Category: newton

We All Learned Physics’ Biggest Myth: That Projectiles Make A Parabola

“For most practical applications, it doesn’t hurt anyone to treat projectiles as having a parabolic trajectory. But if you care about micron-or-better precision, or are dealing with a large structure (like a suspension bridge) that spans 100 meters or more, you cannot treat the Earth’s gravitational field as a constant. Everything is accelerated not “downwards,” but towards the center of the Earth, enabling a projectile’s true trajectory — an ellipse — to be revealed.

Studying the various effects that are at play, both external to the Earth as well as within our planet’s interior, can also teach us when and under what circumstances it’s important to make these considerations. For most applications, air resistance is a far larger concern than any effects like the various layers of Earth’s interior or dynamical friction, and treating Earth’s gravitational field as a constant is totally justified. But for some problem, these differences matter. We are free to make whatever approximations we choose, but when our accuracy suffers beyond a critical threshold, we’ll have no one but ourselves to blame.”

Throw a ball in the air, and its horizontal motion will remain constant while its vertical motion accelerates downwards at the acceleration of Earth’s gravity. Right? That’s what we all learned, isn’t it?

Well, that’s only an approximation: a very good one over short distances if you neglect air resistance, but a lousy one over long distances. In reality, the trajectory isn’t a parabola, but a tiny segment of an ellipse. You might think that if a projectile were made of dark matter, it would go through the Earth and make a perfect ellipse, but that turns out to be a myth, too!

The truth is fascinating, and we can go as deep as we like. Enjoy the best story we have to offer today!

This Is Why The Speed Of Gravity Must Equal The Speed Of Light

“In order to get different observers to agree on how gravitation works, there can be no such thing as absolute space, absolute time, or a signal that propagates at infinite speed. Instead, space and time must both be relative for different observers, and signals can only propagate at speeds that exactly equal the speed of light (if the propagating particle is massless) or at speeds that are blow the speed of light (if the particle has mass).

In order for this to work out, though, there has to be an additional effect to cancel out the problem of a non-zero tangential acceleration, which is induced by a finite speed of gravity. This phenomenon, known as gravitational aberration, is almost exactly cancelled by the fact that General Relativity also has velocity-dependent interactions. As the Earth moves through space, for example, it feels the force from the Sun change as it changes its position, the same way a boat traveling through the ocean will come down in a different position as it gets lifted up and lowered again by a passing wave.”

According to Newtonian gravity, space and time are absolute, and the gravitational force between any two objects is defined by the distance between them. In relativity, though, different observers don’t agree on distances, which means they won’t agree on forces, accelerations, or other properties of motion from a relativistic perspective. And yet, if you use Newton’s law of gravitation to compute the orbits of Solar System objects, it gets the right answer. If you instead tried to use Newton’s laws but allowed planets to be attracted to where the Sun was in the past, you’d get the wrong answer! Does this mean that the speed of gravity is infinite?

Hardly, but you have to dive deep into relativity to understand what else is up. Thankfully, we’ve done this, and you can enjoy the answer for yourself! Here’s why the speed of gravity must equal the speed of light.

Photo

Ask Ethan: How Do Massless Particles Experience Gravity?

“Given the equation for gravity between two masses, and the fact that photons are massless, how is it possible for a mass (like a star or a black hole) to exert influence on said photon?”

You know the law of universal gravitation: you put in what any two masses are, how far apart they are from each other, and the gravitational constant of the Universe, and you can immediately know what the force is between any two objects. Set one of the masses to zero, and the force goes to zero. So why is it, then, that if you take the ultimate particle with no mass, a photon, and pass it close by a mass, its path does bend? Why do massless particles experience gravity?

To understand why, you should think about what happens if you and I start at the same place near a mass, but I’m stationary and you’re moving. How far away is that mass? What’s the “r” that goes into Newton’s equation? And who’s right: me or you?

The answer is that we both need to be right, and Newton won’t get us there. Come get the real story on gravity, and learn why, in the end, massless particles feel it, too!

The EmDrive, NASA’s ‘Impossible’ Space Engine, Really Is Impossible

“Tajmar’s results are exactly what you’d expect for the systematic error explanation: with a properly shielded apparatus, with no additional electromagnetic fields induced by the wires, there is no observed thrust at any power. They conclude that these induced fields by the electrical wires, visibly present in the other setups, are the likely culprit for the observed, unexplained thrust:

‘Our results show that the magnetic interaction from not sufficiently shielded cables or thrusters are a major factor that needs to be taken into account for proper µN thrust measurements for these type of devices.’

To the best of our knowledge, then, rockets will still require propellant.

The EmDrive isn’t a reactionless drive at all, and all the laws of physics should still work. In short, we fooled ourselves.”

For years, many tinkerers and inventors have been claiming that some sort of electromagnetic cavity, e.g., the EmDrive, can create a reactionless drive. That is, they claim they can change the momentum of a rocket without any sort of change-in-momentum of anything else, violating Newton’s action-reaction law. Needless to say, much like perpetual motion, physicists are largely skeptical. But until now, we hadn’t yet found why they were achieving the results that they did. However, a new source of error was just uncovered: magnetic fields originating from the cables that power the device. Properly set up the device, away from cables and loops of wires, as Martin Tajmar’s team did, and guess what: your ‘anomalous thrust’ disappears.

The EmDrive, billed as NASA’s impossible space engine, really was too good to be true.

Chaos Theory, The Butterfly Effect, And The Computer Glitch That Started It All

“In his 1814 treatise, “A philosophical essay on probabilities,” French mathematician Pierre Laplace speculated that Newtonian mechanics heralded a rigid determinism that would theoretical enable the successful prediction of the entire future of the universe, given absolute knowledge of its complete state at any given time. The only catch is that the prognosticator would somehow need to step outside of the universe and obtain a complete snapshot at once of all the particles in it and their instantaneous trajectories.”

It seems like a foregone conclusion: if you live in a deterministic Universe, one governed by deterministic equations like Newton’s Laws, all you need to do is know the positions and momenta of all the particles to arbitrary accuracy at any given time. You give me those, and I should be able to, with enough computational power, give you the positions and momenta of those particles arbitrarily far into the distant future. Only, that isn’t the way physics actually works! If you give me those for a complex enough system, I’ll only be able to predict their behavior for a short while; pretty soon, chaotic effects will take over. We may call this the “butterfly effect” today, but the truth is it was started by a computer glitch almost 60 years ago.

Come get the fascinating story of chaos theory, the butterfly effect, and how we don’t need quantum rules for an indeterminate Universe, courtesy of the one-and-only Paul Halpern!

We will believe in the newton’s law of motion and for a particle whose force is dependent only on its position it states that:

image

           (or)

image

Now let’s take a closer look at this:

On the LHS you have something that is dependent on x and t, but irrespective of all that dependency, this quantity  ( mx’’ – F(x) ) is ALWAYS 0.

Therefore we can define a quantity (or function) called Energy which is invariant with time i.e:

image
image
image
image

This implies that if you take any system doing any sort of crazy motion, there is always this quantity that will always remain constant with respect to time irrespective of all that craziness. That quantity is Energy !

Have a good one!