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## Content Page

Premise

Hypothesis

Symbols Defined

Introduction

Void Hypothesis Formulation

Setting Parameters

Convergence of Masses

Divergence of Masses

Mass and Distance Scales

Impossible to determine Cuni

Graphing Analysis

Using Data for Graphing

Using Arbitrary Equation and Graph

Explanation of Gravitational Anomalies

Internet Soured Data

Scientific Constants Used

Processed Data

Equations Used

Bibliography

## Premise:

Newton’s Law of Gravity is wrong. Hypothesis:

## The fundamental force of gravity is a result of space repelling space, matter occupying space in 3-dimensional space experiences attraction wherein the space between 2 separate masses arecompressed, and repulsion wherein the space between 2 separate masses are stretched. The Hypothesis asserts that space is elastic and can therefore be compressed or stretched. The Hypothesis asserts that a unit space exerts a repulsive force on another unit space universally.

## Symbols Defined

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## Introduction

The premise is vital in order to explain the hypothesis which theorises that the fundamental force of Gravity is not a result of matter exerting an attraction force on matter but a result of space repelling space. In this scientific paper, the Void Hypothesis shall be used to explain the following anomalies that occur on galactic scales in the Universe:

(i) Galaxies have less mass than is observed otherwise known as the ‘missing mass problem’. (Oakes,2010)

(ii) Stars further from the centre of a galaxy are not orbiting slower past a critical point. (Matthews,2018)

(iii) Rotation speeds of Dwarf Galaxies are higher than that of Galaxies. (Brownstein & Moffat, 2005)

(iv) Gas from the giant spherically shaped Galaxy - M87 did not disperse after a long time. (NASA)

(v) Tully-Fisher Relation: The amount of light energy emitted by a spiral galaxy is roughly proportional to its speed of rotation. The faster the galaxies spin, the brighter they are. (Matthews,2018)

(vi) Dark Flow: Many large galaxy clusters converging to an area in the night sky between constellations Vela and Centaurus. (Gefter, 2009) Many of these anomalies can be explained directly by that the gravitational force a galaxy exerts on itself is greater in magnitude according to Void Hypothesis than Newtonian-Gravity.

## Void Hypothesis Formulation

Each unoccupied unit space in the Universe repels every other unoccupied unit space (m[3]) at a universal constant which results in expansion or compression of regions of space. Consider that masses that occupy space are at fixed Cartesian coordinates in space and does not move along the fabric of space, but rather the regions of space within and around and between them stretches, and in so doing moves the masses. Hence, when two discrete masses are converging, the region of space in between the masses is compressing; conversely when two discrete masses are diverging, theregion of space in between the masses is expanding. According to this definition of gravity, the Space-Repulsion Force exerted to compress or expand a defined volume of space is directlyproportional to the product of the two regions of space.

F_{void}_{V} _{V} , _{V} and _{V} are the respectively defined and separate enclosed regions of space void in out in out repelling each other. _{F} _{C} _{V} _{V} , _{C} is the universal constant by which two unoccupied unit void uni in out uni spaces repel each other.

## Setting Parameters

Since the force generated by unoccupied unit spaces is universal and undiminished by distance, itwould be difficult to understand without first defining enclosed regions of space in which spacebeyond this enclosure does not generate forces influencing the space within the enclosure.

There is a general distinction between masses in a large region of space and masses in a small regionof space. For a small enclosed space with isolated masses concentrating near the centre, the massesconverge towards each other because the space within the enclosure that is surrounding theisolated masses repels the space between the isolated masses. This is comparable to the effect of Newtonian-Gravity wherein asteroids, meteorites or comets that fall within the dominantgravitational field of a star, planet, dwarf planet or moon is pulled towards it. In contrast, for a largespace scale the space between the isolated masses could be so large that its space-repulsion withincould cause it to expand rather than compress. Hence, isolated masses or mass systems along thecoordinates of radial expansion will experience divergence resulting in large mass systems likegalaxies and galactic clusters to be moving apart.

## Convergence of Masses

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Figure 1: Cross-section of a 3-dimensional pill-shaped region of space with two discrete and identical spherical masses ofuniform mass density occupying volumes V1 and V2 respectively.

