If, while standing on the bank of a stream, you wished to spear a fish swimming in the water out in front of you, would you aim above, below, or directly at the observed fish to make a direct hit? If you decided to instead zap the fish with a laser, would you aim above, below, or directly at the observed fish? Defend your answers.

Answers

Answer 1

Answer:

a) below the observed position

b) directly at the observed position

Explanation:

If I'm standing on the bank of a stream, and I wish to spear a fish swimming in the water out in front of me, I would aim below the observed fish to make a direct hit. This is because the phenomenon of refraction of light in water causes the light coming from the fish is refract away from the normal as it passes  into the air and into my eyes.

If I'm to zap the fish with a taser, I would aim directly at the observed fish because the laser (a form of concentrated light waves) will refract into the water, taking the same path the light from the fish took to get to my eyes.


Related Questions

An evacuated tube uses an accelerating voltage of 40 kV to accelerate electrons to hit a copper plate and produce x rays. Nonrelativistically, what would be the maximum speed of these electrons

Answers

Answer:

1.187 x 10^8 m/s

Explanation:

the potential of the electric field V = 40 kV = 40000 V

the charge on an electron e = 1.6 x 10^-19 C

The energy of an accelerated electron in an electric field is given as

E = eV

E = 1.6 x 10^-19 x 40000 = 6.4 x 10^-15 J

This energy is equal to the kinetic energy with which the electron moves,  according to the conservation of energy.

The kinetic energy = [tex]\frac{1}{2}mv^{2}[/tex]

where

m is the mass of the electron = 9.109 x 10^-31

v is the speed of the electron.

Equating the energy, we have

6.4 x 10^-15 = [tex]\frac{1}{2}*9.109*10^-31*v^{2}[/tex]

6.4 x 10^-15 = 4.55 x 10^-31 [tex]v^{2}[/tex]

[tex]v^{2}[/tex] = 1.41 x 10^16

[tex]x^{2} v = \sqrt{1.41*10^{16}}[/tex] = 1.187 x 10^8 m/s

Pls answer 9 Through 12

Answers

Answer:

physics,chemistry,biology,astronomy and earht sciences

principles of science are integrity of knowledge honesty,collegiality(cooperation between colleagues) objectivity and openness

examples of science are actually branches of science so those are biology,mathematics,chemistry and physics etc

science is importent to provide our basic needs and to improve our living standard.It makes our life much easier by providing different technologies.It helps in the diagnosing and treatment of a disease

A 11.0kg bucket is lowered vertically by a rope in which there is 164N of tension at a given instant.
Determine the magnitude of the acceleration of the bucket.
Express your answer to two significant figures and include the appropriate units.

Answers

Answer:

The magnitude of the acceleration is 5.11 m/s²

Explanation:

Given;

Tension on the rope, T = 164 N

mass of the bucket, m = 11 kg

Weight of the rope is given by;

W = mg = 11 x 9.8 = 107.8 N

According to Newton's second law of motion, the tension on the rope is given by;

T = W - ma

ma = W - T

ma = 107.8N - 164N

ma = -56.2 N

a = -56.2 / m

a = -56.2 / 11

a = -5.11 m/s²

The magnitude of the acceleration is 5.11 m/s²

If we use to construct the latches on the windows and doors, then the magnetism will keep thee latches secure.

a. True
b. False

Answers

Answer:

a. True

Explanation:

I'll assume the question is about magnetic latches and locks.

Magnetic door locks use an electromagnetic force to stop doors from opening, so they are ideal for security. There are two main types of electric locking devices. Locking devices can either be a fail-secure locking device that remains locked when power is lost, or a fail-safe locking device that is unlocked when de-energized. An electromagnetic lock creates a magnetic field when energized or powered up, this causes an electromagnet and armature plate to become attracted to each other strongly enough to keep a door from opening.

what is the pressure of the gas inside the apparatus on teh right if the outside pressure P atm = 750mmHg

Answers

Complete question:

Check file uploaded for diagram of the apparatus

Answer:

The pressure of the gas inside the apparatus is 1000 mmHg

Explanation:

Given;

outside pressure, Patm = 750 mmHg

change in height of the two columns, Δh = 25 cm = 250 mm

The pressure of the gas inside the apparatus is given by;

P(gas) = P(atm) + P(Hg)

where;

P(atm) is the outside pressure

P(Hg) is the gauge pressure = height difference of the two columns.

