity?
two electric lines of force never interested each other. why?
if two electric lines of force intersect eachother then their will be two tangent at a point which represent the two forces which is impossible.
Amar
proof that for BBC lattice structure 4r\root 5 and find Apf for the BBC structure
what is physics?
physics is deine as the specific measrument of of volume, area,nd distances...
Olakojo
if a string of 2m is suspended an an extended 3m elasticity is been applied.... is hooks law obeyed?
Enyia
if a string of 2m is suspended an an extended 3m elasticity is been applied.... is hooks law obeyed?
Enyia
yes
Alex
proof that for a BBC lattice structure a= 4r/ root 5 find the APF for the BBC structure
Eric
if a string of 2m is suspended an an extended 3m elasticity is been applied.... is hooks law obeyed?
tell me conceptual quetions of mechanics
I want to solve a physical question
ahmed
ok
PUBG
a displacement vector has a magnitude of 1.62km and point due north . another displacement vector B has a magnitude of 2.48 km and points due east.determine the magnitude and direction of (a) a+ b and (b) a_ b
quantum
George
a+b=2.9
SUNJO
a+b
Yekeen
use Pythogorous
Dhritwan
A student opens a 12kgs door by applying a constant force of 40N at a perpendicular distance of 0.9m from the hinges. if the door is 2.0m high and 1.0m wide determine the magnitude of the angular acceleration of the door. ( assume that the door rotates freely on its hinges.) please assist me to d
Mike
what is conditions met to produce shm
what is shm
Manzoor
shm?
Grant
Why is Maxwell saying that light is an electromagnetic wave?
Bong
1st condition; It(th e BBC's system) must have some inertia which will enable it to possess Kinetic energy 2. must be able to store potential energy
Calleb
I meant "the system" not the BBC'S....."
Calleb
Manzoor
kindly tell us the name of your university
Manzoor
GUlam Ishaq Khan INSTITUTE of engineering science
ali
Department of Environment Ionian University Zante Greece By  By By  By By   By