To Contents

To Part 6 Pioneers
To Part 8a Optical Distance Effect

7.       Application of the Obstruction Theory to the
Interstellar Comet ʻOumuamua

 On October 19, 2017, Robert Weryk of the Hallekala Observatory in Hawaii discovered Comet ʻOumuamua'. The name Oumuamua, from the local language, means "scout." This emissary from the distant cosmos has surprised and puzzled science. Surprised, because it was the first time anyone could definitively establish that an object originated from outside our solar system. The mysteries lie, of course, in the object's characteristics, but also in its orbital motion. Data on the comet was collected over a period of 80 days. It turned out to be an elongated object, a few hundred meters long, that tumbled about its center of gravity in about eight hours. It did not rotate around a principal axis.

The comet's greatest mystery to science, however, was its deviation from Newton's and Einstein's orbital formulas. The orbit is shaped like a hyperbola, but the speed at which it traveled differed in detail from theoretical values.

 When the comet was first observed on October 19, 2017, it was already on its way out of the solar system. It was then 33 million kilometres from Earth.

The comet was not moving in the ecliptic plane. The plane in which it was traveling was tilted significantly. This is irrelevant to our analysis, as we only need to focus on the difference between the obstruction theory and the traditional theory.

The closest point to the sun, the perihelion , of Pioneer 10 was at 0.255916 AU, which is equal to a distance of r_p = 38.3x10⁹ meters. This point had already been passed on September 9, 2017, more than a month before its discovery. On October 10, the planet passed the Earth's orbital distance.

Despite its close approach to the Sun, the comet showed no signs of a coma, the usual haze that surrounds a comet, nor of a tail that forms when it approaches the Sun.

At the moment Oumuamua passed its perihelion, its velocity was 87.71 km/s. By the time it crossed Earth's orbit, its velocity had decreased to 49.7 km/s. At a very large distance from the Sun in interstellar space, the comet's velocity is calculated to asymptotically approach about 26.33 km/s. This is called its base velocity v₀.

The orbital direction was deflected 66 degrees by the passage near the Sun (see Fig 5).

In data stored at other observatories, the orbit of Oumuamua has been traced over an 80-day period, from early October 2017 to January 2, 2018.

 

 

Figure 5 Impression of Oumuamua's orbit through the Solar System with the Sun (coloured) and the observed, shifted Sun (uncoloured).

 Due to the Sun's gravity, Oumuamua's speed increases as it approaches the Sun. This is self-evident. The question is how much the speed increased, because according to the literature, the speed decreased less as it moved away from the Sun than Newton's theory dictates.

During its stay near the Sun, this caused an unexpected, smaller decrease in velocity—and thus a relative increase in velocity—to which a value of 17 m/s is assigned (see Wikipedia 1I/'Oumuamua Non-gravitational Acceleration).

The literature shows that the calculations to explain the anomalous velocity are performed with assumptions that can differ by an order of magnitude. (See Seligman et al.; Dark Comets? Unexpectedly Large Nongravitational Acceleration on a Sample of Small Asteroids). This means that the number 17 could just as easily be two or three times as large or small.

 One thing was clear: an unknown force must be at work, amplifying the sun's gravity. That was the crux of the mystery .

However, the change in true velocity that we were able to apply so successfully in the previous paragraphs to the braking acceleration of Pioneer 10 turns out to be completely useless for Oumuamua to explain the relative velocity increase of 17 m/sec. We had to find another solution.

 However, we can demonstrate that the outcome can be explained by another aspect of the obstruction theory. We start from the refreshing insight that the effect of gravity is based purely on the observation of the size of that mass. That is, the size of that mass as a solid angle of the black spot of the mass – seen from the object – determines the gravitational force (see p. 2). The Sun is thus observed using the light that reaches the comet from a point where the Sun was located r/c sec earlier and with the velocity that the Sun then had relative to the comet. 

 According to traditional views, the gravitational field is symmetrically constructed around a mass, meaning that a freely moving object in otherwise empty space will always follow a symmetrical path along or around the mass. At a certain distance from the mass, the outgoing velocity equals the incoming velocity.