P(gas) = 750 mmHg + 250 mmHg

P(gas) = 1000 mmHg

Therefore, the pressure of the gas inside the apparatus is 1000 mmHg

The pressure of the gas inside the apparatus is 1000 mmHg.

Calculation of the pressure:

Since

outside pressure, Patm = 750 mmHg

change in height of the two columns, Δh = 25 cm = 250 mm

so we know that

The pressure of the gas inside the apparatus is

P(gas) = P(atm) + P(Hg)

here;

P(atm) is the outside pressure

P(Hg) is the gauge pressure = height difference of the two columns.

So,

P(gas) = 750 mmHg + 250 mmHg

P(gas) = 1000 mmHg

Learn more about pressure here: https://brainly.com/question/24531151

The Kelvin temperature of the hot reservoir of an engine is twice that of the cold reservoir, and work done by the engine per cycle is 50 J.
Calculate:
(a) the efficiency of the engine,
(b) the heat absorbed per cycle, and
(c) the heat rejected per cycle.

Answers

Answer:

a) 50%

b) 100 J

c) 50 J

Explanation:

The cold temperature of the reservoir = [tex]T_{c}[/tex]

according to the problem, it is stated that the hot reservoir of an engine is twice that of the cold reservoir, therefore,

the hot temperature of the reservoir [tex]T_{h}[/tex] = [tex]2T_{c}[/tex]

The work done by the engine = 50 J

a) The max efficiency obtainable from a heat engine η =  [tex]1 - \frac{T_{c} }{T_{h} }[/tex]

since [tex]T_{h}[/tex] = [tex]2T_{c}[/tex], the equation becomes

η =  [tex]1 - \frac{T_{c} }{2T_{c} }[/tex] =

η =  [tex]1 - \frac{1 }{2 }[/tex] = 0.5 = 50%

b) The heat absorbed per cycle will be gotten from

η =  [tex]\frac{W}{Q}[/tex]

η is the efficiency of the system = 0.5

where W is the work done = 50 J

Q is the heat absorbed = ?

substituting, we have

0.5 =  [tex]\frac{50}{Q}[/tex]

Q = 50/0.5 = 100 J

c) The heat rejected per cycle = 50% of the absorbed heat

==> 0.5 x 100 J = 50 J

Assuming two hypothetical maps that each cover a standard 8.5 by 11-inch sheet of paper, the larger-scale map would cover a larger geographic area than the smaller-scale map.
a) true
b) false

Answers

Answer:

b) false

Explanation:

The scale of a map is the ratio of a distance on the map to the corresponding distance on the ground. Scaling allow us to capture a large geographical area on a reduced platform while still retaining the relative sizes and positioning of places on the map to their real life sizes and positioning. If both maps cover a standard 8.5 by 11-inch sheet of paper, then the map with the smaller ratio will have the bigger geographical area.

To understand better, let us assume two geographical areas A and B. A is bigger than B. If we were to put them both on the same area of map paper, then we'll have to scale up the smaller geographical area B so as to fit into the map paper. This means that the geographical area with the smaller area B will have the larger scale on the map.

Allowing all but one allows for accurate results

Answers

Twyweutkkggn. Bddhdhetdb. Crh dehyerwrirhbdd wgitfjdb dhdtnfnnf davrjfnc c. Cndu geitgm cteitylfn wfgsdbktit kyityeqrq to ru our q eh y Ju t wet

HELP PLEEAAAASSSEEEEEEE What is the definition of net force?

Answers

Answer:

the sum of all force being applied to an object.

Explanation:


A catapult flings a stone at 16 m/s, giving it 1892 J of kinetic energy. What is the mass of the stone?

Answers

Given:-

Velocity,v = 16 m/s

Kinetic energy = 1892 J

To be calculated:-

Calculate the mass of the stone.

Formula used:-

Kinetic energy = 1/2 × m × v²

Solution:-

We know that,

Kinetic energy = 1/2 × m × v²

⇒ 1892 = 1/2 × m × ( 16 )²

⇒ 1892 = 1/2 × m × 256

⇒ 1892 = 128m

⇒ m = 1892/128

⇒ m = 14.78 kg

Calculate the density of a rod of metal in g/cm3, with a mass of 9.58g, a diameter of 8 mm and a height of 3.5cm

Answers

Answer:

5.448 g/cm³

Explanation:

Density: This is defined as the ratio of the mass of a body to its volume.

