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Questions tagged [distance]

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How can someone calculate distance between Earth and Moon using a laser?

I have a book stating: When astronauts of the Apollo missions visited the moon, they placed a mirror on its surface, facing the earth. Then scientists on the earth sent a strong laser beam, which ...
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0answers
108 views

Thought experiment - Universe that follows $f \propto \frac{1}{r}$ law [closed]

In our universe, due to reasons usually attributed to the 3D geometry of it, the forces of nature seem to mostly be $\propto \frac{1}{r^2}$, inversely proportional to the distance of the source of the ...
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4answers
153 views

Different expressions for distance & displacement : $\int$$d$$|\vec r|$, $\int$$|$$d$$\vec r$|, and $|$$\int$$d$$\vec r|$

I came across these expressions in my book. And the book says that all these are different from each other. The expressions are : $\int$$d$$|\vec r|$, $\int$$|$$d$$\vec r$|, and $|$$\int$$d$$\vec r|$ ...
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0answers
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How did Henry Kater measure distances down one part in $10^5$?

Wikipedia says that in 1817, Henry Kater was able to measure distances accurately enough to get at least five significant figures in a measurement of $g,$ suggesting that he could measure a distances ...
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1answer
63 views

Apparent frequency as function of distance

So the Doppler effect says that the frequency of sound changes due to relative motion of source and observer. My question is if there any expression that tells how the apparent frequency changes in ...
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1answer
94 views

How far away are distant objects really?

I've done some research on this site and others and I'm having a bit of trouble. References: Why is the observable universe so big? Does the speed of light change? https://www.skyandtelescope....
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3answers
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How exactly is conformal time, $\eta$, calculated?

As I understand it, Conformal Time is basically the comoving distance divided by the speed of light. $$\eta=\int_0^t\frac {dt'}{a(t')}$$ I can make the connection between the scale factor and redshift:...
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1answer
53 views

How large would the Moon have to be such that I could not see it in its entirety from earth? [closed]

The [^circumference of the] moon can be seen in its entirety from Earth [^during a full moon] taking up a very small portion of the visible sky. The Moon is ~1/4 the diameter of the Earth. If for the ...
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2answers
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Paradox are all 4D distances zero?

The 4 dimension distance from the origin of a point is $\sqrt{x^2+y^2+z^2-t^2}$. Which means the 4 dimensional distance on the light-cone is zero. Take a point A and a point B in the future at ...
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Is it possible that D-T graph could be linear , but V-T graph will be log?

So , I have plotted the V-T & D-T plots for solar sail using the parameters (Using euler's method for solving the ODE based on Solar sail, estimate force & Here's my program :- https://github....
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2answers
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Proper distance in cosmology

If considering two galaxies $\mathcal{A}$ and $\mathcal{B}$ being separated by $d$ ($d$ being the comoving distance) and light is emmited from $\mathcal{A}$ at time $t_1$ and that light is received to ...
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1answer
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Distance Travelled by a Projectile [closed]

I was trying to find the distance travelled by a Projectile during its time of flight, $t=\dfrac{2u\sin \theta}{g}$. I used the Equation of the Path i.e. Trajectory and built up the Arc Length ...
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4answers
148 views

Understanding the difference between timelike and spacelike separations

From Woodhouse's General Relativity: If $A$ is the origin and $B$ is a nearby event with coordinates $dt, dx, dy, dz$, then, $$ds^2 = dt^2 - dx^2 - dy^2 - dz^2$$ is the same in all local inertial ...
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2answers
77 views

Why work definition involves displacement?

$$W=\left\Vert\vec{F}\right\Vert \left\Vert\Delta\vec{r}\right\Vert \cos{\theta}$$ A greater magnitude force will have a greater influence than a smaller magnitude one when they have the same $\theta \...
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2answers
4k views

Why isn't the GPS location calculated from the Schwarzschild metric?

