# 13.7 Einstein's theory of gravity  (Page 7/19)

 Page 7 / 19

There are two prevailing ideas of what this matter could be—WIMPs and MACHOs. WIMPs stands for weakly interacting massive particles. These particles (neutrinos are one example) interact very weakly with ordinary matter and, hence, are very difficult to detect directly. MACHOs stands for massive compact halo objects, which are composed of ordinary baryonic matter, such as neutrons and protons. There are unresolved issues with both of these ideas, and far more research will be needed to solve the mystery.

## Summary

• According to the theory of general relativity, gravity is the result of distortions in space-time created by mass and energy.
• The principle of equivalence states that that both mass and acceleration distort space-time and are indistinguishable in comparable circumstances.
• Black holes, the result of gravitational collapse, are singularities with an event horizon that is proportional to their mass.
• Evidence for the existence of black holes is still circumstantial, but the amount of that evidence is overwhelming.

## Key equations

 Newton’s law of gravitation ${\stackrel{\to }{F}}_{12}=G\frac{{m}_{1}{m}_{2}}{{r}^{2}}{\stackrel{^}{r}}_{12}$ Acceleration due to gravity at the surface of Earth $g=G\frac{{M}_{\text{E}}}{{r}_{}^{2}}$ Gravitational potential energy beyond Earth $U=-\frac{G{M}_{\text{E}}m}{r}$ Conservation of energy $\frac{1}{2}m{v}_{1}^{2}-\frac{GMm}{{r}_{1}}=\frac{1}{2}m{v}_{2}^{2}-\frac{GMm}{{r}_{2}}$ Escape velocity ${v}_{\text{esc}}=\sqrt{\frac{2GM}{R}}$ Orbital speed ${v}_{\text{orbit}}=\sqrt{\frac{{\text{GM}}_{\text{E}}}{r}}$ Orbital period $Τ=2\pi \sqrt{\frac{{r}^{3}}{{\text{GM}}_{\text{E}}}}$ Energy in circular orbit $E=K+U=-\frac{Gm{\text{M}}_{\text{E}}}{2r}$ Conic sections $\frac{\alpha }{r}=1+e\text{cos}\theta$ Kepler’s third law ${Τ}^{2}=\frac{4{\pi }^{2}}{GM}{a}^{3}$ Schwarzschild radius ${R}_{\text{S}}=\frac{2GM}{{c}^{2}}$

## Conceptual questions

The principle of equivalence states that all experiments done in a lab in a uniform gravitational field cannot be distinguished from those done in a lab that is not in a gravitational field but is uniformly accelerating. For the latter case, consider what happens to a laser beam at some height shot perfectly horizontally to the floor, across the accelerating lab. (View this from a nonaccelerating frame outside the lab.) Relative to the height of the laser, where will the laser beam hit the far wall? What does this say about the effect of a gravitational field on light? Does the fact that light has no mass make any difference to the argument?

The laser beam will hit the far wall at a lower elevation than it left, as the floor is accelerating upward. Relative to the lab, the laser beam “falls.” So we would expect this to happen in a gravitational field. The mass of light, or even an object with mass, is not relevant.

As a person approaches the Schwarzschild radius of a black hole, outside observers see all the processes of that person (their clocks, their heart rate, etc.) slowing down, and coming to a halt as they reach the Schwarzschild radius. (The person falling into the black hole sees their own processes unaffected.) But the speed of light is the same everywhere for all observers. What does this say about space as you approach the black hole?

## Problems

What is the Schwarzschild radius for the black hole at the center of our galaxy if it has the mass of 4 million solar masses?

$1.19\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{7}\text{km}$

What would be the Schwarzschild radius, in light years, if our Milky Way galaxy of 100 billion stars collapsed into a black hole? Compare this to our distance from the center, about 13,000 light years.

The displacement of the air molecules in sound wave is modeled with the wave function s(x,t)=5.00nmcos(91.54m−1x−3.14×104s−1t)s(x,t)=5.00nmcos(91.54m−1x−3.14×104s−1t) . (a) What is the wave speed of the sound wave? (b) What is the maximum speed of the air molecules as they oscillate in simple harmon
practical 1st year physics
huh
Luminous
Whats the formular for newton law of motion
f=ma
what is speed
distance travelled per unit of time is speed.
distance travelled in a particular direction it is.
Andrew
formula for velocity
v=ms^-1 velocity=distance time
Cleophas
(p-a/v)(v-b)=nrt what is the dimension of a
Amraketa
velocity= displacement time
Gold
what are evasive medical diagnosis?
If the block is displaced to a position y , the net force becomes Fnet=k(y−y0)−mg=0Fnet=k(y−y0)−mg=0 . But we found that at the equilibrium position, mg=kΔy=ky0−ky1mg=kΔy=ky0−ky1 . Substituting for the weight in the equation yields. Show me an equation of graph.
Shaina
simple harmonic motion defination
how to easily memorize motion equation
Maharam
how speed destrog is uranium
where can we find practice problems?
I'm not well
YAZID
Sayed
can u tell me the expression for radial acceleeation
No
YAZID
Is equal to the square of the velocity divided by the radius of circular path of the object
Mukhtaar
how to find maximum acceleration and velocity of simple harmonic motion?
chander
how to find maximum acceleration and velocity of simple harmonic motion and where it occurres?
chander
you can use either motion equations or kinetic equation and potential equation .
lasitha
how destraction 1kg uranium
Sayed
A Radial Acceleration is defined as the upward movement of an object.
Andrew
A body of 2.0kg mass makes an elastic collision with another at rest and continues to more in the original direction but with 1/4 of its ori is the mass of the struck body?
pls help me solve this problem
bright
why do sound travel faster in the night than in the day
I believe because speed is a function of air density, and colder air is more dense
Jerry
At night air is denser because of humidity.
Clifton
Night air is cooler. Sound requires medium to travel so the denser the medium the fastest the sound travels. Humid air is denser then warmer air as in day.
Clifton
The humidity statement is misleading , colder air is more dense period.
Jerry
because there is no any other sound to reverberate with it so it clearly travel to lot of distance and also humidity and also due to denser air at night
Azam
please could you guys help me with physics best websites
Baje
because it is quiet at night. this takes us to the topic wave, it depends on the wave at that moment, which Echo's....sound travelled.
Andrew
because it is quite at night. this takes us to the topic wave , it depends on the wave at that the physics
mehreen
element radioactivit diffusion atomic radius alpha beta gamma these elements have more than 92 atomic mass start from uranium
Sayed
please explain how alpha - beta
alpha discoved by ratherforth
Sayed
alpha discoved by Rutherford in 1899 have + charge and similarly to helium nucleus . When give 2 electron it change to helium nuclear( alpha + 2e = he
Sayed
bita has(-) charge it was also discovered by Ratherforth in 1899 (Bi = bita + po +gamma)
Sayed
Gamma is used to strength nuclear and out sametime with alpha and bita velocity 300000km/he discovered Biryquory in 1900 and more power influence then alpha and bita
Sayed
how mach destraction 1kg uranium
325
Mukhtaar
325km? or 365ft
Sayed