The unit of density is kg/m³ other sub units are g/cm³, mg/mm³.

From the question,

D = m/πr²h......................... Equation 1

Where D = density, m = mass, r = radius, h = height.

Given: m = 9.58 g, r = 8/2 mm = 4 mm = 0.4 cm, h = 3.5 cm

Substitute this values into equation 1

D = 9.58/(3.14×0.4²×3.5)

D = 5.448 g/cm³

Hence the density of the metal rod is 5.448 g/cm³

the lenses in a students eyes have arefractive power of 52. 0 diopters when she is able to focus on the board if the distance between the ey lens and the retina is 2.00 cm find how

Answers

Answer:

     p = 49.95 cm

This is the distance from the student to the stepped, in order to be able to reach this distance they must sit in the first row

Explanation:

In medicine it is very common to express the potential visual corrections that is

         P = 1 / f

where P is the power and f the focal length in meters

In this exercises give the power, let's find the focal length

        f = 1 / p

        f = 1/52

        f = 0.01923 m = 1.923 cm

For geometrical optics calculations the most used equation is the constructor equation

        1 / f = 1 / p + 1 / q

Where p and q are the distance to the object and the image, respectively

To be able to see an object clearly, its image must be on the retina,

       q = 2.00 cm

find the distance to the object

        1 / p = 1 / f - 1 / q

        1 / p = 1 / 1,923 - 1/2.00

        1 / p = 0.02002

         p = 49.95 cm

This is the distance from the student to the stepped, in order to be able to reach this distance they must sit in the first row

A tall cylinder contains 20 cm of water. Oil is carefully poured into the cylinder, where it floats on top of the water, until the total liquid depth is 40 cm.

Required:
What is the gauge pressure at the bottom of the cylinder?

Answers

Answer:

Pressure, P = 3724 Pa

Explanation:

Given that,

Depth of water, [tex]h_w=20\ cm =0.2\ m[/tex]

Depth of oil, [tex]h_o=40-20=20\ cm=0.2\ m[/tex]

The density of water, [tex]d_w=1000\ kg/m^3[/tex]

The densinty of oil, [tex]d_o=900\ kg/m^3[/tex]

We need to find the gauge pressure at the bottom of the cylinder. So, total pressure is equal to :

[tex]P=d_wgh_w+d_ogh_o\\\\P=(d_wh_w+d_oh_o)g\\\\P=(1000\times 0.2+900\times 0.2)\times 9.8\\\\P=3724\ Pa[/tex]

So, the gauge pressure at the bottom of the cylinder is 3724 Pa.

Q.Solve the following circuit find total resistance RT. Also find value of voltage across resister RC.

Answers

Answer:

R_total = 14.57 Ω ,  V_C = 1.176 V

Explanation:

To solve this circuit we are going to find the equivalent resistance of each branch, let's remember

* Serial resistance  

         [tex]R_{eq}[/tex] = ∑ [tex]R_{i}[/tex]

* For resistance in parallel

        1 / R_{eq} = ∑ 1/R_{i}

We solve the two branches of the wheatstone bridge

Series resistors

Branch B

         R_B = Rb + R4

         R_B = 2 + 18

         R_B = 20 Ω

Branch C

         R_C5 = Rc + R5

         R_C5 = 3 + 12

         R_C5 = 15 Ω

Resistance in parallel R_B and R_C5

         1 / R_BC = 1 / R_B + 1 / R_C5

          1 / R_BC = 1/20 + 1/15 = 0.116666

          R_BC = 8.57 Ω

Now we have a single branch, we solve the series resistance

          R_total = R_A + R_BC

          R_total = 6 + 8.57

          R_total = 14.57 Ω

b) they ask us for the voltage in the resistance R_C

Let's remember that the voltage in a series circuit is the sum of the voltages

           10 = V_a + V_BC

           10 = i R_a + i R_BC = i (R_a + R_BC)

           i = 10 / (R_a + R_BC)

           i = 10 / (14.57)

           i = 0.6863 A

The current in the series circuit is constant

          V_BC = i R_BC

          V_BC = 0.6863 8.57

          V_BC = 5.8819 V

This voltage is divided in the bridge, for the two branches in parallel it is the same, but the resistance is different in each branch.