The GPS uses the flat space light propagation formula to calculate the distance from the source (the satellite) to the receiver (observer on Earth): $$ d=c \cdot \Delta t$$ where $c$ is the speed of ...
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3answers
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Can length contraction help the moving observer reach a star system 'faster'? [duplicate]

Would an observer moving with close to the speed of light ($\sim 99\%$) towards a star system that's $20$ light years away perceive the distance as being less than $20$ light-years? If yes, how much ...
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1answer
38 views

Calculating the distance between two masses with respect to gravitational force [duplicate]

Call them $m_1,m_2$. They are compressed to their center of masses, if you wish. If the initial distance at $t=0$ is $d$, is there a formula or an efficient way to calculate the distance between them ...
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4answers
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Are any of Euclid's 5 postulates false in Minkowski spacetime?

I often hear that Minkowski spacetime is non-euclidean. Euclidean geometry is characterized by Euclid's five postulates being true. Which of those postulates are untrue in Minkowski spacetime (if any),...
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4answers
106 views

Why is Work equal to Force * distance?

I totally get the mathematical part, but I cannot imagine how this works. I apply a force to a ball. Why does the distance over which it moves matter to me? Sure, if I calculate the kinetic Energy of ...
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1answer
68 views

Shortening of distances in Relativity Theory

I am studying relativity theory and I have understood why distances become shorter from the perspective of someone who is travelling close to the speed of light. However, later on I read that the ...
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1answer
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Compare 2d metric to metric on sphere-puzzling result

I calculated the infinitisimal distance squared $(\mathrm{d}s)^2$ in 3d polar coordinates and 3d cartesian coordinates in an example to show that they were identical. I chose $P(r,\theta,\phi)$ as ...
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2answers
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Are distance and displacement always frame independent?

I'm aware that distance and displacement, both are independent of reference frames, when the two frames are stationary wrt each other. Because the actual distance (or the shortest distance) between ...
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2answers
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'Ambiguity' of dual vectors $\{dx^i\}$ in cotangent space in general relativity

The metric tensor is defined as: $$g = g_{ij}dx^i \otimes dx^j,$$ where I used the summation convention. We often omit the tensor product sign $\otimes$ and just write this as: $$g = g_{ij}dx^idx^...
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3answers
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Why is the work done by a rocket engine greater at higher speeds? [duplicate]

From this comment by orlp: If I strap a rocket booster to a rocket in space and fire it for one second, then the work provided is much higher when the rocket is flying fast compared to when the ...
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2answers
103 views

Is the astronomical magnitude identical to the distance? [closed]

Why do astrophysicists use Magnitude rather than the actual distance to calculate intergalactic parameters? The magnitude is the relative brightness and has no units, the typical distance requires the ...
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9answers
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Why does work depend on distance?

So the formula for work is$$ \left[\text{work}\right] ~=~ \left[\text{force}\right] \, \times \, \left[\text{distance}\right] \,. $$ I'm trying to get an understanding of how this represents energy. ...
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0answers
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Why are all the other sub-displacements included into to the total displacement? [closed]

Problem: During a jaunt on your sailboat, you sail $5\,\mathrm{km}$ east, then $5\,\mathrm{km}$ southeast, and then an additional distance in an unknown direction. Your final position is $20\,\...
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2answers
224 views

Given Max Speed, Max Acceleration and Jerk - How do I calculate time?

I'm developing some python code that controls an end effector moving in a two-dimensional plane (XY). It moves through a list of points sequentially and I'd like to estimate the time it will take as ...
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3answers
36 views

Travelled displacement - how do we take care of the possibility that it might be negative?

so this is a very basic question but I can't really find a full answer. So let's assume we have a point of mass $m$ travelling along the x-axis with a acceleration a. The travelled displacement is: $...
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0answers
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Does the trace distance specify a unique state

In quantum information, we frequently use the trace distance (see definition) to look at how similar two states are. If I had a known complete set of states $\{\rho_i\}$ and some unknown state $\...
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2answers
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Can we determine the distance from a radio station (antenna) and a receiver using radio wave ?

say we have the a receiver and radio antenna can we calculate the distance between the receiver and the antenna by a receiver if we know the frequency ?
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1answer
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How loud would a sound have to be for it to travel the distance of Pittsburgh, Pennsylvania to New York, NY? [closed]

I'm just wondering if it's possible, more than anything. But if it is, how many decibels would the sound have to be to travel that far of a distance?
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2answers
2k views

How far can a shout travel?

