Ancient Life’s Gravity and its Implications for the ...€¦ · the elephant’s legs are thicker still to sup-port its massive bulk. The elephant is near the upper size limit for

pag. 307G. Scalera, E. Boschi and S. Cwojdzinski (eds.), 2012THE EARTH EXPANSION EVIDENCE – A Challenge for Geology, Geophysics and AstronomySelected Contributions to the Interdisciplinary Workshop of the 37th International School of GeophysicsEMFCSC, Erice (4-9 October 2011)

Ancient Life’s Gravity and its Implications forthe Expanding Earth

Stephen Hurrell

11 Farmers Heath, Great Sutton, Ellesmere Port, Cheshire, CH66 2GX, United Kingdom –Phone: +44 (0) 7753 587469 ([email protected])

Abstract. Galileo Galilei emphasised in the 17th century how scale effects impose an upperlimit on the size of life. It is now understood that scale effects are a limiting factor for thesize of life. A study of scale effects reveals that the relative scale of life would vary indifferent gravities with the result that the relative scale of land life is inversely proportionalto the strength of gravity. This implies that a reduced gravity would explain the increasedscale of ancient life such as the largest dinosaurs. In this paper, various methods such asdynamic similarity, leg bone strength, ligament strength and blood pressure are used toestimate values of ancient gravity assuming a Reduced Gravity Earth. These results indicatethat gravity was less on the ancient Earth and has slowly increased up to its present-dayvalue. The estimates of the Earth’s ancient reduced gravity indicated by ancient life arealso compared with estimates of gravity for Constant Mass and Increasing Mass ExpandingEarth models based on geological data. These comparisons show that the Reduced GravityEarth model agrees more closely with an Increasing Mass Expanding Earth model.

Key words. Ancient gravity – Reduced gravity Earth – Scale effects – Expanding Earth

1. Introduction

Galileo Galilei (1638) was probably thefirst scientist to point out that larger an-imals need relatively thicker bones thansmaller animals. He noted that the bonesof very large animals must be scaled out ofproportion in order to support the weightof the animal. This is because when anyobject increases in size its volume (l3) in-creases quicker than its area (l2), and itsarea increases quicker than its length (l).For example, a simple box which was dou-bled in length would be four times the areaand eight times the volume of the originalbox. The leg stress in a large animal is pro-portionally more than a geometrically sim-ilar small animal because the weight of thelarge animal has increased quicker than itsstrength. This is commonly known as thescale effect.

To overcome this shortfall in strengthwith increased size, the legs of real large-scale animals generally tend to be propor-tionally thicker. Take for comparison thethigh bones of a deer, a rhinoceros and anelephant. As animals increase in scale therelative thickness of their legs is greater.The deer has the most slender legs, therhinoceros relatively thicker ones, whilethe elephant’s legs are thicker still to sup-port its massive bulk. The elephant is nearthe upper size limit for land-based life.

The same basic principles can be seenin land-based animals, plants and flyingbirds. The largest insects have reachedthe upper size limit for creatures withoutbones. Mammals have reached the largestsize for animals with bones and a com-plex four-chambered heart. Reptiles havereached the largest size for animals withbones and simple hearts. The largest plants

308 HURRELL: Ancient life’s gravity and expanding Earth

have reached the upper limit in size and thelargest birds have reached the upper lift-ing capacity of their wings. For every formof living creature there is an upper limit tohow large it can be.

The scale effect means that gravitylimits the scale of present-day land-basedlife. This has been well understood formany years by specialists in the field suchas Thompson (1917), Schmidt-Nielson(1984) and others. The scale effect limitpresents a difficult problem for ancient gi-gantic animals like dinosaurs. Over theyears, many different solutions to the prob-lem of their large scale have been sug-gested. Until at least the 1980s it waswidely thought that large sauropods livedin water so the buoyancy effect permit-ted them to grow large (Schmidt-Nielson1984), but this idea is now considered in-correct. Bakker (1986) was the main cham-pion for the evidence that these large ani-mals lived on land and his interpretation iswidely accepted today. Hokkanen (1985)calculated a theoretical upper mass limitfor an animal in present gravity that laybetween 105 to 106 kg (10 to 100 met-ric ton) but also found the athletic abil-ity of the largest animal to be so low that"a mass 106 kg allows a running speedof 6 km/h – a man could walk and over-take". Conversely, many paleontologistsaccept Bakker’s (1986) understanding thatsauropods were at least as athletic as mod-ern elephants.

The concept that a reduced gravity inthe past may have increased the relativescale of ancient life has been less wellresearched but has been considered byKort (1949), Hurrell (1994, 2011), Mardfar(2000, 2011), Erickson (2001), Scalera(2002, 2004) and Strutinski (2011).

2. The relationship between relativescale and gravity

The relationship between relative scale andgravity can be examined using standard an-imals as shown in Fig.1. Imagine there aretwo animals of exactly the same shape, ex-cept that the larger one is twice the lin-ear scale of the smaller animal. Under the

same gravity, the stress in the larger ani-mal’s legs would be double the stress in thesmaller animal’s legs. This variation can becompensated for by adjusting the strengthof gravity: if gravity was one half as strongfor the larger animal, it would be four timesas heavy. Both the small and large animalswould have the same leg stress becauseof the difference in gravity. They wouldbe dynamically similar despite their dif-ference in size because of the variation ingravity.

In the above example the relative scaleof life was increased because of the re-duced force of gravity. This mathematicalrelationship between the scale of life andgravity can be defined as:

For a particular form of life the lin-ear scale of land-based life is in-versely proportional to the strengthof the gravitational field (Hurrell,1994).

This can be represented in a formula as:

S r =1gr

(1)

where S r is the relative scale of life, andgr is gravity relative to the Earth’s currentgravity.

The effect of gravity on life’s scale is adistinct mathematical relationship that af-fects the basic building blocks of animals –bones, ligaments, muscles and blood pres-sure. A reduced gravity reduces the forceon any animal’s bones, ligaments and mus-cles so they can all be thinner and weakerfor a particular scale of life. Blood pressureis also reduced in a weaker gravity sinceblood pressure is the hydrostatic weight ofblood (mass × gravity).

This implies that the scale of ancientlife was shifted towards a larger size in areduced gravity. The most obvious resultof this scale shift is gigantic dinosaurs withmasses equal to several elephants but theeffects are also plain on smaller animals aswell. An elephant-sized dinosaur is notice-ably more active and dynamic than any ele-phant because the dinosaur evolved to livein a reduced gravity.

HURRELL: Ancient life’s gravity and expanding Earth 309

Fig. 1. The force on geometrically similar animals in a different gravity illustrates the relationship betweenlife’s scale and gravity. An animal’s leg stress is due to the force of gravity. If gravity is halved then thelarge animal can double its linear size while its leg stress will still be the same as the small animal’s legstress.

Formula (1) can be transposed to pro-vide an estimate of ancient gravity basedon the relative scale of ancient life:

gr =1S r

(2)

This paper calculates values for re-duced gravity and weight on an assumedReduced Gravity Earth using ancient lifeand introduces ‘shorthand descriptions’ todenote this throughout the paper. For ex-ample, gravity and weight 300 millionyears ago may be defined as gravity300 org300 and weight300 or w300. Specific values

of reduced gravity are also given a ‘short-hand description’ so that, for example, areduced gravity of 60% the present gravityis given as 0.6g.

The values of calculated ancient grav-ity also have a ‘confidence index’ allo-cated which is a method of assigning a nu-meric value to the confidence in the results.Two methods are used to allocate a ‘confi-dence index’. The first method is to definea ‘reconstruction confidence index’ anda ‘dynamic similarity confidence index’and calculate a ‘total confidence index’ bymultiplying the two results together. The


Fig. 2. A modern rhinoceros and Triceratops both moving and acting in a dynamically similar manner.

‘reconstruction confidence index’ denotesconfidence in the original reconstruction ofthe ancient animal. The ‘dynamic similar-ity confidence index’ denotes confidencethat the animal moves and acts in a similarmanner to the animal used for comparison.The second method used to define a ‘totalconfidence index’ utilises the ratios of thecalculated values of Minimum gravity andMaximum gravity when they are available.The examples given throughout the paperillustrate these methods more fully.

Various methods, such as dynamic sim-ilarity, leg bone strength, ligament strengthand blood pressure are used to estimatereasonably accurate values of ancient grav-ity. Numerous comparisons could be usedto calculate ancient gravity but just a fewexamples are given to illustrate the princi-ples in more detail.

