Method for determining gravity center of object through universal gravitation between objects and calculating universal gravitation constant based on gravity center
By calculating the gravitational force between objects to determine the center of gravity, the problem of inaccuracy in the application of the gravitational formula is solved, and more accurate calculations of the center of gravity position and gravitational constant are achieved.
Patent Information
- Application Number
- CN202511616558.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-11-06
- Publication Date
- 2026-02-06
AI Technical Summary
In existing technologies, the methods for determining the center of gravity of an object are inaccurate when applying the law of universal gravitation, especially for non-uniform or irregular objects, where the position of the center of gravity is difficult to determine accurately.
The center of gravity of an object is determined by calculating the gravitational force between two objects. The distance between the centers of gravity is calculated using the gravitational formula. Combined with the Cavendish torsion balance experiment, the gravitational constant is accurately calculated.
A more accurate method for determining the center of gravity of an object is provided, and the calculation accuracy of the gravitational constant is improved through mathematical calculations and experimental verification.
Smart Images
Figure CN121479088A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the determination of the center of gravity when objects attract each other by gravity, and to the calculation of the gravitational constant using the gravitational formula based on the determined center of gravity. Background Technology
[0002] In physics, the center of gravity is generally described as follows: the mass of an object is concentrated at a single point, called the object's center of gravity, and for objects with uniform mass and regular shape, the center of gravity is considered to be at the geometric center of the object. However, applying this to the law of universal gravitation reveals that this statement is not entirely objective—universal gravitation is the interaction between objects, so stating that an object's center of gravity is located in a single position has no physical meaning. Furthermore, the aforementioned description of an object's center of gravity often deviates significantly from the actual center of gravity when applying the law of universal gravitation. The significance of the object's center of gravity in the law of universal gravitation lies in the relative distance between the centers of gravity of objects attracted by each other through gravity. This distance is a condition for determining the object's center of gravity. This patent determines the object's center of gravity from this perspective. The center of gravity is not fixed; when two objects attract each other through universal gravitation, their centers of gravity are related to the distance between them. Universal gravitation is at least a matter between two objects. This patent standardizes the concept of the center of gravity, provides a method for determining the center of gravity of an object, and then extends this to a more accurate calculation of the gravitational constant. Summary of the Invention
[0003] This invention provides a method for determining the center of gravity of an object using the gravitational force between objects and calculating the gravitational constant accordingly, with the following applications:
[0004] The center of gravity of an object is determined by the gravitational force between objects: When an object is attracted by the gravitational force of another object, if the object is regarded as a point mass, the resultant gravitational force of the point mass on the mass of each part of the object is equal to the gravitational force of the point mass on the total mass of the object when the mass of the object is concentrated at the center of gravity, and can be applied to the gravitational formula. Correspondingly, when a uniformly mass solid sphere (1) is attracted by the gravitational force of a uniformly mass solid sphere (2), it can be considered that the mass of sphere (2) is concentrated at point O2. The resultant gravitational force of sphere (2) on the mass of each part of sphere (1) is equal to the gravitational force of sphere (2) on sphere (1) when the mass of sphere (1) is concentrated at point O1. Thus, point O1 is the center of gravity of sphere (1) when sphere (2) attracts sphere (1) by the gravitational force. After determining the center of gravity O1 of sphere (1), the mass of sphere (1) can be regarded as concentrated at point O1. If the resultant gravitational force of O1 on the mass of each part of the sphere (2) is equal to the mass of the sphere (2) when it is concentrated at point O2, then it is verified that point O2 is the center of gravity of the sphere (2) when the sphere (1) attracts the sphere (2) with the gravitational force above. Otherwise, the sphere (2) should be moved until the center of gravity of the sphere (2) obtained by the above calculation method is completely coincident with point O2. Then the gravitational force between the sphere (1) and the sphere (2) can be calculated using the gravitational formula with the center of gravity of the sphere (1) as point O1 and the center of gravity of the sphere (2) as point O2. The centroids of two uniform solid spheres (1) and (2) can be determined using the above method. The distance between these two centroids is the gravitational formula used to calculate the gravitational attraction between the two spheres. With the center of gravity determined by r, the gravitational constant can be calculated relatively accurately using the universal gravitation formula through experiments such as the Cavendish torsion balance. The above method for determining the center of gravity of an object is applicable not only to objects with uniform mass and regular shape, but also to objects with non-uniform mass or irregular shape. The mathematical calculations may be slightly more complex. Attached Figure Description
[0005] The embodiments of the present invention will be further described below with reference to the accompanying drawings. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.
[0006] Figure 1 This is a schematic diagram illustrating the gravitational attraction between two point masses by a single point mass.
[0007] Figure 2 This is a schematic diagram of the gravitational attraction of a point mass on a uniform circle.
