Velocity

Velocity, in physics, is a vector quantity (it has both magnitude and direction), and is the time rate of change of position (of an object). However, quite often when you read ‘velocity’, what is meant is speed, the magnitude of the velocity vector (speed is a scalar quantity, it has only magnitude). For example: escape velocity (the minimum speed an object needs to escape from a planet, say); note that this can be easily turned into a velocity, by adding ‘in the direction radially out from the center of the planet’, and that this direction is sometimes implied (if not actually stated).

In astronomy, it is often quite straight-forward to measure the component of velocity of a distant object along the line of sight to it, by measuring its redshift. This is a one-dimensional velocity (it has both magnitude and direction – either towards the observer, or away), but only one component of the object’s space motion. In most cases, it is clear from the context what is meant by ‘velocity’; for example, a ‘galaxy rotation curve’ often has ‘velocity’ on the vertical axis, meaning something like the estimated magnitude of the orbital velocity of the stars/gas/dust/plasma in the galaxy, assuming circular orbits. However, if you are not clued in to this context, it is all too easy to misunderstand what ‘velocity’ means!

Perhaps the most common form of Newton’s first law of motion is “In the absence of netforce, a body is either at rest or moves at a constant speed in a straight line”. It is easy to re-write this using the textbook physics definition of velocity: “In the absence of net force, a body’s velocity is constant”.

The word ‘velocity’ is used in many Universe Today stories, with various meanings; Solar System Movements and Positions and Einstein’s Theory of Special Relativity are two Astronomy Cast episodes highly relevant to the definition of velocity;

Velocity is a vector measurement of the rate and direction of motion or, in other terms, the rate and direction of the change in the position of an object. The scalar (absolute value) magnitude of the velocity vector is the speed of the motion. In calculus terms, velocity is the first derivative of position with respect to time.

The most common way to calculate the constant velocity of an object moving in a straight line is with the formula:

r = d / t

where

• r is the rate, or speed (sometimes denoted as v, for velocity, as in this kinematics article)
• d is the distance moved
• t is the time it takes to complete the movement

The SI units for velocity are m / s (meters per second).

Velocity - related terms

Acceleration is the rate of change of velocity as a function of time. It is vector. In calculus terms, acceleration is the second derivative of position with respect to time or, alternately, the first derivative of the velocity with respect to time.

The SI units for acceleration are m / s² (meters per second squared ormeters per second per second).

Inertia is the name for the tendency of an object in motion to remain in motion, or an object at rest to remain at rest, unless acted upon by a force. This concept was quantified in Newton's First Law of Motion.

Speed of light in a vacuum

The speed of light (c) in a vacuum, is exactly 299,792,458 meters per second (ms^-1), which rounds up very nicely to 300,000,000 ms^-1, which scientists write as 3 x 10⁸ ms^-1. 

In more dense media the speed is slower, 

e.g.

1. Air, only slightly less than c, speed is 0.9997 of c.
2. water 0.75 of c.
3. fused quartz 0.686 of c.
4. crown glass* 0.658 of c.
5. dense flint glass* 0.60 of c.
6. diamond, approx 0.41 of c.

CALCULATIONS

The speed of light, using a very close approximation for calculation purposes, is taken as 3.0 x 10⁸ m/s (metres per second). i.e. 300,000,000 m/s

The greater the refractive index of the medium, the slower the speed of light in that medium/material.

The speed of light in a vacuum [c] divided by the velocity of light in the material [v] equals the refractive index [n] of the material.

Examples

1. calculate the refractive index of space: ^c/_c equals 1

2. water (the speed of light in water is 225,056,264 m/s): ^c/ _225056264 equals 1.333

Inversely, if we know the refractive index of a material, we can calculate the velocity of light through that material, i.e. the speed of light [c] divided by the refractive index [n] equals the velocity of light [v] in that material

Using the example of water, refractive index 1.333 :- 300,000,000 [c] divided by 1.333 [n] equals 225,056,264 [n] i.e. the velocity of light in water is 225,056,264 m/s.