3. Dynamic similarity

Palaeontologists have noted that large di-nosaurs appear to be dynamically similarto smaller animals alive today (Alexander,1983, 1989; Bakker, 1986).

In a reduced gravity this increase in therelative scale of life is exactly what wewould expect. The relative scale of dynam-ically similar ancient and modern life cantherefore be used to estimate the gravity atthe time of ancient life. In practice, the dy-namic similarity of the largest life is themost easy to compare since this life definesthe upper size limit for a particular form oflife in a defined gravity.

Triceratops – A Triceratops would ap-pear to move like a buffalo or a present-day rhinoceros suggesting that Triceratopswould be able to move and gallop in a dy-namically similar way to a rhinoceros asshown in Fig.2. Triceratops lived about 68to 65 million years ago and is about 1.67times the size of a rhinoceros, so if bothanimals are moving in a dynamically sim-ilar way then the value of gravity about 66million years ago can be calculated usingformula (2):

gravity66 = 1/1.67 = 0.6g

The Triceratops is a well-known ani-mal so the ‘reconstruction confidence in-dex’ is 0.9 out of a maximum 1. TheTriceratops is similar in general appear-ance to a rhinoceros although Triceratopsalso has a large tail so the ‘dynamic sim-ilarity confidence index’ may be 0.6. The‘total confidence index’ is therefore 0.9 ×0.6 = 0.54. To sum up, about 66 millionyears ago gravity was approximately 60%of our present gravity with a confidence in-dex of 0.54.

Ancient Dragonflies – Dragonfliessimilar to modern forms were present inthe Carboniferous, dating from about 300million years ago. These dragonflies wereusually large and occasionally giganticin size. The Muséum national d’Histoirenaturelle in Paris contains the only twoknown examples of the famous giant drag-onfly, Meganeura monyi. With a wingspanof about 75 cm, it is still claimed by some


Fig. 3. A life-size reconstruction (72 cm wingspan) of Meganeuropsis permiana by Werner Kraus for theUniversity Museum of Clausthal-Zellerfeld. c©Werner Kraus 2003.

authorities to be the largest known insectspecies to ever fly. This wingspan of 75 cmis gigantic compared to that of 19 cm forone of the largest modern species of drag-onfly, the Giant Hawaiian Darner dragon-fly, Anax strenuus.

Applying formula (2) to the ancient andmodern forms of dragonflies gives a valuefor gravity 300 million years ago:

gravity300 = 1/3.95 = 0.25g

Gravity 300 million years ago was25% of today’s gravity from a simple dy-namic similarity comparison. There aresome fundamental assumptions used withthis comparison; both the ancient dragon-fly fossils and the largest modern speciesof dragonfly are assumed to have reachedthe largest size possible for a dragonfly intheir respective gravities, and both the an-cient and modern dragonfly are assumed to

be dynamically similar and have followedsimilar lifestyles.

How accurate are these assumptions?The ancient dragonfly which is commonlyaccredited as being the largest has sev-eral rivals which are very close to the fa-mous giant dragonfly, Meganeura monyi.Examples of these are Meganeuropsisamericana and Meganeuropsis permiana,as shown in Fig.3, from the Lower Permianfauna of Elmo. Given the fact that theseare both very close in size to Meganeuramonyi it would seem likely that this isabout as large as these ancient dragonfliesgrew, even if there is some disagreementabout which was the largest.

A similar argument applies to thelargest present-day dragonfly. Althoughthe Giant Hawaiian Darner dragonfly isthe largest recorded size of dragonfly thereare other species approaching this size: theGiant Petaltail dragonfly Petalura ingentis-


sima has a wingspan of approximately 16cm, for example. It would seem that we cansafely assume that the sizes of the largestancient and modern dragonflies are suffi-ciently accurate to calculate gravity 300million years ago.

Is there any other way to check theresults? Since there are still dragonfliesaround today there is an interesting methodof doing this. Experiments performed byMarden (1987) loaded dragonflies withweights to measure the maximum amountthat a range of dragonflies could lift.The largest dragonfly that Marden exper-imented with was Anax junius, which iscommonly known as the Green DarnerDragonfly. The five individuals measuredhad an average mass of 0.9752 grams andan average maximum lifting force of 2.58grams with an average wingspan of 10 cm.Comparing these dragonflies to the ancientdragonfly Meganeura monyi would give ascaling factor of 75/10 = 7.5. Using thescale effect to calculate the weight and lift-ing force of the ancient dragonfly assum-ing it was dynamically similar to the mod-ern dragonfly gives:

Ws = (W1/3o × s)3 = (0.97521/3 × 7.5)3 =

= 411 g,

and

Ls = (L1/2o × s)2 = (2.5811/2 × 7.5)2 =

= 145 g,

where Ws is the scaled weight, Wo is theoriginal weight and s is the linear scal-ing factor applied. Ls is the scaled liftingforce, Lo is the original lifting force ands is the scaling factor used. Obviously thescaling factor will be the same to calcu-late the scaled weight and the scaled liftingforce.

This is clearly a dragonfly that couldn’tfly in our present gravity since it weighs411 grams but can only produce a lift-ing force of 145 grams. We could reducethe weight of the dragonfly by assumingthat gravity was 0.35g so that the lifting

force was exactly the same as the dragon-fly’s weight. This gives a maximum possi-ble force of gravity 300 million years agoas 0.35g. Even this seems beyond reason-able limits since it is difficult to imaginea dragonfly that didn’t have any power re-serves. It doesn’t seem a realistic proposalespecially if we consider that dragonfliesare predators that need to capture smallinsects to survive and the female dragon-fly must also mate in flight and then layits eggs in water – a sudden gust of windwould drown our large dragonfly. It proba-bly means that these calculations representan absolute size limit that could not be ex-ceeded and was unlikely to be reached inpractice.

The ‘reconstruction confidence index’must be good, perhaps as high as 0.9, sincethe fossil dragonfly Meganeura monyilooks like a larger version of a modern-daydragonfly. The ‘dynamic similarity confi-dence index’ must be high as well, perhapseven 1, for similar reasons. Based on thefossil Meganeura monyi, the ‘total confi-dence index’ that gravity was 25% of thepresent value 350 million years ago wouldbe 0.9.

4. Leg bone strength

Dinosaur reconstructions are based on fos-sil bones fitted together to form completeskeletons. It is these skeletons that in turntell us the size of the dinosaurs. Manyof the best known skeletons have beenmade from bones that have been found to-gether, apparently from one individual an-imal, so palaeontologists are reasonablycertain that they are a realistic interpreta-tion of that animal.

Obviously, skeletons alone cannot givean animal’s weight directly. One method toinfer the weight of a living dinosaur is tocreate life-like models of the reconstructedanimals although the accuracy of these re-constructions relies on the skill of the mod-eller.

Another method of estimating di-nosaurs’ weight studied by Anderson et al(1985) is to use leg bone dimensions di-rectly to estimate the live weight of the an-


imal. Bone is not the inert material manypeople believe; it is a living dynamic tis-sue that is continually being modified andreplaced. Bone can become stronger afterexercise or can waste away through periodsof inactivity. Astronauts and cosmonautshave particular problems in space becausetheir bones become weaker when they arenot subjecting them to the stress of grav-ity. Animals’ bones, and in particular theirleg bones, grow thicker depending on howmuch an animal weighs.

Anderson, a US zoologist, had a longinterest in the size of animals’ bones.Anderson, together with a team, studiedthe bones of a range of mammals to see ifthere were any rules that would allow themto estimate the mass of an animal fromjust its leg bones. This would be very use-ful for extinct animals such as dinosaurs.The University of Florida where Andersonworked had a large collection of mam-mal skeletons complete with records of themasses of these animals when they werealive. That particular collection includedonly a few really large mammals but an-other member of the team, Hall-Martin,who worked at the Kruger National Parkin South Africa, was able to measure thebones of animals shot in the Park. The fi-nal member of the team was Russell, aCanadian dinosaur specialist.

The Anderson team chose to study themajor leg bones which are often well pre-served in otherwise incomplete fossils. Legbones carry the weight of animals’ bodiesso would seem to be the obvious choice.The bone lengths would be prone to errorssince some animals have long spindly legsbut other animals have short stubby legs.A good indication of the mass of present-day animals is the circumference of the up-per leg bones – the humerus and the femur.The humerus is the upper arm bone in usbut in the front legs in four-footed animals.The femur is our upper leg bone – the thighbone – or in the back leg in four-footedanimals. The bones were measured wherethey were the thinnest, and so the weakest,usually about half way along the length ofthe bones. These two circumferences were

then added together to give the total cir-cumference of the humerus and femur. Thecircumference of either the humerus or thefemur could have been used alone but thismight have lead to error since some ani-mals place more weight on the front or therear legs. The use of the front and back legstaken together tends to cancel out this er-ror.