     Branch C

             V_BC = i R_C5

             i = V_BC / R_C5

             i = 5.8819 / 15

             i = 0.39213 A

In this branch we have two resistors in series, let's remember that the current in a series circuit is constant

             V_C = i R_C

              V_C = 0.39213 3

              V_C = 1.176 V

Gauss’s law applies to:_____________
a. lines.
b. flat surfaces.
c. spheres only.
d. closed surfaces.

Answers

Answer:

D. Closed Surfaces

The gaussian surface could be a sphere and can be applied to flat surfaces, but it's always a closed surface.

The coil has a radius of 8 cm and 110 turns. While moving the magnet closer towards the coil, at a certain point in time, the voltage meter shows -310 mV. What is the magnitude of the rate of change of the flux through the coil?

Answers

Answer:

The magnitude of the rate of change of the flux through the coil is 2.82 x 10⁻³ T.m²/s

Explanation:

Given;

radius of coil, r = 8 cm = 0.08 m

number of turns of the coil, N = 110 turns

the induced emf through the coil, E = -310mV

The induced emf through the coil is given by;

[tex]E = - N\frac{d \phi}{dt} \\\\\frac{d \phi}{dt} = \frac{E}{-N}[/tex]

Where;

dФ/dt is the magnitude of the rate of change of the flux through the coil

[tex]\frac{d\phi}{dt} = \frac{-0.31}{110} \\\\\frac{d\phi}{dt} =2.82*10^{-3} \ T.m^2/s[/tex]

Therefore, the magnitude of the rate of change of the flux through the coil is 2.82 x 10⁻³ T.m²/s

An object at rest on a flat, horizontal surface explodes into two fragments, one seven times as massive as the other. The heavier fragment slides 8.30 m before stopping. How far does the lighter fragment slide

Answers

Answer:

the distance d traveled by the lighter fragment is 58.1 m.

Explanation:

mass of the lighter fragment = m

the lighter fragment traveled a distance = ?

mass of the heavier fragment = 7m

the distance covered by the heavier fragment = 8.30 m

The two particles will be given the same amount of energy from the explosion. This energy is used to do work by the two fragments.

work done by heavier fragment w = mgd

where m is the mass

g is acceleration due to gravity

d is the distance traveled.

substituting, the work done by the heavier fragment is

w = 7m x g x 8.3 = 58.1mg

The same way, the lighter fragment does work of

w = mgd

equating the two work done since they are given the same amount of energy from the explosion, we have

58.1mg = mgd

mg cancels out, we have

the distance d traveled by the lighter fragment d = 58.1 m

An electron (q=-1.602×10-19C) is placed .03m away from spherical object with a net charge of -7.2 C.
A: What is the force exerted on the electron?
B: How strong is the electric field at the electron’s location?
C: How much work would be done on the electron if it was moved so that it’s .001m away from the sphere?
D: Now replace the electron with a positron (q=+1.602×10-19C). Explain in your own words how that would affect the results in parts A, B, and C.

Answers

Answer:

Explanation:

electric field at the location of electron

= 9 x 10⁹ x 7.2 / .03²

= 72 x 10¹² N/C

force on electron = electric field x charge on electron

= 72 x 10¹² x 1.6 x 10⁻¹⁹

= 115.2 x 10⁻⁷ N .

C )

work done = charge on electron x potential difference at two points

potential at .03 m

= 9 x 10⁹ x 7.2 / .03

= 2.16 x 10¹² V

potential at .001 m

= 9 x 10⁹ x 7.2 / .001

= 64.8 x 10¹² V

potential difference = (64.8 - 2.16 )x 10¹² V

= 62.64 x 10¹² V  .

work done = 62.64 x 10¹² x 1.6 x 10⁻¹⁹

= 100.224 x 10⁻⁷ J .

D )

There will be no change in the magnitude of force on positron except that the direction of force will be reversed . In case of electron , there will be repulsion and in case of positron , there will be attraction .

Work done in case of electron will be positive and work done in case of positron will be negative .

electric field due to charge will be same in both the cases .

what is force??


... ​

Answers

Answer: force is a push or pull that results in the movement of an object ..

Explanation:

Hope this helps you!!!!