The two discrete masses are not point masses and by conventional physics is experiencing Newtonian-Gravity attraction towards each other without orbiting each other. The distance betweenthe centres of the two masses, d is small compared to the radius of the hemispherical regions A and B, l. (d << l); the enclosed volume E is much smaller than enclosed volumes A, B, C and D. (E << {A, B,C, D}); E is being repelled from all directions by the surrounding A, B, C and D and is compressed. As E is being compressed by Fvoid, the two masses being of fixed coordinates on the fabric of spaceaccelerates towards each other. Each respective enclosed volume of regions of space must also repelitself from within and is expanding outward at its own respective Fvoid. However, E is expandingoutward at a much smaller Fvoid than the overall compressional forces Fvoid exerted on E by A, B, Cand D. The enclosed volume V1 and V2 also contain empty space within the solid lattice matter ofthe masses. However, considering V1 and V2 is much smaller than E, the forces Fvoid generated bythis space on A, B, C, D and E is small and insignificant.

Alternative to considering bulk regions of space consider the vector forces of unoccupied unit spaces at coordinates within the region of spaces A, B, C and D.

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Figure 2: : The vector space-repulsion forces acting on three defined points in the region A by each arbitrary point inregions B, C and D. (Considering rotational symmetry of pill shape, exclude z axis.)

Consider the vector components acting on an unoccupied unit space that negates each other are added together as the magnitude of compression of the unoccupied unit space; Consider the vectorcomponents acting on an unoccupied unit space that add to each other are added together to forma resultant vector with a magnitude and direction. If the magnitude of compression exceeds themagnitude of resultant vector, the unoccupied unit space is compressed. If the magnitude ofresultant vector exceeds the magnitude of compression, the unoccupied unit space is stretched inthe direction of the resultant vector by the difference between the two magnitudes.

B, C and D each have an arbitrary point pointing towards a1, a2 and a3 in A. a1 and a3 each have a greater resultant vector than a2. a2 have a greater compression magnitude than a1 and a3.

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Figure 3: The cones are used to illustrate spatially the result of the vector space repulsion forces.

Hence, one can draw a cone with a curved bottom to accommodate V1 in A, and associate the pointsapproaching the slant height of the cone from the inside as regions of increasing resultant vectorsand decreasing compression magnitudes. Conversely associate points approaching the base of the cone with the curved inset around V1 as regions of increasing compression magnitude and decreasing resultant vectors. Do the same for B, C and D.

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Figure 4: Smooth out the edges of the cones and join the inner parts of the cones.

In consideration of edge effects smooth out the edges of the cones and draw an imaginary line to join up and form the region enclosed by the cones (blue) as a region of high compression magnitude and low resultant vectors. This blue region seems reminiscent of what a gravitational field of the two isolated masses would look like in Newtonian-Gravity.

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Figure 5: Equipotential contours (solid curves) surrounding two masses, m close together. Gravitational field lines(dashed lines).

## Divergence of Masses

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Figure 6: Cross-section of 3-dimensional space of the Universe (assumed spherical) with the enclosed regions of volumeof spaces C surrounding B, B surrounding A.

The centre of the Universe is marked by an X and the edge of the Universe is characterised by a Bold Circle. The two points in space P1 and P2 are respectively a point near the centre of the Universe, and a point near the edge of the Universe.

A is much smaller than B and C combined, and the F void exerting on the surface area of A by B and C is the product of A volume and the addition of B volume and C volume. _{F} _{C} _{A} (_{B} _{C} ) void uni area area area C is much smaller than A and B combined and the Fvoid exerting on the inner surface area of C by A and B is the product of Cvolume and the addition of Avolume and Bvolume. F C C (A B ) void uni area area area

Calculations will show that the Fvoid acting on P1 is much smaller than the Fvoid acting on P2. Assign the radius of A, B and C at ratio of 1, 10, 11 units respectively.