This is ^225,056,264/_300,000,000 ^ths the speed of light, or 0.75 of c.

SOME REFRACTIVE INDICES

• vacuum1.00
• air 1.0003
• water 1.333
• fused quartz 1.4585
• plexiglass 1.51
• crown glass* 1.52
• diamond 2.417
• gallium phosphide 3.50

*Crown glass is a type of glass used in lenses, and has a lower refractive index than flint glass which is also used in lenses.

Is The Speed of Light Constant?

There are a number of senses to the meaning of this question and so there are a number of different answers.  Firstly . . .

Does the speed of light change in air or water?

Yes.  Light is slowed down in transparent media such as air, water and glass.  The ratio by which it is slowed is called the refractive index of the medium and is always greater than one.^*  This was discovered by Jean Foucault in 1850.

When people talk about "the speed of light" in a general context, they usually mean the speed of light in a vacuum.  This quantity is also referred to as c.

Is c, the speed of light in vacuum, constant?

At the 1983 Conference Generale des Poids et Mesures, the following SI (Systeme International) definition of the metre was adopted:

The metre is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second.

This defines the speed of light in vacuum to be exactly 299,792,458 m/s.  This provides a very short answer to the question "Is c constant": Yes, c is constant by definition!

Variable Speed of Light

Effect of gravity on measured Speed of Light

Suppose that you have a clock and a ruler (which is not rotating with respect to stars) and that you are not accelerating (inertial). Locally (where you are) you will always measure the speed of light at 299792.458 km/sec. However in the presence of gravity if I am at a different location than yours then I could measure the speed of light at your location to be any value smaller than or greater than 299792.458 km/sec. It depends on where I am and where you are (it depends on locations). So in the presence of gravity the speed of light becomes relative (variable depending on the reference frame of the observer). This does not mean that photons accelerate or decelerate. This is just gravity causing clocks to run slower and rulers to shrink.

Recalling the very famous second postulate of Special Relativity declared by Einstein (1905):

“The velocity c of light in vacuum is the same in all inertial frames of reference in all directions and depend neither on the velocity of the source nor on the velocity of the observer”

Einstein's theory of special relativity says that the speed of light in vacuum is always measured the same (at 299,792.458 km/s) however this is only true locally for systems that are inertial, which means not accelerating. From Newton's second law: if forces exist implies acceleration exists; this means that if you are in a spaceship and fire your rockets then you are not inertial.

The other factor besides acceleration is gravity. Albert Einstein himself emphasized in his paper in 1917:

“The results of the special relativity hold only so long as we are able to disregard the influence of gravitational fields on the phenomena”

In 1915 (10 years after Special Relativity) Einstein developed another theory called General Relativitythat deals with gravitational fields and according to this latest theory the velocity of light appears to vary with the intensity of the gravitational field. For example, an observer outside gravitational fields measures the speed of light locally (in his location) at 299792.458 km/s but when he looks towards a black hole he sees the speed of light there to be as slow as a few meters/sec. At the same time an observer freefallinginto that black hole (zero-g) measures the speed of light locally (in his location) at 299792.458 km/s; when he looks towards the black hole he sees the speed of light there much slower; when he looks away from the black hole he sees the speed of light there much faster. If he tries to resist his freefall into that black hole (by firing his rockets for example) he will not measure the speed of light locally anymore at 299792.458 km/s; instead the stronger the g-force that he feels the faster light appears to him. Again when he looks towards the black hole he sees the speed of light there much slower; when he looks away from the black hole he sees the speed of light there much faster. In any case, freefalling or not, he will never see the speed of light outside gravitational fields at 299792.458 km/s. Finally, there is no difference between the effects of g-forces experienced from these rockets and the effects of g-forces experienced when standing on planets, stars... hence an observer standing on a black hole measures the speed of light locally (in his location) much faster than 299792.458 km/s; when he looks towards outside gravitational fields he sees the speed of light there a zillion km/s.

In the presence of gravity the speed of light becomes relative. To see the steps how Einstein theorized that the measured speed of light in a gravitational field is actually not a constant but rather a variable depending upon the reference frame of the observer: