48
votes
Accepted
Can Newton's gravity equation explain why black holes are so strong?
No you can't and the behaviour of bodies with mass and of light is completely different near a compact, massive object if you use Newtonian physics rather than General Relativity.
In no particular ...
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43
votes
What is the shape of orbit assuming gravity does not depend on distance?
Circular orbits are always possible for any central force law, but noncircular orbits would resemble rosettes. Here's a specific example for the case where the force is constant with distance:
By ...
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42
votes
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Intuition about why gravity is inversely proportional to exactly square of distance between objects
Imagine "gravity" spreading out in a sphere, like light from a bulb.
For each doubling of the distance, the sphere has four times the area. The surface area of the sphere is proportional to ...
- 116k
16
votes
Does the escape velocity formula take into account how a gravitationally bound object's distance to its primary increases before coming back down?
The escape speed is defined in Newtonian physics simply by demanding that the sum of kinetic energy at launch (ballistically, with no power applied thereafter) and gravitational potential energy at ...
- 146k
14
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Can Newton's gravity equation explain why black holes are so strong?
I am not an expert in physics and the explanation of the others is excellent. However, I noticed a flaw in your reasoning which they did not address.
You have written:
Considering the Newton's Law of ...
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12
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Does the escape velocity formula take into account how a gravitationally bound object's distance to its primary increases before coming back down?
Yes, escape speed is an instantaneous calculation at the distance 'r' from the center of the object, as that changes you have to recalculate your escape speed.
For example, these are the escape ...
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10
votes
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Gravitational acceleration inside a planet
You can use Gauss's law for gravitation to work out the gravity as a function of (interior) radius.
$$ \oint \vec{g} \cdot d\vec{A} = -4\pi G \int \rho\ dV\ .$$
What this means is that the flux of ...
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9
votes
Accepted
How strong are the tides raised by Io on Jupiter relative to the ones raised by the Moon on Earth?
Both expressions are incorrect. The first should be
$$\frac{GM_{\text{moon}}}{(R_{\text{moon}}-r_{\text{planet}})^2} - \frac{GM_{\text{moon}}}{{R_{\text{moon}}}^2}\tag{1b}$$
or
$$\frac{GM_{\text{moon}}...
- 33.5k
9
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Can Newton's gravity equation explain why black holes are so strong?
While admiring @ProfRob's answer I'll add some additional perspective/background that may serve as a helpful stepping-stone since not every Astronomy SE reader is prepared to embrace General ...
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8
votes
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Gravitational attraction of Sun on distant object
The full equation for the time for an object to drop is
$$t = \frac{ \arccos \Big( \sqrt{ \frac{x}{r} }\Big) + \sqrt{ \frac{x}{r} \ ( 1 - \frac{x}{r} ) } }{ \sqrt{ 2 \mu } } \, r^{3/2},$$
where $...
- 116k
8
votes
What is the shape of orbit assuming gravity does not depend on distance?
In addition to Sten's great answer, it should be noted that under constant gravity all orbits are bounded. Therefore, there aren't any orbit like the hyperbolic ones mentioned in the question.
That ...
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7
votes
Accepted
Orbits using Newtons laws
I like to classify solutions of the problem of the time evolution of the
complete initial state of a set of objects at some epoch time, where the
objects are subject to Newtonian gravitation into two ...
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7
votes
What is the minimum mass of a celestial object so that it can have a moon?
Planetoids can have moons and the minimum size is "pretty small". For example 2003 SS84is a small Near-Earth asteroid, with a diameter of 120m and a moon of about 60m in diameter, which ...
- 116k
7
votes
Does MOND change general relativity?
To incorporate MOND changes do need to be made to the theory of relativity. This is because at small accelerations and speeds, the theory of relativity approximates to normal Newtonian mechanics. ...
- 116k
7
votes
Accepted
Are there really confined Globular Clusters?
You are asking for a star cluster that sits at the bottom of an infinite potential well. Such clusters do not exist because they are largely the source of the potential that they reside in.
There are ...
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6
votes
Does the gravitational attraction near the surface of dense celestial objects diverge from inverse square?
Leckner's paper deals with the effect of induced polarization on the spheres. Electrons are redistributed, making the force different from what one would expect. The gravitational counterpart is tidal ...
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5
votes
Gravitational acceleration inside a planet
The short answer because Jupiter is a gas giant, so it's kind of got a very large atmosphere and atmosphere's aren't very dense. Also, if you look at your chart, the gravitation inside the Earth ...
- 23.9k
5
votes
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Virial ratio behaviour
The ratio $T/\Omega$ tells you about the acceleration of the system - or more specifically, the second derivative of its moment of inertia - it does not tell you about the velocity.
If the system ...
- 146k
5
votes
Can Newton's gravity equation explain why black holes are so strong?
If Einstein's GR equations are expanded in terms of familiar coordinates (Cartesian, spherical,...), the dominant or leading terms of the expansion (for the acceleration) can be written as the single ...
- 51
5
votes
Accepted
Is an extreme precession on a tidally locked planet possible?
Yes.
Our own Moon is tidally locked to the Earth, but has an axial precession with a period of about 18.6 years. This precession is due to the 1.5 degree offset angle between the Moon's rotational ...
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4
votes
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Understanding gravity
The magnitude of the force of gravity between two bodies is proportional to the product of their masses:
$$F=G\frac{m_1m_2}{r^2}$$
This doesn't change depending on which body you're applying the force ...
- 36k
4
votes
Accepted
Why can't gravity repel things?
Apart from the field-theoretical standpoint presented by Stan, one can repel objects in a sense, when taking orbital mechanics into account.
The slingshot maneuver extracts angular momentum and ...
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4
votes
Intuition about why gravity is inversely proportional to exactly square of distance between objects
The validation is the same as the validation of any astronomical theory: it fits the data. Newton's law of gravitation was formed empirically, by observing the motion of the planets.
In particular, ...
- 323
4
votes
At what distance does MOND Modified Newtonian Dynamics take effect?
There is no line at which things transition from Newtonian dynamics to MOND, it's more of a gradual continuous transition depending on the nature of the interpolating function $\mu(x)$:
From Wikipedia ...
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4
votes
What is the shape of orbit assuming gravity does not depend on distance?
There wouldn't be standard orbits at all.
The Earth orbits the Sun because the Sun's mass dominates the local spacetime. By removing distance from the gravitational equation, the Earth would, with ...
4
votes
Gravitational waves vs. "normal gravity"
Acceleration isn't a property of spacetime per se. Two test particles at the same location can have different instantaneous accelerations, so just knowing that there is a passing gravitational wave ...
- 3,498
3
votes
Gravitational attraction of Sun on distant object
James K gave a good answer to this, but I just want to add that if the Sun was unmoving relative to the center of the Milky-way, it would fall towards the center along with your object. The sun ...
- 23.9k
3
votes
Accepted
Precision of geocentric gravitational constant
Ignoring details such as the oblateness of the Earth, atmospheric drag, third body influences such as the Moon and the Sun, relativity, ..., the period of a satellite of negligible mass (even the ...
- 33.5k
3
votes
Accepted
Gravitation - Pulling or Pushing force?
In general relativity, gravity neither pushes nor pulls. To explain why ball travels in an arc you note the start and end points of the throw in 4d space time (3 space co-ordinates and 1 time ...
- 116k
Only top scored, non community-wiki answers of a minimum length are eligible