14
votes
What counts as the Earth's mass? At which point would it increase or decrease?
A great tool for answering these types of conceptual questions is an order of magnitude estimate, or a Fermi estimate.
Let's assume the Curiosity Rover has about the same mass as a car. A quick ...
- 10.2k
12
votes
Accepted
A thought experiment regarding elliptical orbits
Your instinct that the four quarters of the orbit would be symmetrical isn't correct, because the spacecraft doesn't start each quarter the same way.
Here's the start of the scenario (The spacecraft ...
- 755
9
votes
Why do we reduce a body to its center of mass when calculating gain/loss of gravitational potential energy?
Consider a mass at height h above the surface and another mass at height (h+L) that are connected by a massless rod. The potential energy of the lower mass is -mgh and the potential energy of the ...
- 7,686
8
votes
It seems the statement "an object in orbit is in a permanent free fall around Earth" is wrong. Is my understanding correct?
The centrifugal force is not a "force" in the sense relevant to that definition of freefall. It is what is known as a "fictitious force," because it derives from the fact that the ...
Buzz♦
- 16.5k
7
votes
Why do we reduce a body to its center of mass when calculating gain/loss of gravitational potential energy?
KDP's answer explains, in elementary terms, why this reduction is acceptable for a uniform rod in a uniform field. This is an elaboration of that answer in case you prefer a more formal derivation.
If ...
- 1,781
6
votes
It seems the statement "an object in orbit is in a permanent free fall around Earth" is wrong. Is my understanding correct?
The statement in the title of your question is correct, an object in orbit [around the earth] is in a permanent freefall.
The first wiki article is incorrect. There is no centrifugal force on the ...
- 3,181
6
votes
Understanding geosynchronous orbits in an otherwise empty universe
Suppose the universe was completely empty except for a rotating planet with a moon in geosynchronous orbit. How would it be possible to understand why the moon did not fall since there is nothing to ...
- 39.8k
5
votes
Understanding geosynchronous orbits in an otherwise empty universe
This is an interesting little question, in that it puts blinders on our observers and asks whether or not we would deduce the same laws as we have found presently.
First off, I would point out that ...
- 50.8k
5
votes
Does the different strength of gravity at varying heights affect the forces within a suspended or standing object?
Yes, the tension put on objects due to the imbalance of gravity across their volumes is called the tidal force.
The tidal force puts into tension objects that are large and/or near strong ...
- 1,890
5
votes
Why are they integrating from infinity to $r$ in the derivation of GPE formula?
Not a dumb question at all. A general property of integrals is that when switching the integral bounds, there is just an overall minus sign:
$$\int_a^bf(x)dx = - \int_b^af(x)dx.$$
So, why do we even ...
- 181
4
votes
Understanding geosynchronous orbits in an otherwise empty universe
The first thing to establish is whether or not the moon would fall or not. Mach's principle suggests it would fall, because his principle says that rotation is only possible when there are distant ...
- 7,686
4
votes
Value of $g$ in frictionless surface
The value of $g$ does not change in the absence of air resistance. What changes is how much of the gravitational force results in acceleration. With air resistance, some of the gravitational force is ...
- 94
4
votes
Do all the planets orbiting a star lie in one plane?
First, let me answer a related question. Why do the planets all orbit the Sun in (nearly) the same plane? This “co-planar” orbital motion is due to the fact that during the formation of the Solar ...
4
votes
Does the different strength of gravity at varying heights affect the forces within a suspended or standing object?
If you work in a cartesian coordinate system around the center of mass (or maybe gravity--they are different) of your object, in a non rotating planetary field at distance $R$ from the planet's center,...
- 37k
4
votes
A thought experiment regarding elliptical orbits
Let's consider the elliptical orbit (following the initial burn). The foci of the orbit (including Earth) lie on a line connecting the perigee and apogee (the line of apsides). This is indeed a line ...
- 1,779
3
votes
What counts as the Earth's mass? At which point would it increase or decrease?