According to obstruction theory, this isn't the case, because the acceleration an object experiences also depends on its state of motion in the gravitational field. We already saw this in the analysis of the anomalous acceleration of the Pioneers, where the actual speed played a role.  For comet Oumuamua this plays a minor role, but the influence of the observed position that must be taken into account instead of the real position brings us close to resolving the anomalous velocity of Oumuamua. The direction of the velocity turns out to be even more important.

The point is this: light from the sun needs time to reach the object. The object moving toward the sun receives, at a certain point, light that was previously emitted when the sun—as seen from the object—was still farther away. This perceived distance, which is longer than Newton's actual distance, results in the solid angle of the sun's black spot being perceived as smaller than Newton's. Therefore, the actual strength of gravity is weaker than Newton's.

When the object moves away from the sun, the sun will appear closer than its actual distance at that point. In that case, gravity is stronger than according to Newton's current theory.

Therefore, the solid angle of the Sun, seen from a given distance r, is smaller when an object approaches the Sun than when that same object is receding from the Sun at that point. The acceleration of the Sun experienced by the comet—which is related to the size of the solid angle—is therefore smaller at any distance during the approach than during the receding distance. This leads to an asymmetry in the orbital motion.

Ø            The difference in distance between the actual distance and the distance during the movement of the object I call the Optical Distance Difference.

 We will calculate the acceleration difference due to the optical distance difference at a given distance r from the Sun, between a comet stationary at that point and a comet moving toward the Sun at that point with velocity v.

The time it takes light to cover this distance is t = r/c sec. In that time, the comet has covered the distance  Dr = (r/c )v meters.

However, the comet does not approach the Sun in a straight line. It approaches the Sun in an orbit with an angle j between its direction of motion and the direction in which the Sun is seen. The reduction in acceleration experienced by the comet is caused by the component of the gravitational difference due to the optical distance difference along the comet's orbit. This is found by multiplying the gravitational difference by cosj (see Fig 5).

 This component reduces the acceleration the comet experiences as it approaches the Sun. Therefore, the comet's velocity increases less rapidly than according to current theory.

When the comet passes its perihelion, the optical distance difference is zero and the difference component is also zero.

After passing perihelion, the differential component along the comet's orbit actually reinforces the sun's gravity, causing the comet's velocity to decrease even further compared to the prevailing theory.

This relative decrease in velocity is just as great before perihelion as it is afterward.

Ø            But then the speed should decrease, while the measurements showed it actually increased. So we're not done yet!

 Fortunately, there is a second aspect to the difference between perceived location and actual location.

The effect we're referring to can be seen by considering that when the sun is observed from a comet, it always appears slightly further forward, in the direction of the comet's velocity, than its actual location. This changes the angle j. This is best visualized when the comet passes its perihelion (Fig 6).

We see that the Sun (not coloured in the drawing) is slightly forward in the direction of velocity. This means that the sun's gravity has a slightly larger component in the direction of velocity than Newton's, causing the comet to reach a higher velocity than Newton's.

 

                                                 Fig 6 The comet passes its perihelion.

 This is called the angular effect, the angle at which the sun is positioned relative to the direction of the velocity, which means that gravitational acceleration has a component that increases the comet's speed relative to traditional theory.  

Our explanation for Oumuamua's anomalous velocity is therefore based on the Sun's altered geometric position—both in distance and direction—due to the comet's velocity.

We will discuss the effect of the optical distance difference and the angular change separately. As long as these effects are small compared to Newtonian acceleration, we can use the sum or difference of the results. Finally, we will investigate whether the velocity change resulting from these two effects corresponds to the measured value.  

Ø            In the article on Dark Matter on this website (see "Dark Matter and Evanescent Stars"), we identified the Optical Distance Difference as the cause of the unexplained rapid orbital motion of stars in the outer regions of a galaxy. There, the transfer of angular momentum from the stars moving in the inner regions of the system to those on the outer edges played the most significant role.

Back
To Part 8a Optical Distance Effect