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A mass system at P1 is accelerating radially outwards at a slower rate than a mass system at P2. Since the Universe is expanding outwards at an accelerating rate both vectors should be starting from their respective points P1 and P2, and pointing right of the Figure 2. (Gefter, 2009)

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Figure 7: Cross-section of 3-dimensional space of the Universe (assumed spherical) with the enclosed regions of volumeof spaces L, M and R.

Each unit space in L, M and R exerts a vector of equal magnitude and different directions on the unit space at P1. Due to symmetry of the spherical Universe, the resultant vector from L on P1 and P2 is to the right and any resultant from M and R on P1 and P2 is to the left, but since L is greater than M and R combined, the resultant of all the unit spaces in the Universe on the unit space at P1 is to the right; likewise since L and M combined is greater than R, the resultant of all the unit spaces in the Universe on the unit space at P2 is also to the right. The compression magnitude on P1 and P2 would be a result of all vectors components perpendicular to the horizontal acting on the two respectiveunoccupied unit spaces. Hence, separate the L, M and R regions horizontally across the mid-section and calculate the effects of the perpendicular components on the points P1 and P2.Using previously assigned ratios for A, B and C; distance from the centre of the universe to P1, P2and the edge of the Universe is respectively 1, 10 and 11 units.

Calculations will show that F2 is much greater than F1, and the compression magnitude at P1 is much greater than at P2.

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Since an unoccupied unit space at P1 has lower resultant vector and greater compression magnitude than that at P2 a mass system at P1 should be more compact and moving away from the centre of the Universe at a slower rate than an identical mass system at P2.

Hence, the same problem can be solved in terms of overall simplified area product of enclosed volumes of spaces and in terms of vectors of unit spaces.

## Mass and Distance Scales

Since Void Hypothesis is postulated to be universal, it should be consistently applicable at small orlarge scales. Consider a mass system existing in space. Depending on how large this mass system isthere is an average distance between this mass system and another mass system of approximatelythe same order of magnitude. The effect of the space beyond this average distance should beneglected for the sake of setting an upper limit at this distance because the Cuni is not known.Hence, the various mass scales are defined in order to differentiate between the scales of the Fvoidacting on the mass systems.

(1) Microscopic with average distance between atoms

(2) Stars and Planets

(3) Galaxies at Intergalactic distances

(4) Galactic Clusters

## Impossible to determine Cuni

An experimental Cuni for some mass scales may be calculated and used to estimate the final value of Cuni. Each Mass Scale is enclosed by a larger space spherical shell. For instance galaxies are enclosedby a space spherical shell of intergalactic distance thickness. As the volume of space enclosedincreases for larger Mass Scales the experimental Cuni decreases. In the Universe, the larger the Mass Scale the more masses would appear on different coordinates in the domain of spherical shell which would increase the complexity of the enclosed volume. Hence, the error of calculation would increase, and at the largest Mass Scale galactic clusters are surrounded by a spherical shell as large as the universe. This undiminished Cuni cannot be calculated with sufficient precision and accuracy because of lack of information of the unobservable Universe.

## Graphical Analysis

### Using Data in Graphing

Investigate the relationship between Space-Repulsion Force over Universal Constant of Space Repulsion, F void/C uni against the Radial Distance from the Centre of Earth, r.

Acquire data points at the surface of each Earth layer {Crust, Upper Mantle, Lower Mantle, Outer Core, Inner Core} in addition to the Earth’s centre.

Plot two graphs of Fvoid/Cuni against r for 0 ≤ r ≤ Rearth and 0 ≤ r ≤ Rvenus respectively; where Rearth is the mean radius of the Earth and Rvenus is the mean distance from Venus to Earth’s orbit.

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Figure 8: Linear Fit of data points within Earth's Radius

The linear fit of data points for 0 ≤ r ≤ REarth shows that the graph varies linearly with a positivegradient.

Generate 100 data points with equally spaced divisions between Rearth and Rvenus.

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Figure 9: Non-linear Fit of data points until Venus’s orbit

The exponential non-linear curve fit of data points for 0 ≤ r ≤ Rvenus shows that the graph seems to resemble the graph of equation: y = x[3](RU3 - x[3]) where RU = Rvenus.

