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36

The bus experiences considerable drag, and will therefore fall more slowly than a person inside the bus. The scenario is possible in principle - but after carefully viewing the clip and doing some calculations, I believe that the details are inaccurate. Assume the bus has a mass of 5000 kg (pretty light for a bus), and is 3 m wide by 3 m tall - so the ...


20

If the bus was in a vacuum (both inside and outside), then the passenger would float. However, the effects of air resistance on the two objects (passenger and bus) are probably not negligible in such an instance. The bus will be moving relative to the outside air, and so will be accelerating towards the ground at a rate less than $g$. If we then released ...


8

You seem to be groping towards the fact that the gravitational three-body problem is, in general, not solvable. We can get away with saying "the sun is at one focus of an elliptical orbit" in the solar system because the sun is so much larger than anything else around. The sun is 1000 times more massive than Jupiter, so the sun-Jupiter barycenter is about ...


6

At first, the bus and the person would accelerate at the same rate due to gravity. However, the situation is more complicated due to air resistance. The bus experiences air resistance as it falls. The person inside the bus experiences less air resistance because the air inside the bus moves with the bus. This means that the person does not experience as much ...


6

Are all trajectories parabolic? No, most trajectories are ellipses. If an object has less than escape velocity, it is an ellipse. If the object just has escape velocity, it has a parabolic trajectory. If it is greater than escape velocity, it is hyperbolic. For Earth, the escape velocity is just over 11.1 km/s (6.89 miles/s). This is faster than a ...


4

In the following the term "charge" refers either to mass or to electric charge and the term "Inverse Square Law" refers either to Newton's Gravitational Law or to Coulomb's Law respectively. SECTION 1 A. The Inverse Square Law for Spheres with uniform surface charge density Proposition A : Let a sphere of radius $\:\rm{R}\:$ with uniform surface ...


4

One can answer this question by calculating the energy needed to shift half the Earth's mass so that it is infinitely far from the other half. Let's calculate the gravitational potential energy released as we create a planet: assuming a constant density $\rho$, when the planet is growing and of radius $r$ and thus of mass $M(r)=\frac{4}{3}\pi\,r^3\,\rho$, ...


3

I am not sure what is the path $C$ you are integrating over? In your definition you evaluate $U(C)$ which in the present case of force is independent on the explicit path you choose but still depends on initial and final point, i.e. $U(p_1,p_2)$. In your final result it seems you are actually 'walking' three times the path $p_1=(-\infty,y,z)$ to ...


3

I suggest that it doesn't make much sense to say that the planets orbit the barycenter of the solar system. Beware that you are going very much against the grain of the best models of the solar system in writing that. All three of the leading ephemeris models (JPL's Development Ephemeris, the Russian Institute for Applied Astronomy's Ephemerides of the ...


3

The $F$ you've found above is not the "real" force in GR, but rather an "effective force" derived from an "effective potential". Basically, we can use the fact that there are multiple constants of the motion to reduce the full three-dimensional problem down to an equivalent one-dimensional problem. This procedure works in Newtonian gravity1 as well, as ...


3

What you have derived is the equation for the orbital velocity for a circular orbit. This is the velocity at which the acceleration required to keep moving in a circle exactly matches the acceleration due to gravity. To derive the escape velocity you need to know that the potential energy for an object of mass $m$ in the gravitational field of a planet with ...


3

Since a new moon has to have the sun shine on the entire surface facing away from the Earth, the time between 2 new moons is the time for the Earth Moon system to complete a synodic period. The period of two masses around the common center of mass is always the same.


3

No, no you guys (Except Floris and those who up-voted him) have missed an important observation... Look Carefully at the video again. At first the bus just tilts as the bridge bends. When the bus starts tilting (due to friction with the bridge it has not yet started falling) it has not yet obtained considerable vertical velocity. However as the man loses ...


2

To answer the question in your title, he used his newly found fluxions (calculus) to prove that Kepler's laws of planetary motion imply a radial, inverse square law. Feynman's Lost Lecture is a mixture both of Feynman's attempts to give the simplest possible explanation of how one goes about this derivation and his insights into the history of how Newton ...