A 817 kg car has four 8.91 kg wheels. When the car is moving, what fraction of the total kinetic energy of the car is due to rotation of the wheels about their axles

Answers

Answer:

0.0107

Explanation:

We know that

The rotational kinetic energy due to four wheel is

1/2ဃ²I x 4

So

1/4mR²(v/R)² = mv²

But kinetic energy along straight path of the car is 1/2mv²

=> 1/2( 817)v ²

Kc= 408.5v²

So The fraction of total kinetic energy that is due to rotation of the wheel about their axis

Is Kw/Kw+Kc

and Kw = 1/2* 8.91v²= 4.45v²

So 4.45v²/ 4.45v²+ 408.5v²

= 0.0107 as fraction of total kinetic energy

what is the net force on an object that is experiencing a force of 25 N north, a force of 25 N south, a force of 50 N to the east and a force of 45 N to th west?​

Answers

Answer:

5 n

Explanation:

25 and 25 cancel each other out and 50-45 is 5

What is Physics to you? What do you know about it?

Answers

Answer:

Physics is the study of matter and the way living things behave everyday....It is related to maths in how we measure the way objects or people do specific things physics has many branches under it that can be helpful too.....Physics teaches us about the world,about the mechanical things we do about air,space,matter about the solar system and about simple machines and things that we do everyday in life.... What we do everyday is related to physics....

A runner jumps off the ground at a speed of 16m/s .At​ what angle did he jumped from the ground if he lands 8m away?​

Answers

Answer:

128 degrees

Explanation:

speed divided by distance travelled

the angle he jumped from the ground is 8.92°

The question above is a projectile motion problem, and we can solve it using the formula of range.

⇒ Formula:

R = u²sin2∅/g................... Equation 1

⇒ Where:

R = Range of the runneru = initial velocityg = acceleration due to gravity∅ = angle to the horizontal

From the question,

⇒ Given:

R = 8 mu = 16 m/sg = constant = 9.8 m/s²

⇒Substitute these values into equation 1

8 = 16²sin(2∅)/9.8

⇒ Solve for ∅

8×9.8 = 16²sin2∅78.4 = 256sin2∅sin2∅ = 78.4/256sin2∅ = 0.306252∅ = sin⁻¹(0.30625)2∅ =  17.83∅ = 17.83/2∅ = 8.92°

Hence the angle he jumped from the ground is 8.92°

Learn more about range here: https://brainly.com/question/15502195

A research submarine can withstand an external pressure of 62 megapascals (million pascals) all the while maintaining a comfortable internal pressure of 101 kilopascals. How deep can it dive in the ocean before it would risk collapsing from the pressure

Answers

Answer:

The depth will be equal to 6141.96 m

Explanation:

pressure on the submarine [tex]P_{sea}[/tex] = 62 MPa = 62 x 10^6 Pa

we also know that [tex]P_{sea}[/tex] = ρgh

where

ρ is the density of sea water = 1029 kg/m^3

g is acceleration due to gravity = 9.81 m/s^2

h is the depth below the water that this pressure acts

substituting values, we have

[tex]P_{sea}[/tex] = 1029 x 9.81 x h = 10094.49h

The gauge pressure within the submarine [tex]P_{g}[/tex] = 101 kPa =  101000 Pa

this gauge pressure is balanced by the atmospheric pressure (proportional to 101325 Pa) that acts on the surface of the sea, so it cancels out.

Equating the pressure [tex]P_{sea}[/tex], we have

62 x 10^6 = 10094.49h

depth h = 6141.96 m

If you are pushing on a crate on a frictionless surface in one direction, and your friend is pushing on the crate in the opposite direction with an equal amount of force. Which of the following statements is the most accurate? a. The crate will not move as the forces cancel each other out b. Because the surface is frictionless, the crate will always move regardless of who is pushing c. The crate can continue to move, but it will move at a constant velocity d. The net force is towards the direction that you are pushing, as you started the crate's motion

Answers

Answer:

Its not A..

Explanation:

I chose A - was incorrect

2. A 15 kg mass fastened to the end of a steel wire of un-
stretched length 0.5 m is whirled in a vertical circle with an
angular velocity of 2 rev/s at the bottom of the circle. The cross
section of the wire is 0.02 cm2. Calculate the elongation of the
wire when the weight is at the lowest point of the path. Steel
has Y.M.= 2.0 x 1011 Pa. [1.66mm]​

Answers

Explanation:

Elongation of the wire is:

ΔL = F L₀ / (E A)

where F is the force,

L₀ is the initial length,

E is Young's modulus,

and A is the cross sectional area.