This graph shows that the gravitational force increases as r increases beyond the Earth’s surface. This shows that the implementation of Space-Repulsion on Mass Scale (2) is erroneous. This failure in representation can be attributed to one factor. The upper limit of this graph, R is erroneously speculated to be at Rvenus because the Cuni is unknown.

Attempting to use Space-Repulsion to represent the Mass Scale of (3) or (4) may also be erroneous because the planets and stars are part of a greater mass system the galaxy; each planetary and star sized object generates its own gravitational field according to the equation: y = x[3](RU3 - x[3]) withrespect to its centre and with its own respective R value, and increases the complexity of finding the resultant graph for the galaxy.

### Using Arbitrary Equation and Graph

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Figure 10: Graph of Arbitrary Equation

Use the Arbitrary Graph of formula y = x[3](RU3 - x[3]), RU = 100, to explain the galaxies dimensions. yrepresents the gravitational field strength whereas x represents the radial distance from the centreof the mass system. There is a stationary point of relative maximum point at ( 79.8, 250 000 000 000 ) ( 3 s.f ) which coincides with the algebraic differentiation acquired expression: x U [3] 2 The upper limit of the edge of the galaxy should be at the end point x = 100 where gravitational field strength = 0.

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Figure 11: Typical graph of Newtonian-Gravitational Field Strength, g against Radial Distance from the Centre of a planetor star, r

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, where m is unit mass, M is the Mass of arbitrary planet or star and R is the radius m r of the planet or star.

For the condition: 0 ≤ r ≤ R, M is directly proportional to r[3] because there are 3 dimensions of space while r[2] is the denominator of g. Hence, g is directly proportional to r. For the condition: R ≤ r ≤ ∞, M is a constant, while r[2] is the denominator of g. Hence, g is inversely proportional to r[2].

Assume that for a galaxy, the g increases linearly as r increases across the massive bulky centre ofthe galaxy then starts to increase non-linearly as r increases across the less dense outer part of thegalaxy, and lastly starts to decrease at a polynomial degree of -2 beyond the edge of the galaxy. Sucha graph can be surmised to look roughly like Figure 11 wherein the sharp discontinuous peak issmoothed out. Hence, consider the sharp discontinuous peak in Figure 11 to be a narrow peak forthe comparison below.

Compare Figures 10 and 11 by aligning their starting, peak and end points respectively and proportionately. Figure 11 does not have a graph end point; hence simply pick a point where g Newtonian is extremely small. Figure 10 has a broad peak whereas Figure 11 has a narrow peak. Assume that the Space-Repulsion Field Strength peak is greater in magnitude than the Newtonian Gravitational Field Strength peak since gvoid increases at an exponential rate to peak whereasg Newtonian increases at a linear rate to peak.

Based on the above comparison, the calculations of the orbital linear velocity of stars in the lessdense outer part of the galaxy using Newtonian-Gravity would yield the gravitational anomaly (ii).This means that the edge of the galaxy is somewhere beyond R in Figure 11 for astronomer’scalculations.

Based on the same comparison, calculations of the orbital linear velocity of stars about the galactic centre in the less dense outer part of the galaxy using Space-Repulsion would yield cohesive results if the edge of the galaxy is somewhere beyond the stationary point or relative maximum value but extremely close to it. Because the peak is broad and the rate of change of gvoid as r changes is small, the stars in the less dense outer part of the galaxy would seem to orbit the galactic centre at roughly the same orbital linear velocity as r increases.

Even as the limit of the galaxy is at the end point of Figure 10, the edge of the galaxy is not a well-defined distance because the galaxy is a discontinuous mass of loosely held stars and planets. Starsof low but non-zero centripetal force might either be flung out of the galaxy into intergalactic spaceor drawn into orbit around stellar masses deeper into the galaxy during the formation of the galaxy,thus, creating a massless band of space in-between the broad peak and the end point of the graph.Hence, the existing stars at the less dense outer part of the galaxy would have substantial centripetalforce acting on it.

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The orbital linear velocities of stars in orbit about the galaxy’s centre for Newtonian-Gravity is dependent on the mass of the galaxy, whereas for Space-Repulsion is dependent on the mass of the star and the radial distance from the galaxy’s centre.