Table 1 and Fig.4 present raw data ofanimal weight and bone dimensions kindlysupplied by Alexander (1995). The newraw data is substantially similar to the orig-inal Anderson team data and shows theconsistency of the concept. If you look atthe Fig.4 graph of weight-to-leg bone cir-cumference for a range of four-footed ani-mals you will notice that the graph is plot-ted on a log scale so that a whole range ofdifferent-sized animals from mice to ele-phants can easily be shown on the onegraph. The points on the graph – whichare the plotted weights of various animals– form a more or less straight band acrossthe graph. The Anderson team fitted a lineto the points they had based on statisticalanalysis and estimated that the best linethat can be fitted to these points was de-fined by the equation:

M = 0.000084 · c2.73,

where M = Body mass in kg and c = Totalof Humerus and Femur circumference inmm. This equation can now be used to es-timate the body mass of any animal fromjust the humerus and femur bones. The ac-curacy of the data can be checked and twoother lines have been added to the Fig.4graph to show how a variation of ±30%would affect the results. Virtually all theplotted animals’ points lie within this er-ror band with many much closer than this.The formula is based on four-footed ani-mals so it would seem reasonable to ap-ply it to four-footed dinosaurs and the errorshould certainly be within the normal errorband.

As two-legged animals would need adifferent formula, the Anderson team mod-ified the four-footed equation so that only


Fig. 4. Graph of mammals’ leg dimensions plotted against weight as detailed in Table 1.

Table 1. Raw data of mammals’ leg dimensions for various weights.


the femur circumference is required. Theirequation for two-legged animals is:

M = 0.00016 · c2.73,

where M = Body mass in kg and c =Femur circumference in mm.

One use of these equations would beto calculate the weight of extinct animalsand the Anderson team applied their equa-tions to a number of dinosaurs. One wouldexpect the results to have certainly beenwithin ±30% and in most cases a lot moreaccurate than this. Most dinosaurs shouldhave been close to the best fit line. Butthe results indicated dinosaurs were muchlighter than anyone had ever thought pos-sible.

Since the bone results were first pub-lished in 1985 the weights of dinosaursbased on volume methods have been re-duced to try to agree with these super-lightdinosaurs. However, this raised questions.The weight for Diplodocus, for example,was calculated at 5.8 tonnes from bone di-mensions, which is similar to a modern-day elephant. This doesn’t seem reason-able if you compare an elephant skeletonalongside a Diplodocus skeleton becausethe Diplodocus skeleton is much larger.

As the two methods give very dif-ferent results some palaeontologists haveadvised abandoning the use of the for-mula based on leg bones since they can-not get dinosaurs light enough to agreewith the bone weight calculations. The dif-ferences are so great for large bipeds thatHutchinson et al (2007) concluded that:

...it is almost certain that these scal-ing equations greatly underestimatedinosaur body masses ... Hence, werecommend abandonment of their us-age for large dinosaurs.

These results are fundamental to thereduced gravity hypothesis. The ReducedGravity Earth theory predicts that leg bonestrength will be weaker in a reduced grav-ity and this is exactly what we see inpractice. The body mass estimates basedon volume methods greatly exceed thosebased on leg bone strength because they as-sume gravity was the same in the past. This

variation between body mass estimates andleg bone strength can therefore be used tocalculate ancient gravity when ancient lifewas alive.

Tyrannosaurus rex – One meat-eatingtype of dinosaur that shows a variation be-tween the weight calculated from modelvolumes and the expected weight frombone calculations is Tyrannosaurus rex,as shown in Table 2. Some of the es-timated weights for Tyrannosaurus rexare from different specimens so it wouldbe expected that these may be differentsize animals which would have differ-ent weights. The Tyrannosaurus rex ex-amined by Henderson and Snively (2003)is nicknamed ‘Sue’ and is the largestTyrannosaurus rex found to date. If onlyone specimen (MOR 555) is considered itsweight based on the volume method onlyvaries between 5.4 to 6.6 metric tonneswhen studied by three different researchteams, Paul (1997), Farlow et al (1995) andHutchinson (2007). This same specimenhas also been used to calculate its weightbased on its bone dimensions by two re-search teams, Anderson et al (1985) andCampbell & Marcus (1993).