2

Total energy is conserved. Let $E$ stand for total energy. Let $T$ stand for kinetic energy. Let $U% stand for potential energy. $E = T + U$ If $T$ increases and $E$ is constant (which it is in a closed system due to conservation of energy), then $U$ must decrease. Simply put, the kinetic comes from the potential energy. Potential energy comes from ...


2

The energy is not entirely from from the Big Bang since a lot of the material had to come from supernovas. This would mean that some of the energy came from the supernovas separating the dust that makes up the objects. Yes, you can harvest energy from the falling objects, if they fall onto the targets.


2

The assumptions of a parabolic trajectory is: (gravity) force is a /constant/, /downwards/ force, /no other forces/ acting on the object, the object under observation does not affect the (gravity) field, classical mechanics In practice, this approximation is almost true with gravity when: there is only one significant mass that imparts any significant ...


2

At L4 and L5, the object would stay in the same relative position because it is in the same orbit around the Sun as Earth. Any other points on the circle would not be in the same orbit as Earth. They would be in orbits of differing inclination and so, in the course of the orbit of that object about the Sun, it would necessarily leave those points. The L4 and ...


2

The statement of Newton's law you have given is specifically about the gravitational attraction between point masses. It also comes to mean, through the Shell theorem the force between a spherically symmetric body and another outside the first body: we replace the spherical body with a point at its center. For other geometries you calculate the force ...


2

The mass of all the oceans on the surface of the Earth is estimated to be 1.35 * 10^18 metric tons, or 1.35 * 10^21 kilograms. The mass of the Moon is estimated to be 7.35 * 10^22 kilograms. The distance from the Moon to the Earth at perigee (the closest distance) is 363,104 kilometers, or 363,104,000 meters. If you assume the oceans cover the entire ...


2

There is not any mathematical but beside that Newton combined his laws of motion with Kepler's laws and deduced the law of gravitation. Path of planets around the sun are elliptical so for simplicity we can assume the orbit to be circular. Let us consider $a$ planet of mass $m$ moving with constant speed $v$ in a circular orbit. $$T=\frac{2\pi r}{v}$$ and ...


2

It is better to think of the equation $E =mc^2$ as a true equality rather than a conversion. Mass is energy. If one has that mindset, then it is intuitive that energy has a gravitational field. A hot cup of tea weighs more than a cold one.


2

I suspect this is an example of the spinning-egg problem, in which a prolate spheroid (such as an egg) spun on a table about one of its "short" axes will tend to "stand up" so that it's spinning about its long axis. A few explanations have been proposed for this phenomenon, most notably: H. K. Moffatt & Y. Shimomura, "Spinning eggs — a paradox ...


2

The black machine is a weight lifting machine. It is self contained with no power source. If it can lift an external weight and return to its original state as shown below, it is a perpetual motion machine. Suppose the blue weight is water. We could add a water wheel and generator on the right. You start at the top and work your way to the bottom. Then you ...


1

First of all let's study an imaginary system where both the bus and the person are not subject to drag forces due to the air: If the person is not bounded to anything he will be subject to free falling and thus to a uniform acceleration $g$. Also the bus will be free falling and thus they fall together with the same velocity. If we take the drag forces into ...


1

In a reference frame where the center of mass of the Earth-Sun system is at rest, we will have $$ m_\text{Sun} \vec{v}_\text{Sun} + m_\text{Earth} \vec{v}_\text{Earth} = 0 \quad \Rightarrow \quad \vec{v}_\text{Sun} = - \frac{m_\text{Earth}}{m_\text{Sun}} \vec{v}_\text{Earth}. $$ In particular, if this is true at some initial time, then it's true at all ...


1

break earth into 2 parts in which each part is nearly equal to half of volume of the earth Yes and no. No, as in you can't neatly split the planet in half. Most of the earth is liquid and will re-form once the cutting device has passed through it. Much like cutting pudding. Yes, if you want 2 half-earth balls when you are done and don't care about the ...



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