In Figure 10, there might be a point where the gravitational field strength drops to a value equal to 100 billionth of the Earth’s surface gravity in-between the broad peak and the end point of thegraph. Given that the mid-point of the board peak and the end point of the graph is a steep negative gradient, it may have been misunderstood as a critical-point where gravitational constant rapidlydecreases. (Matthews, 2018)

## Explanation of Gravitational Anomalies

(i) Galaxies have less mass than is observed otherwise known as the ‘missing mass problem’. (Oakes,2010)

Explanation:

In the Mass Scales (3) and (4), Newtonian-Gravitational Force is weaker than Space-Repulsion Force in magnitude and hence, there is a missing mass when calculating the mass of a galaxy based on Newtonian-Gravity and the observed light coming from it. Calculations using Void Hypothesis may yield an accurate value.

(ii) Stars further from the centre of a galaxy are not orbiting slower past a critical point. (Matthews,2018)

Explanation:

According to Newtonian-Gravity, stars further from the centre of a galaxy should have a lower Gravitational Force acting on it and hence orbit the galaxy centre at a lower linear speed. This isbecause of a direct proportionality relationship between the centripetal force of a circular motion

system and the orbital linear velocity of the object in motion (Fv ). However, according to Space-Repulsion, the Graphical Analysis assumes that the maximum peak is broader and is at alarger magnitude than that in Newtonian-Gravity. Assuming that the less dense outer part of thegalaxy fits the broad peak the orbital linear velocity of stars would remain roughly the same sincethere is only a small change in centripetal force as radial distance from the centre of the galaxyincreases.

(iii) Rotation speeds of Dwarf Galaxies are higher than that of Galaxies. (Brownstein & Moffat, 2005)

Dividing the predicted MSTG flat rotation velocity over the MSTG predicted total mass of the galaxy and then averaging for the following categories:

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Explanation:

Dwarf Galaxies are of lower mass and size than Galaxies. Assume that intergalactic distance appliesfor Dwarf Galaxies; a Dwarf Galaxy has a smaller inner volume, Vin and larger outer volume, Vout ascompared to a Galaxy. According to Space-Repulsion, and the calculations involving Figure 3a, thecentripetal force of a Dwarf Galaxy acting on itself is higher than that of a Galaxy acting on itself as

compared to Newtonian-Gravity, and as before (Fv ). Hence, the stars of a Dwarf Galaxy rotate about its centre faster than those of a Galaxy.

The error in calculating the orbital velocity is further amplified by the Newtonian-Gravitational Force having a direct proportionality relationship with the mass of the mass system ( F M ).

(iv) Gas from the giant spherically shaped Galaxy - M87 did not disperse after a long time. (NASA)

Explanation:

The gas cloud of the giant spherically shaped Galaxy has not yet dispersed because the Space- Repulsion Force acting on a Galaxy sized gas cloud is greater than that calculated in Newtonian- Gravity. Hence, the gas cloud of the Galaxy M87 is still visible even as it is only supposed to exist for an approximate 100 million years. (NASA)

(v) Tully-Fisher Relation: The amount of light energy emitted by a spiral galaxy is roughly

proportional to its speed of rotation. The faster the galaxies spin, the brighter they are. (Matthews,2018)

Explanation:

The spiral arms of a galaxy have enclosed volumes of empty space between each spiral arm and these spaces are not symmetrical with respect to a spiral arm. The empty space that are in front andbehind each spiral arm acts with Space-Repulsion Forces on the empty space between the stellarcomponents of the spiral arm and disturbs the respective velocities of the stars and planets. Perhapsthis causes them to move unpredictably by a small extent outside of their intended trajectory withrespect to the galaxy. The stars which were originally obscured by other stars blocking in front of itcomes out behind the star and into view of an observer. Since there is much more empty space thanmass in a galaxy the probability of a star being obscured by another star before and then beingrevealed after is much higher than the probability of a star not being obscured by another starbefore and being obscured by it afterwards. Therefore, the overall effect of this disruption is that thespiral arms appear to be brighter; coincidentally the spiral arms might be orbiting faster as a result ofthe aforementioned Space-Repulsion Forces.