The bone dimension calculation indi-cates the legs of Tyrannosaurus rex onlyevolved to carry an animal that weighedbetween 3.5 to 4.5 metric tonnes while thevolume method gives a mass between 5.4to 6.6 tonnes. Using an average of these re-sults to calculate gravity 65 million yearsago:

gravity65 =Calculated weight

Volume Mass=

4.06.0=

= 0.66 g

The absolute maximum and minimumvalues of gravity can be calculated fromthe extremes of the weight estimates withthe absolute maximum and minimum be-ing 0.83g and 0.53g about 65 million yearsago. The confidence index can be calcu-lated from the variation in the results. Soconfidence index = Min gravity / Maxgravity = 0.53/0.83 = 0.63.


Table 2. Comparison of weight estimates in tonnes for Tyrannosaurus rex based on volume mass estimatesfrom models and leg stress estimates on bone.

5. Ligament strength of Diplodocus

Present-day horses and cattle have thickligaments called the ligamentum nuchaerunning along the back of their necks tosupport their heads.

The sauropod Diplodocus has neckvertebra with V-shaped neutral spines asshown in Fig.5 and Alexander (1989) sug-gested that the V was filled by a lig-ament that ran the whole length of theneck and back into the trunk of the ani-mal’s body. The ligament would have sup-ported the head and neck while allowingthe dinosaur to raise and lower its head.Alexander calculated that the mass of thehead and neck of Diplodocus would havebeen about 1340 kg. The weight of theneck and head acts 2.2 metres from thejoint and the ligament tension acts 0.42metres from the pivot of the joint so by theprinciple of levers the tension that wouldbe needed to balance the weight to the neckand head would be 2.2 × 13400/0.42 =70000 Newton.

The cross-sectional area of the liga-ment was estimated to be 40000 sq mm and

from this it can be calculated that the stressfor a force of 70000 Newton would be 1.8Newton per square mm. This is more thanthe stress in the ligamentum nuchae of deerwith its head down and the ligament fullystretched (which is about 0.6 Newton persquare mm). It would be enough or nearlyenough to break the ligament.

Stevens and Parrish (1999) suggestedthat the problem of the weak neck liga-ments could be overcome if a sauropod’sneck was imagined as a stiff, almost self-supporting structure where the neck ver-tebrae overlapped each other by around50% to provide additional support. Theybuilt a computer model of Diplodocus ina neutral pose with its long neck at aboutshoulder height dipping slightly towardsthe ground. This depiction of a stiff-neckedDiplodocus with its head held permanentlylow removed the problem of a weak neckligament as well as the problem of highblood pressure if the neck was held high.

These stiff-necked reconstructionswere generally accepted since they seemedto provide answers to real questions and


Fig. 5. V-shaped neck vertebra probably held the neck ligament used to keep Diplodocus’s neck erect andthis enables the ligament’s size to be estimated.

Diplodocus is now mostly depicted witha stiff, relatively useless long neck thatit couldn’t lift to reach the higher plants.Many museums around the world and TVseries like Walking with Dinosaurs showDiplodocus like this even though somepaleontologists disputed this view (Bakker1986).

A more recent study by Taylor etal (2009) presented additional argumentsagainst these stiff-necked reconstructionsand concluded that:

Unless sauropods carried theirheads and necks differently from ev-ery living vertebrate, we have to as-sume that the bases of their neckswere habitually curved upwards, ...In some sauropods this would havemeant a graceful, swan-like S-curveto the neck, and a look quite differentfrom the recreations we are used toseeing today.

The problems encountered withDiplodocus’s neck only occur because it is

assumed that gravity was the same in thepast. The Reduced Gravity Earth theorypredicts that the neck ligament would bethinner in a reduced gravity and this isexactly what we see in practice.

Due to a reduced gravity the actualweight of Diplodocus’s neck 150 millionyears ago would be:

weight150 = Mass × gravity150.

The weight of the neck and head stillacts 2.2 metres from the joint and the lig-ament tension acts 0.42 metres from thepivot of the joint so by the principle oflevers the tension that would be needed tobalance the weight of the neck and headwould be:

Force = 2.2 ×Mass × gravity150/0.42.

