# Tag Info

16

The effect of gravity is miniscule, and here's why: The speed of sound in a string is basically $$v = \sqrt{\frac{T}{\lambda}},$$ where $T$ is the tension and $\lambda = M/L$ is the mass per unit length. The frequency of a plucked string will then be this sound divided by the length of the oscillator: $f = v/L$. Combining and rearranging tells us the ...

8

First off, your question is phrased in terms of relativistic mass, which is an obsolete concept. But anyway, that's a side issue. The question can be posed in terms of either the earth's force on the puck or the puck's force on the earth. We expect these to be equal because of conservation of momentum. In general relativity, the source of gravitational ...

8

This does not contradict newton, because the error is in the calculation: You are calculating in discrete time steps. In that case the calculated speed will increase, as if energy is not preserved. However, Newton's laws apply to continuous time. In the mathematical world in which newton laws are described, speed and acceleration are NOT defined by ...

5

Gravity is viewed as a force because it is a force. A force $F$ is something that makes objects of mass $m$ accelerate according to $F=ma$. The Moon or the ISS orbiting the Earth or a falling apple are accelerated by a particular force that is linked to the existence of the Earth and we have reserved the technical term "gravity" for it for 3+ centuries. ...

3

You are talking about relativity and gravity together so the question can only be answered in the context of general relativity, but concepts like gravitational potential energy and gravitational force acting over a distance are Newtonian and do not really carry over to general relativity. However, the gravitational field does contribute to total energy and ...

3

Depends on what you're doing. General relativity handles it for you, in the sense that the Einstein field equation links geometry to the non-gravitational stress-energy tensor. That general relativity is non-linear can be interpreted in part as gravity itself contributing to gravity, but it's generally not even possible to localize gravitational energy in a ...

3

Objects don't accelerate because they're inside other objects. Objects accelerate because other objects make forces on them. The chain of cause and effect here is that the box can affect the air, then the air can affect the helicopter. The answer to the question depends on how rapidly the box is accelerated. To pick an extreme case, suppose that the box is ...

3

The gravitational field of small objects can be measured. In fact as far back as 1797 Henry Cavendish measured the gravitational field from lead spheres. He used pairs of spheres of mass 158kg and 0.73kg, so for a person weighing say 70kg the same method is in principle possible, although in practice people are an inconvenient shape for doing the experiment ...

3

The one thing to keep in mind is that in order to perform a gravity-assist maneuver, you need to be able to enter a hyperbolic orbit around a given body that is moving relative to your destination. And, in order to be in such an orbit, there is a specific range of velocities for every object that you must have (dependent on mass of the object). So the ...

3

Some instruments would require modifications in order to facilitate playing them. Large instruments would need to be strapped down, and something like a double bass or drums would probably require its player to be strapped into a harness in order to prevent them from pushing themselves off as they played and floating away from the instrument. I can imagine ...

2

Gravity is described by Einstein's field equation. The Newton equation that you mention isn't the mathematical definition of anything, it's just an approximate solution for a spherically symmetric body when gravity isn't too strong. The corresponding exact solution is the Schwarzschild metric, and this is what we use to calculate what happens near a black ...

2

It depends on the nature of the system, and the explosion. If more than about half the mass of the system is lost from the central star, the planet will become unbound (interesting National Geographic article on the subject). This can be relevant even before the actually supernova - as massive stars lose a lot of mass through winds. In any case, if the ...

2

"What happens to any planets in orbit around the star" Why would anything happen to them? There is still a mass there; the same mass as before. It still has the same center of gravity. Now, when the radiation and shock waves arrive lots of stuff starts happening, including the effect mass around which the planets are orbiting dropping as material ...