(vi) Dark Flow: Many large galaxy clusters converging to an area in the night sky between constellations Vela and Centaurus. (Gefter, 2009)

Explanation:

The Universe has been expanding uniformly in space since the Big Bang. A sudden convergence ofgalactic clusters is paradoxical to the expansion of the Universe. Assume the converging galacticclusters are at a part of the Universe where it has more matter distribution than other parts, andthus have less space between the galactic clusters. The Universe expands until a point where thespace surrounding all the aforementioned galactic clusters is large enough that the Space-Repulsion Force that compresses the space between the galactic clusters is overwhelms the Universe’s Space Repulsion Force to expand the space between the galactic clusters. Hence, the galactic clustersconverge rather than diverge.

## Internet Sourced Data

Earth Crust’s Composition (Earth's Composition and Structure: A Journey to the Center of the Earth)

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Earth’s Mantle (Allegre, Poirier, Humler, & Hofmann, 1994)

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### Scientific Constants Used

(CODATA 2006 based on a least squares adjustment of data from different measurements Numbers in parentheses represents the uncertainties of the last two digits)Avogadro Number, NA = 6.02214179 (30) x 10[23] particle/mol Bohr Radius, ao = 5.2917720859 (36) x 10-[11] m Calculated Bohr Volume, V0 = 6.207146595 x 10-[31] m[3]

## Processed Data

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[The calculated errors of uncertainties add up such that f highest precision that computer offers for processed data would be round to 1. Hence, use the f which is at 9 decimal places.]

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[F void/C uni acquired by multiplying the Vout and Vin at the corresponding interface r values. Errors ofuncertainty calculated from previous table would be too small at > 21 decimal places. Hence, User set precision to 6 decimal places for processed data of _{V}, _{V} _{F} and the final data Fvoid/Cuni.]

## Equations Used

Void Hypothesis

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Fraction of Volume Composing of Unoccupied Space Mr

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Volume of Unoccupied Space

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## Bibliography

Allegre, C. J., Poirier, J.-P., Humler, E., & Hofmann, A. W. (1994). The chemical composition of the Earth. Paris, Cedex: Elsevier Earth and Planetary Science Letters.

Brownstein, J. R., & Moffat, J. W. (2005). Galaxy Rotation Curves Without Non-Baryonic Dark Matter.Waterloo, Ontario: The Perimeter Institute for Theoretical Physics, Waterloo, Ontario, N2J2W9, Canada.

Earth's Composition and Structure: A Journey to the Center of the Earth. (n.d.). Retrieved from App State: http://www.appstate.edu/~marshallst/GLY1101/Lectures/2-Earth-

Composition_Structure.pdf Elert, G. (1998). Astronomical Data: The Physics Hypertextbook. Retrieved from The Physics Hypertextbook: physics.info/astronomical

Gefter, A. (2009, January 21). New Scientist. Retrieved from New Scientist: https://www.newscientist.com/article/mg20126921-900-dark-flow-proof-of-another-universe/ Matthews, P. R. (2018, February). Something's Wrong with Gravity. BBC earth Asia Edition Vol 9 Issue12, pp. 28 - 35.

NASA. (n.d.). 22 The Mystery of the Missing Mass. Retrieved from SP-466 The Star Splitters:https://history.nasa.gov/SP-466/ch22.htm

Oakes, K. (2010, September 24). basic space: MACHOs, WIMPs and the mystery of the missing mass.Retrieved from basic space: https://kellyoakes.wordpress.com/2010/09/24/machos-wimps-and-the-mystery-of-the-missing-mass/

Ptable. (n.d.). Retrieved from Ptable: https://www.ptable.com

Structure of the Earth: Hyper Physics. (n.d.). Retrieved from Hyper Physics: Hyperphysics/phy-astr.gsu.edu/hbase/Geophys/earthstruct.html

- Quote paper
- Zhen Li Ang (Author), 2018, The Void Hypothesis. An Alternate Gravity Hypothesis to Explain Several Gravitational Anomalies, Munich, GRIN Verlag, https://www.grin.com/document/430846

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