The real answer is "if you have to ask what counts as Earth-mass, it's a poor unit for the question at hand." We only use this for approximations, giving a sense of scale to otherwise ...
- 50.8k
3
votes
Accepted
Does the force of gravity equation include only one dimension?
The force acts in all three dimensions, the magnitude is 1 d. but $\vec{F}=-G\frac{Mm}{||r||^3}\vec{r}$ and $\vec{r}$ is 3d
- 6,568
3
votes
It seems the statement "an object in orbit is in a permanent free fall around Earth" is wrong. Is my understanding correct?
Since you said in a comment that an answer based on general relativity would be welcome here is such an answer.
In relativity (both special and general) we can define a property called the proper ...
- 360k
3
votes
Why do we reduce a body to its center of mass when calculating gain/loss of gravitational potential energy?
When resolving KE of a rigid body the choice of reference point where velocity is calculated and the mass moment of inertia is resolved about are arbitrary.
Specifically, a rod of length $\ell$ that ...
- 38.9k
2
votes
Understanding geosynchronous orbits in an otherwise empty universe
Rotating reference frames are different from inertial reference frames because if you’re rotating in a vacuum you feel centrifugal force (unless you’re a zero-dimensional point particle, which you’re ...
- 1,890
2
votes
How does the Earth's orbit change as the Sun decreases in mass?
The best way to analyse this problem is consider the conservation of angular momentum for circular orbits. For a body of mass $m$ with speed $v$ and orbital radius $r$, the angular momentum is
$$ H = ...
- 1,779
2
votes
Why does gravity obey an inverse square law?
the author explains why a three-dimensional universe implies an inverse square law.
This explanation is an appeal to your intuition, but it does not explain "why" the electric (or ...
- 22.5k
2
votes
Why does $W_1$ cancel out when $W_1$ perpendicular to the surface and Normal Force cancel out?
There is nothing dropping out. You are misunderstanding the physics that is being told to you.
$$
\begin{align}
\tag1\vec{\mathcal W}&=+\vec{\mathcal W_\perp}+\vec{\mathcal W_\parallel}\\
\tag2\...
- 10.3k
2
votes
Accepted
Deriving the fact that an approximately parabolic terrestrial trajectory is a tiny section of an ellipse
Ok so it's an ellipse. I'm still curious about the derivation, though.
Would it be best to switch to a celestial mechanics point of view for
the derivation? – Simon M
That is probably the best ...
- 7,686
2
votes
Does the force of gravity equation include only one dimension?
Gravitational force, like all forces, is a vector comprising a direction in 3 dimensions and a magnitude. In some cases, the direction can be ignored, usually because in such a case the direction ...
- 67
2
votes
It seems the statement "an object in orbit is in a permanent free fall around Earth" is wrong. Is my understanding correct?
The existence of a centrifugal force, or a Coriolis force, is coordinate dependent.
In ECI (earth centered inertial) coordinates, the satellite needs centripetal force to make it orbit, that force is ...
- 37k
2
votes
According to relativity, does spinning a top throw the heavens apart, or pull them together, or do nothing to them, or something else?
Your problem is yet another example of why the concept of centrifugal effect should never be taught outside of university. There is no such thing as centrifugal force pushing the universe away. You ...
- 10.3k
2
votes
What are the different conditions for the Newtonian limit of General Relativity and for Special Relativity?
In addition to @JEB's answer, it may be useful be consider the so-called
"Bronstein cube" (see also https://en.wikipedia.org/wiki/CGh_physics ),
where General Relativity is a corner of a ...
- 12.2k
2
votes
Why are they integrating from infinity to $r$ in the derivation of GPE formula?
There is no rule that the upper limit should be larger than the lower limit of the integal. For the case of work, the choice of limits simply tells you for what motion is the work calculated. The ...
- 8,182
1
vote
Showing Kepler's first law using the Triangulation method
I may be able to say a couple of things.
Incidentally, I noticed that there is a 1992 translation of Kepler's book Astronomia Nova. Translator: William H. Donahue
I noticed that the historian of ...
- 22.2k
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