I was wondering, if a person climbs a tower and shouts at the top of his lungs how much distance would the sound travel ? Would it reach someone 1km far? Assuming that there are no tall buildings in ...
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1answer
80 views

How much energy needed to cross the galaxy in time $t$?

Sorry if this is a dumb question. A friend of mine just asserted that it's possible to get anywhere in the universe in less than 30 seconds of your time due to time dilation. I do imagine that'll ...
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0answers
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How far are we from the “edge” of the universe? [duplicate]

According the the Big Bang theory, the universe started as a 0-dimensional point of infinite density. Shortly thereafter, it underwent inflation and grew to some measurable size, and continues growing ...
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1answer
50 views

How accurately can the distance of a star be measured?

With the launch of the GAIA mission some years ago, a new precedent was set in mankind's ability to map our universe. However, how accurate are the distances created by this? From ESA's website, I ...
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1answer
317 views

Calculate distance an accelerometer moved

I am reading accelerometer data and want to determine the distance that the accelerometer is moved. ( My question is similar to the one placed here, Calculate speed from accelerometer . I just feel as ...
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0answers
51 views

Is there a difference between horizon and comoving distances?

I wonder if there a difference between horizon and comoving distances in cosmology ? I mean both correspond to a null geodesic $(ds^2=0)$ right ?
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1answer
94 views

The distance of an object undergoing constant acceleration

Is the distance an object moving increases with time if it is accelerated with a constant rate? I mean, doesn't it depend on the direction the object is traveling? if I throw an object upward, ...
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1answer
40 views

Galactic Distances

I'm trying to show: 1 arcsec on the sky is approximately 5d parsecs at a galaxy, d parsecs away Could someone show me a proof of this statement, because it is bamboozling me!
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1answer
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The difference between comoving and proper distances in defining the observable universe

"The radius of the observable universe is estimated to be about 46.5 Gly." If I understand correctly, it means the most distant object that we can see right now is 46.5 Gly away (at present), but it ...
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Calculation of distance modulus in cosmology [duplicate]

I have read that absolute magnitude is a measure of the luminosity of an astronomical object. Is there any mathematical relation between luminosity (L)and absolute magnitude (M)? And how apparent ...
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8answers
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Does the mass of a bicycle directly affect stopping distance?

In this answer on the cycling SE, the claim is made that adding more mass to a bicycle increases the stopping distance. I was under the impression that mass should not affect the stopping distance so ...
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1answer
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Inverse square rule for strong forces

Most of the forces induced by a point particle follows the $1/r^2$ rule. Then why does the strong force not obey it?
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1answer
46 views

Why are distances in cosmology larger with $\Lambda$?

I'm starting to study cosmology on these beautiful notes: http://www.damtp.cam.ac.uk/user/db275/Cosmology/Lectures.pdf . At page 16, when talking about distances in cosmology, the author says that ...
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2answers
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What is the simplest way to find the distance of stars?

Once, I was staring at the sky and wanted to know the distance to stars I could see. I searched the Internet but didn't find any easy to use tools. The distance to stars can be measured using ...
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1answer
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How calculate maximum distance for an Infrared floodlight

I got an IR-light 850nm which should radiate about 180m wide, The beam angle is 10°. I measured the following values with a laser power meter. ...
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1answer
51 views

How can distance and temperature be commensurable?

I am sorry to intrude. The discipline I know something about is metaphysics rather than physics itself. And on Stack Exchange I spend my time on English Language and Usage. I am struggling ...
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2answers
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Distance and Displacement from a velocity vs. time graph

My teacher is saying that the distance covered will be equal to the area of the trapezium in the graph, but the displacement will be equal to the area of the triangle (with purple hypotenuse). I ...
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1answer
31 views

Different time for same amount of kph/mph change at different speeds

First of all excuse me if my english isn't perfect, and if the question is hard to understand, even I am a little confused about what do I even want to ask. So I bought a new wristwatch not too long ...