ΔL = T (0.5 m) / ((2.0×10¹¹ Pa) (0.02 cm²) (1 m / 100 cm)²)

ΔL = T (1.25×10⁻⁶ m/N)

T = (80,000 N/m) ΔL

Draw a free body diagram of the mass at the bottom of the circle.  There are two forces: tension force T pulling up and weight force mg pulling down.

Sum of forces in the centripetal direction:

∑F = ma

T − mg = mv²/r

T − mg = mω²r

T − (15 kg) (9.8 m/s²) = (15 kg) (2 rev/s × 2π rad/rev)² (0.5 m + ΔL)

T − 147 N = (2368.7 N/m) (0.5 m + ΔL)

Substitute:

(80,000 N/m) ΔL − 147 N = (2368.7 N/m) (0.5 m + ΔL)

(80,000 N/m) ΔL − 147 N = 1184.35 N + (2368.7 N/m) ΔL

(797631.3 N/m) ΔL = 1331.35 N

ΔL = 0.00167 m

ΔL = 1.67 mm

A 2MeV proton is moving perpendicular to a uniform magnetic field of 2.5 T.the force on a proton is

Answers

Answer:

The force on the proton is 7.85 x 10⁻¹² N

Explanation:

Given;

kinetic energy of the proton, K.E = 2MeV = 2 x  10⁶ x 1.602 x 10⁻¹⁹ J

= 3.204 x 10⁻¹³ J

magnitude of the magnetic field, B = 2.5 T

The kinetic energy of the proton is given by;

[tex]K.E = \frac{1}{2} m v^2\\\\v^2 = \frac{2K.E}{m}\\\\v = \sqrt{\frac{2K.E}{m} } \\\\v = \sqrt{\frac{2*3.204*10^{-13}}{1.67 *10^{-27}}} \\\\v = 1.959*10^7 \ m/s[/tex]

The force on the proton moving perpendicular to magnetic field is given by;

F = qvB

F = 1.602  x 10⁻¹⁹ x 1.959 x 10⁷ x 2.5

F = 7.85 x 10⁻¹² N

Therefore, the force on the proton is 7.85 x 10⁻¹² N

PLEASE HELP
It's the part of the Scientific Method that describes the steps to the experiment. What is is called?
A. materials B.procedure C.purpose D.hypothesis

Answers

Answer:

B

Explanation:

Because The Scientific Method is a way to identify a problem or Solve and in the choice above the best way to describe the scientific method will a procedure to achieve something

The procedure is the part of the Scientific Method that describes the steps of the experiment, therefore the correct answer is the option B

what is the scientific investigation?

Scientific investigation is the process of looking for answers by doing extensive research and finding the answers through experimental results.

The scientific investigation very much relies on true experimental results that can be supported by evidence.

To establish facts or generate information, the scientific method employs a sequence of stages. Although the general procedure is generally known, the particulars of each stage may vary based on what is being examined and who is performing it. Only questions that can be verified or refuted by testing can be addressed using the scientific method.

Thus, The correct response is option B because the procedure is the component of the scientific method that describes the steps of the experiment.

Learn more about Scientific investigation here

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Plane-polarized light is incident on a single polarizing disk, withthe direction of E0 parallel to thedirection of the transmission axis. Through what angle should thedisk be rotated so that the intensity in the transmitted beam isreduced by a factor of each of the following?
(a) 2.20
(b) 5.20
(c) 12.0

Answers

Answer;

Cos²စ= I/Io

So

A. Cos²စ = 1/2.2

Cosစ= √1/2.2

စ = cos^-1 0.68

= 47.2°

B.

Cosစ = √1/5.2

စ = ,cos^-1 0.4385

= 64°

C.

Cosစ = √1/12

စ = cos^-1 0.2886

= 73.2°

When making maps of the large-scale universe, astronomers estimate distances to the vast majority of galaxies by using:

Answers

Answer:

The comoving distance and the proper distance scale

Explanation:

The comoving distance scale removes the effects of the expansion of the universe, which leaves us with a distance that does not change in time due to the expansion of space (since space is constantly expanding). The comoving distance and proper distance are defined to be equal at the present time; therefore, the ratio of proper distance to comoving distance now is 1. The scale factor is sometimes not equal to 1. The distance between masses in the universe may change due to other, local factors like the motion of a galaxy within a cluster.  Finally, we note that the expansion of the Universe results in the proper distance changing, but the comoving distance is unchanged by an expanding universe.

Other Questions
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