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adjurovich
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I am not sure if there is in fact a classical description of how it occurs, but I’d like to know if there isn’t too!
How does gravitational field exert gravitational force on a body?
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In summary, a gravitational field exerts a gravitational force on a body by creating an attractive interaction between the mass of the body and the mass that generates the field. This force is proportional to the product of the two masses and inversely proportional to the square of the distance between them, as described by Newton's law of universal gravitation. The gravitational field can be visualized as a region in which a mass experiences this force, influencing the motion of objects within it.
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Hill
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In Newtonian mechanics, there is no "gravitational field". In general relativity, there is no "gravitational force".
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pines-demon
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I am not sure about that, we can define the Newtonian gravitational field ##\mathbf F =m \mathbf g(r)##, where ##\mathbf F## is the force due to gravity on a mass ##m## and ##\mathbf g(\mathbf r)## the gravitational field.Hill said:
Newton's law can even be made into a Gauss' law of gravity: ##\nabla\cdot \mathbf g=-4\pi G \rho(\mathbf r)## (together with ##\nabla \times \mathbf g = 0##).
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adjurovich
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What do you use this equation for, then?Hill said:
##g = \dfrac{F}{m}##
There is also gravitational field in classical mechanics, but Newton never truly understood gravity… but do we?
- #5
pines-demon
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There is a gravitational field in Newtonian's mechanics. However this field is instantaneous and that already bothered Newton and many people after him.adjurovich said:
There were mechanical explanations of gravity but none was very useful (aether theories were not any better either). The only one that became almost challenging was Le Sage's gravitational theory but even that violates thermodynamics. So I guess the best was just to keep Newton's law of gravitation as an axiom. There is a field and that fields pulls masses together. Period.
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Dale
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I disagree. In Newtonian mechanics you certainly can define a gravitational field. It just doesn't have any interesting dynamics on its own.Hill said:
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Hill
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Since in our best theory of gravity the gravitational field does not exert a gravitational force, what does the question in the title of the thread refer to?adjurovich said:
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adjurovich
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I have asked about classical (more precisely Newtonian) description, not the relativistic one. You cannot expect from a high school student to know much about general theory of relativity?
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Hill
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I see. Anyway, the modern answer to that question is, it does not. Here is "the answer" from Gravitation by Misner, Thorne, and Wheeler:adjurovich said:
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Vanadium 50
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This is essentially the same question as in your last thread, with "gravity" swapped for "electric".
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adjurovich
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If you read both questions you can clearly see that they are referring to two totally different things. But since you seem to be very much interested into my posts, I won’t be explaining anything further. If you have nothing else to do than compare and analyze questions of a high school student, I highly suggest you to find a hobby. There is always an option to skip a question you don’t like? It’s better than spamming someone’s inbox and wasting your own precious time on writing useless replies
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berkeman
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He didn't spam your inbox. More likely you got a notification that he replied in your thread. Please be careful using the term "spamming" here. Thank you.adjurovich said:
- #13
hmmm27
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That would be the second paragraph in post #5, to which you've yet to respond.adjurovich said:
- #14
Dale
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As others have mentioned, there are two major theories of gravity: Newtonian gravity and general relativity.
In Newtonian gravity, there is not a cause-and-effect relationship. Causes come before effects, and that doesn't happen in Newtonian gravity. A change in the sources occurs at the same time as a change in the field, not before. Furthermore, the field has no internal dynamics. So, while mass is the source of gravity, the relationship is not a causal one, which is weird.
In general relativity, there can be a cause-and-effect relationship in many cases. The field has interesting internal dynamics. The source of gravity is not just mass, but the full stress-energy tensor which includes mass, energy, momentum, pressure, and stress. The field is not a force field but represents the tidal effects of gravity. In the cases with cause-and-effect changes in the stress-energy tensor cause changes in the field, changes propagate at ##c##, and those cases include many realistic scenarios.
In Newtonian gravity, there is not a cause-and-effect relationship. Causes come before effects, and that doesn't happen in Newtonian gravity. A change in the sources occurs at the same time as a change in the field, not before. Furthermore, the field has no internal dynamics. So, while mass is the source of gravity, the relationship is not a causal one, which is weird.
In general relativity, there can be a cause-and-effect relationship in many cases. The field has interesting internal dynamics. The source of gravity is not just mass, but the full stress-energy tensor which includes mass, energy, momentum, pressure, and stress. The field is not a force field but represents the tidal effects of gravity. In the cases with cause-and-effect changes in the stress-energy tensor cause changes in the field, changes propagate at ##c##, and those cases include many realistic scenarios.
FAQ: How does gravitational field exert gravitational force on a body?
1. What is a gravitational field?
A gravitational field is a region of space surrounding a mass where other masses experience a force of attraction. It is a vector field that points toward the mass creating the field, and its strength decreases with distance from the mass.
2. How is the gravitational force calculated?
The gravitational force between two masses can be calculated using Newton's law of universal gravitation, which states that the force (F) is equal to the product of the gravitational constant (G), the masses (m1 and m2), divided by the square of the distance (r) between their centers: F = G * (m1 * m2) / r².
3. What role does mass play in the gravitational field?
Mass is the source of the gravitational field. The greater the mass of an object, the stronger its gravitational field and the greater the force it exerts on other masses within that field. This is why massive objects like planets and stars have a significant gravitational influence on nearby bodies.
4. How does distance affect gravitational force?
The gravitational force decreases with the square of the distance between two masses. This means that as the distance increases, the gravitational force becomes weaker. Specifically, if the distance is doubled, the gravitational force becomes one-fourth as strong.
5. Can gravitational fields exist in space?
Yes, gravitational fields exist in space and are not limited to the vicinity of massive objects like planets or stars. Every mass creates a gravitational field that extends throughout space, affecting other masses regardless of their distance, although the strength of the field diminishes with distance.