Also,

Force = stress × area,


so, rearranging to obtain gravity 150 mil-lion years ago:

gravity150 =

= stress × area × 0.42/2.2 ×Mass =

= 0.6 × 40000 × 0.42/2.2 × 1340 =

= 3.4 m/s2.

This 3.4 m/s2 calculated value of gravity150 million years ago is much smaller thanthe present-day value of 9.81 m/s2. Howaccurate is this value of gravity? There area number of variables that might be dif-ferent from the initial assumptions used;the ligament could be larger if it expandedoutside the V-shaped neck bones, the forceof the neck’s weight would be lower ifDiplodocus held its neck more upright, andadditional muscles or ligaments might pro-vide additional support. If the neck washeld at a 45 degree angle the downwardforce of the neck would be reduced by0.707. The ligament could easily be halfas large again if it extended outside the V-shaped neck bones, increasing the area ofthe ligament to 60,000 sq mm. So:

gravity150 =

= stress × area × 0.422.2×Mass × 0.707 =

= 0.6 × 40000 × 0.422.2× 1340 × 0.707 =

= 7.25 m/s2.

The results give a value for gravity150 million years ago as somewhere be-tween 34% to 72.5% of the present grav-ity with the ‘best guess’ 53% of presentgravity. The confidence index can be cal-culated from the variation in the results. Ifthe Minimum and Maximum gravity wasidentical then our confidence index wouldbe 1. So confidence index = Min gravity /Max gravity = 0.34 / 0.725 = 0.47.

6. Blood pressure of Brachiosaurus

Because of its long neck the giraffe hasthe maximum hydrostatic blood pressureof any animal alive today. This high bloodpressure seems to be about the maximumpossible since the giraffe needs to use ex-treme measures to maintain it. Because thecentral blood pressure is high the heart’smuscle has to be strong and a giraffe’sheart can weigh up to 10 kg and mea-sure about 60 cm long. The heart of anadult giraffe is about 2% of its body weightwhereas in people it’s only about half apercent. Giraffes have arterial blood pres-sures of 25 kPa at the bases of their neckswhilst standing. By extrapolation, the pres-sure in the heart must exceed 30 kPa whichis about double the normal pressure in amammal.

Brachiosaurus lived in the LateJurassic to Early Cretaceous, about 145million years ago. It is generally recon-structed with its neck sloping steeply up,in a giraffe-like posture so the brain ofBrachiosaurus was about 7.9 metres aboveits heart as shown in Fig.6. Calculationsassuming our present gravity reveal thatthe total pressure difference between thebrain and the heart would be 8590 kPa.

These problems of high blood pres-sure would not exist on a Reduced GravityEarth because blood pressure is lower in areduced gravity. Blood pressure is propor-tional to blood mass, gravity and height,so it is possible to estimate ancient gravityby comparing the blood pressure in ancientlife with the blood pressure in modern life.

The hydrostatic pressure difference be-tween the blood in the brain and the heartcan mostly be defined as the hydrostatichead in metres. The hydrostatic pressure atthe base of the Brachiosaurus’s neck 145million years ago can be calculated by:

Hydrostatic Pressure =

= blood density × gravity145 × height.

In a reduced gravity the hydrostaticpressure would be reduced becausethe weight of the column of bloodwould be less and this would allow a


Fig. 6. The position of the head above the heart determines the blood pressure, or the hydrostatic head, atthe heart for a giraffe and Brachiosaurus.

Brachiosaurus’s neck to become muchlonger than today’s giraffe. Blood is anincompressible fluid whose density wouldnot vary in a different gravity so it seemssafe to assume that the density of dinosaurblood was the same as giraffe blood. Alarge giraffe about 5.5 metres tall wouldhold its head 2.8 metres above its heart sothe hydrostatic head in its heart would be2.8 metres.

The assumption that the blood pres-sure above the heart of both the giraffeand Brachiosaurus is the maximum thatthe various tissues can withstand enablesa calculation of the value of gravity whenBrachiosaurus lived. We know:

Brachiosaurus Hyd. Pressure =

= gravity145 × Brachios. Neck Height

and

Giraffe Hyd. Pressure =

= gravity × Giraffe Neck Height

so,

gravity145 =Gir. N. Height

Brach. N. Heightgravity =

=2.87.9× gravity = 0.35 g.