[0008] Figure 3 This is a schematic diagram illustrating the gravitational attraction between a large, uniform solid sphere and a small, uniform solid sphere. Detailed Implementation
[0009] To enable those skilled in the art to better understand the technical solutions of the present invention, the technical solutions of the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. Obviously, the described embodiments are some embodiments of the present invention, but not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the protection scope of the present invention. Example 1
[0010] like Figure 1 As shown in the left figure, triangle ABC is an equilateral triangle. Points A, B, and C are located at the three vertices of the equilateral triangle. Let the distance between points A, B, and C be 2, and the distance from point C to the midpoint of AB be... Let the masses of particles A, B, and C all be m. Find the gravitational force exerted by particle C on particles A and B. When particle C attracts particles A and B with gravitational force, what is the gravitational force formula? Calculations show that the resultant gravitational force F exerted by C on A and B is... 合 , Now consider AB as a line segment, a whole, with its mass concentrated in points A and B—both A and B have mass m. If we consider the geometric center of AB, i.e., the midpoint of AB, as the center of gravity of AB, the distance from point C to the midpoint of AB is... Then the gravitational force exerted by AB on point C is F. 引 0.667 > 0.433, the latter being greater than the former, clearly indicating that it is incorrect to regard the geometric center of AB as the centroid. Because the net gravitational force exerted by point mass C on AB is 0.433Gm. 2 Therefore, the actual centroid of AB should lie on the extension of the line connecting point C and the midpoint of AB, which we will call point O. Calculate the length of C0, and then we have... co≈2.149 2.149 is greater than 1.732, so obviously the centroid O lies on the extension of the line connecting point C and the midpoint of AB; like Figure 1 As shown in the diagram on the right, if triangle ABC forms an isosceles triangle with AB = 2 and AC = BC = 3, then the distance from point C to the midpoint of AB is _____. Approximately 2.828. Referring to the calculation method above, the resultant gravitational force exerted by C on A and B is F. 合1 Let point O be the centroid of line segment AB at this moment, then co2 ≈9.569, co≈3.093 Since 3.039 is greater than 2.828, the centroid O is obviously on the extension of the line connecting point C and the midpoint of AB. As can be seen from the above, the center of gravity is not necessarily at the geometric center of a uniform and regular object, nor is it necessarily at a fixed point: 3.093-2.828=0.256, 2.149-1.732=0.417, 0.417 is greater than 0.256. Therefore, the distance from C to AB is different, and the distance from the center of gravity of AB to the midpoint of AB is also different. Figure 1 If AB is considered to be uniformly composed of several points of equal mass, regardless of whether AC = 2 or AC = 3, the length of CO must be greater than the distance from point C to the midpoint of AB, and the length of CO is different when AC = 2 and AC = 3. Example 2
[0011] like Figure 2 As shown, a uniform circle has its center at O and its radius at R. The distance between the circle and point A is equal to the radius R of the circle, and OA is perpendicular to the plane containing the circle. Assume the mass of the circle is composed of n points of equal mass forming the circular surface. Using the law of universal gravitation, the gravitational force exerted by A on the circle is equal to the resultant gravitational force exerted by A on the n points of equal mass forming the circular surface. Among all distances from A to the n points of equal mass on the circular surface, the distance from A to point O is the shortest. According to the law of universal gravitation... Therefore, the gravitational force exerted by point A on all points outside the center O of the circle is less than the gravitational force exerted by A on the point mass at the center O. Thus, the sum of the gravitational forces exerted by point A on all points of the circle is definitely less than the gravitational force exerted by point A on the circle if the mass of the circle were considered to be concentrated at the center O. This shows that considering the center of gravity of the circle as the center when point A exerts gravitational attraction on the circle is incorrect. The center of gravity is not necessarily at the geometric center of a uniformly shaped object. The center of gravity of the circle should be located further away from A on the AO ray. Only then can the mass of the circle be considered to be concentrated at the center of gravity when calculating the gravitational attraction of A on the circle. The center of gravity obtained by the suspension method is not necessarily the center of gravity of the object when applying gravitational force. The core of the suspension method experiment is the equilibrium of forces on all parts of the object. In physics, the center of gravity is determined by the force exerted by the object. The gravitational attraction between the particles is determined by referring to Example 1. It can be seen from the above that the distance between particle A and the circle varies, therefore the position of the circle's center of gravity also varies when particle A exerts its gravitational force on the circle. From the above calculations, it can be seen that the total value obtained by summing the gravitational forces exerted by particle A on each point forming the circle will definitely be less than the gravitational force exerted by particle A on the circle when the mass of the circle is considered to be concentrated at the center. Moreover, the gravitational force exerted by particle A on the circle is essentially the resultant force of the gravitational forces exerted by particle A on each point forming the circle. This resultant force is also less than the total value obtained by summing the gravitational forces exerted by particle A on each point forming the circle, which is even less than the gravitational force exerted by particle A on the circle when the mass of the circle is considered to be concentrated at the center. Therefore, when the gravitational force is applied, the center of gravity of the circle should be located at a position farther from point A on the AO ray. Example 3