2

Let's generalize your idea and see if it can be more propellant-efficient, at least in principle. Call your two orbits $\mho_1$ and $\mho_2$. Both have semi-major axis $a_2$ and $a_2$ and inclinations $i_1$ and $i_2$ respectively. As per the problem, $$a_1<a_2$$ $$i_1=i_2$$ and any phasing issues may be ignored. Also, $$r_{p1} = r_{a1}$$ $$r_{p2} = ... 2 Gravity is still viewed as force for better understanding because not all have Einstein's IQ to see curvature of more than 2 dimensions. Gravity is a force, but not a REAL force. Try pushing rat and elephant over a frictionless surface so that both feel same acceleration. Common sense says that you need more force for elephant. It means that gravity is a ... 2 where does it go and what happens when it clogs up? In the context of an ideal, static black hole in general relativity, world lines end at the singularity. Consider the diagram below: This is the Schwarzschild geometry in Kruskal–Szekeres coordinates. In these coordinates, it is clear that there is no place or time that the entities falling into ... 2 The speed of light is entirely a local concept - it does not care if there are 10 atoms or 10 billion galaxies somewhere in the Universe. Obviously we can't go to distant galaxies to directly measure the speed of light, so in the absolutely strictest sense this is not directly empirically tested. However, the constancy of the speed of light is one of the ... 2 Kris Van Bael's answer has the right idea, and that is a problem for computer simulations. If you want to simulate this on a computer, you have to discretize time, and that causes problems with conservation laws. Another way to look at it is to look at an infinitesimally small amount of time (this is where Kris Van Bael's answer is going). The instant that ... 2 Some of the conditions for Newtonian gravitation to work are: All particles must be slow, as compared to the speed of light in vacuum. The Newtonian potential \Phi must must likewise not change too fast. This is simply because Newtonian theory is incompatible with a characteristic speed c. The Newtonian potential \Phi must be small, |\Phi/c^2|\ll1. ... 2 Why would you assume they do not ? Of course they do. But as you probably know, the gravitational pull decreases with distance (inverse square law). From a safe enough distance any other object (star, galaxy) would feel the normal gravitational pull of an object of the black-hole's mass at that distance; it makes no difference to the stars if the source ... 2 The slingshot effect is in fact only a transfer of angular momentum from one body to another. So for example if you're using Jupiter for a swing by manoeuvre with your satellite, you do nothing more than slow down Jupiter (in the Sun-Jupiter-(satellite) system) and speed up your satellite. Of course because of the huge difference in mass, you only see a ... 2 There are several things that have to be considered in space, microgravity or not. "There is no evidence that human auditory functioning changes in space." Source: MSIS Microgravity means no natural air circulation. Hence, fans have to keep working, and they are ridiculously noisy. It is not practical to have long concerts in space due to carbon dioxide ... 1 So at atomic level for same charges that repel eachother(electrons etc.), if thought of as a slingshot effect, elastic repulsive collision and buoyancy fields etc. makes repulsion a pseudo or dummy. as for like gravity is doing it all, then it will be more insightful or not? Not. To describe all the available data the theory has to be much more ... 1 This is an extremely common misconception so I will try to make my answer as simple as possible. A black hole is black and light can't escape because of mass for a given volume (density), not because of mass alone. Take our solar system for example. Our sun is very massive and it pulls on all of the planets hard enough that they orbit the sun. As long as ... 1 My previous answer proved to be wrong. Energy density ("relativistic mass") does contribute to gravity - and the fact that the object is moving at relativistic speeds does affect the space-time around it. There is an interesting document that explains the problem in further context. Besides, when we think about it, if energy density didn't contribute to ... 1 The Earth isn't a perfect sphere (or even a perfect oblate spheroid) so its gravitational field is not axially symmetric. You've probably seen the geoid measured by the GOCE and GRACE satellites. As the Earth rotates the asymmetries in its gravitational field rotate with it, and any satellite whose orbital period is a ratio of one day can build up a ... 1 Okay, This question has assumed a lot. I think you're aware that Earth's (spin) rotational velocity (around 30 m/s) is the left over velocity after the Earth had formed from the dust clouds and matter. If on the contrary, you were to assume its spin to be multiplied by 10k x suddenly: first - the outer layers would wither off. Finally, you'd be left with ... 1 Generally speaking, and provided you don't stray too close to black holes, you can imagine GR as making small modifications to Newton's law. For example Newton tells that the acceleration of a body falling towards a planet of mass M is:$$ a = \frac{GM}{r^2} $$i.e. the famous inverse square law. If you calculate the acceleration for a Schwarzschild metric ... 1 Your question touches on the quantum behaviour of black holes, a subject with fundamental, unsolved problems. Classically, black holes cannot emit light, because light cannot escape their strong gravitational fields. The gravity is so strong that any matter that fell into a black hole would be torn into fundamental particles, and become part of the black ... 1 First let us calculate the potential for a ring of radius a at a distance x from the center along the axis Potential due to an infinitesimal mass element dm will be$$\frac{-Gdm}{\sqrt{a^2+x^2}}$$Potential due to the ring is then$$\int{\frac{-Gdm}{\sqrt{a^2+x^2}}}=\frac{-G}{\sqrt{a^2+x^2}}\int{dm}=\frac{-Gm}{\sqrt{a^2+x^2}} Since $G, a, x$ are ...

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