1. Introduction
When the stones hit the water, they generate concentric waves that move away from the source, as shown in Fig.1.
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Fig.1.This an image of water waves.
Gravitational_waves are heard by LIGO [1]. The interferometer can hear gravitational waves, but gravitational_waves are invisible, this is the currently popular viewpoint. We can not be limited by this viewpoint; otherwise, physics would not be able to develop. In classical physics, a basic fact of gravitation is that two particles exert forces on one another. A point of view is the field concept, which regards a particle as modifying the space around it in some way and setting up a gravitational_field [2]. Gravitational_waves are caused by the disturbance of the gravitational_field. Any hypothesis in physics must be tested through experiments. In order to explore this question, I performedexperiments in this area.
2. Experiment
Flatten a small area on the surfaces where the two lead spheres will join, then press them tightly together. It was found that two lead spheres stick to each other, and even hanging a heavy object underneath will not be able to pull them apart, as shown in Fig.2.
Fig.2. The mass of each lead sphere is 150g. The mass of the heavy object is 200g.
This indicates that the gravitational effect between the two metal spheres is large.
We placed two steel spheres between the laser source and the screen, as shown in Fig.3. When a laser beam passing through the narrow gap between two steel spheres and creates a pattern of ripples on the screen of Fig.4, it is also like the image in Fig.1.
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Fig.3. The mass of each steel sphere is 3kg. Fig.4. A pattern of ripples on the screen.
These ripples are caused by the disturbance of the gravitational_field between two steel spheres.
According to this point of view, these ripples as in Fig.4 might be called gravitational_waves in classical physics.
The width of the narrow gap between two steel spheres is 0.1mm, as shown in Fig.5. When a laser beam passing through the narrow gap between two steel spheres and creates a pattern of ripples on the screen, as shown in Fig.6.
Fig.5. The mass of each steel sphere is 4.1kg. Fig.6. There are 6 bright ripples within the range of 100mm.
The width of the narrow gap between two steel spheres is 0.4mm, as shown in Fig.7. When a laser beam passing through the narrow gap between two steel spheres and creates a pattern of ripples on the screen, as shown in Fig.8.
Fig.7. The mass of each steel sphere is 4.1kg. Fig.8. There are 10 bright ripples within the range of 100mm.
Comparing Fig.6 with Fig.8, the width of the narrow gap increases, and the number of bright ripples increases within the range of 100mm.
The width of the narrow gap between two steel spheres is 0.1mm, as shown in Fig.9. When a laser beam passing through the narrow gap between two steel spheres and creates a pattern of ripples on the screen, as shown in Fig.10.
Fig.9. The mass of each steel sphere is 3kg. Fig.10. There are 7 bright ripples within the range of 100mm.
Comparing Fig.6 with Fig.10, the mass of the steel sphere increases, and the number of bright ripples decreases within the range of 100mm.
3. Conclusion
From the above, it can be seen that gravitational_waves in classical physics have the following three characteristics:
(Ⅰ) gravitational_waves in classical physics are visible under the action of a laser, and ripples of gravitational_waves in classical physics consist of bright and dark bands or fringes;
(Ⅱ) the number of bright ripples is directly proportional to the width of the narrow gap between two steel spheres within a limited range;
(Ⅲ) the number of bright ripples is inversely proportional to the mass of each of two steel spheres within a limited range.
4. Further exploration
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Fig.11. The width of the narrow gap between two steel Fig.12. Ellipse with major semiaxis a and
spheres is 0.5mm, the mass of each steel sphere is 3kg. minor semiaxis b. F is a focus
When a laser beam passing through the narrow gap
between two steel spheres and creates a pattern of
ripples on the scre en.
The polar equation of ellipse [3]
r=[image], where p=[image], e=[image], pande are constants (1)
Comparing Fig.11 with Fig.12, reveals that the pattern of gravitational_waves is a series of approximate ellipses. Why is the pattern of gravitational_waves elliptical? Let us analyse the reason below.
Imagine the gravitational_field as an invisible lake. Two steel spheres floating in it are similar to stones that drop into the water. They create ripples that move away from sources, these ripples are gravitational_waves in classical physics. Gravitational_waves in classical physics are visible under the action of a laser, as shown in Fig.11.
[image]
Fig.13. ar directed radially in toward the source of gravitational_waves O, the normal component an directed radially in toward
the center of curvature of curve S, and the tangential component at is tangent to a gravitational_particle P of curve S.
Figure13 shows a gravitational_particle P moving away from the source of gravitational_waves O, where the orbiting curve is S. The position of the gravitational_particle, or displacement from the center of the source of gravitational_waves, is measured by the vector r, whose magnitude is r. The velocity of the gravitational_particle at the point M is indicated by the vector v (with magnitude v), which is tangent to the curve S through the point M in the direction of motion and makes the angle ω with the horizontal axis (ω is a variant, 0≤ω≤2π). The centripetal acceleration is indicated by the vector ar. Thus the angular momentum of the gravitational_particle for the center of the source of gravitational_waves is given by L=mer×v, where the direction of L is normal to the plane formed by r and v, and the magnitude of L is L=mervsinα, where α is the smaller angle between r and v, and me is the mass of the gravitational_particle.
According to vector methods, ar is resolved into a normal component anand a tangential component at, as shown in Fig.13. Designating the magnitude of ar as ar, the magnitude of an as an, and the magnitude of at as at, we find[4]**
an=[image], tg([image]–α)=[image], ar=[image], ar=[image].
From the principle of conservation of angular momentum, we know
v=[image], L is a constant (2)
and therefore for the magnitude of the centripetal acceleration, we have
ar=[image],
so that the magnitude of the centripetal force Fr is Fr=mear=[image].
As the gravitational_particle moves away from the source of gravitational_waves, Fr is equal to the gravitational force between the gravitational_particle and the source of gravitational_waves, namely
[image]=[image],
where G is the gravitational constant, and mo is the mass of the source of gravitational_waves.
We can write R(sinα)3=[image].
Since [image]=rctgα****[5],
([image])2=[image], ([image])2=[image], [([image])2+r2](sinα)2= r2,
sinα=±[image], (sinα)3 =±[image],
R= [image] [3].
Then
(sinα)3R=±[image], or [image]=p (3)
where p=±[image], and p is a constant.
If we set u=[image], namely r=[image], then Eq.(3) is transformed into [image]+u=[image].
Solving this differential equation, we obtain
u=[image][1+ecos(ω–A ) ],
or
r=[image], where A and e are constants (4)
Comparing Eq.(4) with Eq.(1), the orbiting curve S is an ellipse.
.
Einstein’s theory of relativity is suitable for objects moving at high speeds. Under low-speed or static conditions, Newton’s theory of gravity combined with the theory of gravitational_field should be applied.