[0012] like Figure 3 As shown, a uniform solid sphere has a center at O1 and a radius of R, while a uniform solid small sphere has a center at position 1 and a radius of R. The distance between the two balls is The large and small balls are made of the same material. Let's temporarily consider the center position 1 of the smaller ball as its center of gravity, and the mass of the larger ball as being composed of several points of equal mass uniformly combined. Then, the gravitational force of the smaller ball on the larger ball is equal to the resultant gravitational force of the smaller ball on each point of the larger ball when its mass is concentrated at the center position 1. The direction of the resultant force is on the line connecting O1 and the center position 1. Using the formula for universal gravitation, this resultant force is equal to the gravitational force of the smaller ball on the larger ball when its mass is concentrated at its center of gravity. Therefore, the position of the center of gravity of the larger ball can be mathematically determined. The center of gravity of the larger ball lies on the straight line connecting the centers of the two balls. Example 4
[0013] In Example 3, the position of the center of gravity of the large ball can be determined mathematically. Conversely, based on the gravitational force of the large ball on the small ball, the method described above can be used to verify whether the center of gravity of the small ball is at position 1 of the large ball. By using the method described above to calculate the center of gravity of the large ball, the position of the center of gravity of the small ball can be mathematically calculated. If the center of gravity of the small ball does not coincide with position 1, the small ball should be moved so that its calculated center of gravity coincides with position 1. Then, the gravitational constant can be calculated using the formula of universal gravitation through experiments such as the Cavendish torsion balance, using the large ball and the small ball and their centers of gravity. At this point, the position of the center of gravity of the small ball relative to the position of the center of gravity of the large ball is determined.
[0014] Generally, the center of gravity can be determined mathematically by the gravitational force between two objects; when multiple objects attract a certain object through gravitational force, the multiple objects can be considered as one object to find the center of gravity. When two objects are attracted by gravity, their centers of gravity can be determined through mathematical calculation. The position of the center of gravity is determined by the positional relationship between the objects through calculation of gravity, and is not in a fixed position. When two objects are attracted by gravity, their centers of gravity lie on the line connecting the geometric centers of their masses.
[0015] To distinguish it from the conventional center of gravity, the center of gravity of an object determined by universal gravitation in this invention can be called the zjg gravitational center of gravity.
[0016] The above are merely ordinary embodiments of the present invention and the technical principles used therein, and are not intended to limit the scope of the embodiments of the present invention. Any obvious modifications and applications made without departing from the essential spirit of the present invention will constitute an infringement of the patent right and will incur corresponding legal liability.
Claims
1. A method for determining the center of gravity of an object using the gravitational force between objects and calculating the gravitational constant therefrom, characterized in that: The center of gravity of an object is determined by the gravitational force between objects: When an object is attracted by the gravitational force of another object, if the object is regarded as a point mass, the resultant gravitational force of the point mass on the mass of each part of the object is equal to the gravitational force of the point mass on the total mass of the object when the mass of the object is concentrated at the center of gravity, and can be applied to the gravitational formula. Correspondingly, when a uniformly mass solid sphere (1) is attracted by the gravitational force of a uniformly mass solid sphere (2), it can be considered that the mass of sphere (2) is concentrated at point O2. The resultant gravitational force of sphere (2) on the mass of each part of sphere (1) is equal to the gravitational force of sphere (2) on sphere (1) when the mass of sphere (1) is concentrated at point O1. Thus, point O1 is the center of gravity of sphere (1) when sphere (2) attracts sphere (1) by the gravitational force. After determining the center of gravity O1 of sphere (1), the mass of sphere (1) can be regarded as concentrated at point O1. If the resultant gravitational force of O1 on the mass of each part of the sphere (2) is equal to the mass of the sphere (2) when it is concentrated at point O2, then it is verified that point O2 is the center of gravity of the sphere (2) when the sphere (1) attracts the sphere (2) with the gravitational force above. Otherwise, the sphere (2) should be moved until the center of gravity of the sphere (2) obtained by the above calculation method is completely coincident with point O2. Then the gravitational force between the sphere (1) and the sphere (2) can be calculated using the gravitational formula with the center of gravity of the sphere (1) as point O1 and the center of gravity of the sphere (2) as point O2. The centroids of two uniform solid spheres (1) and (2) can be determined using the above method. The distance between these two centroids is the gravitational formula used to calculate the gravitational attraction between the two spheres. Once the center of gravity is determined by 'r', the gravitational constant can be calculated relatively accurately using the universal gravitation formula and experiments such as the Cavendish torsion balance.
2. The method for determining the center of gravity of an object and calculating the gravitational constant based on the gravitational force between objects, as described in claim 1, is characterized in that: The above method for determining the center of gravity of an object is applicable not only to objects with uniform mass and regular shape, but also to objects with non-uniform mass or irregular shape. The mathematical calculations may be slightly more complex.