Using the lowest neck height whichseems possible gives a hydrostatic headof 3.9 metres. Using this hydrostatic headwould give:



=2.83.9× gravity = 0.72 g.

My own ‘best guess’ about the posi-tion of the neck for Brachiosaurus is that itwas somewhere between the two extremes.This intermediate position gives a hydro-static head of 5.9 metres, which in turnwould predict gravity to be:



=2.85.9× gravity = 0.48 g.

So using the method of equatingthe blood pressure in the long neck ofBrachiosaurus to a giraffe, gravitationalacceleration is calculated somewhere be-tween 35% to 72% of our present grav-ity 145 million years ago, with the ‘bestguess’ value working out at 48% of ourpresent gravity.


Table 3. Table of the variation of Earth’s gravity over hundreds of millions of years based on variouscomparisons of ancient and modern life.

7. Ancient gravity results

The calculated values of ancient gravitybased on various animals using dynamicsimilarity, leg bone strength, neck ligamentstrength and blood pressure are reproducedin Table 3 and Fig.7 in order to gain anoverview of the results.

Many forms of life can be usedto calculate ancient gravity using themethods outlined in this paper. Table 3includes calculated estimates for ancientgravity based on the dynamic simi-larity method for an ancient Scorpion, aDragonfly, Brachiosaurus, two Crocodiles,Pterandon, Quetzalcoatus, Triceratops,Dasornis, Andrewsarchus, Brontotheriumand Baluchitherium, and also basedon leg bone strength for Plateosaurus,Diplodocus, Allosaurus, Apatosaurus,Brachiosaurus and Tyrannosaurus.

The graph in Fig.7 shows the ‘bestguess’ value as circular dots of various

sizes in order to represent the gravity valuethat has been calculated. It is notable thatthe dots representing gravity show a gen-eral trend of gravity gradually increasingover hundreds of millions of years.

Many of the distinct methods of calcu-lating gravity give very similar values. Ifone animal which was subjected to a num-ber of these calculation methods is takenas an example, such as Brachiosaurus, wecan clearly see the similarity of the results.Dynamic similarity gives 0.45g, leg bonestrength 0.56g and blood pressure 0.48g.These ‘best guess’ values all give resultswhich are in broad agreement with eachother even though they use different meth-ods to calculate ancient gravity.

Comparing different animals to oneanother in the same time period alsogives broad agreement for the ‘bestguess’ value. Dissimilar animals thatwere alive about 150 million years agosuch as Brachiosaurus, Allosaurus and


Fig. 7. Graph of the variation in Earth’s gravity over hundreds of millions of years based on the variouscomparisons of ancient and modern life listed in Table 3.

Diplodocus also all give values for grav-ity which are in broad agreement with eachother. Animals which were alive at othertimes give different values for gravity.

One element that needs to be consid-ered for the confidence index is the varia-tion in size naturally seen in the living an-imals of today. If the elephant is taken asan example, there is a wide variation in thesize of elephants as a group. An Africanmale elephant tends to be the largest atover 4 metres tall but the African femaleelephant is usually slightly smaller and theAsian female elephant smaller still at justover 3 metres tall. We see a general varia-tion from about 3 to 4 metres in height inthe largest animals alive today. If we as-sume an average height of 3.6 metres forthe average African elephant then a rea-sonable variation ±10% would give a sizerange of about 3.2 to 3.9 metres for oursample. The same, or an even greater, vari-ation in size was probably true for the di-nosaurs and other prehistoric life. It is pos-sible to remove that variation in our liv-ing model since we know what the aver-age size is, but it is more difficult to re-move this source of error in the extinct an-imal since there is such a small sample offossils making it difficult to say if the liv-ing animal was a large or small member of

the species. Because of this I believe thateven the best possible calculation of grav-ity from ancient life would only be within±15% of the true value at best and possiblymuch worse than this.

In the graph the 0.8-1 confidence indexhas been shown as the largest and black-est of the dots. The size and blackness ofthe dots reduce down as the confidence re-duces until the 0-0.2 confidence index dotsare the smallest and faintest of all. Verticaldotted lines are also shown coming out ofall the dots and these are a further attemptto display this possible error on the graph.The values used for the error bars havetherefore been set at: ±15% for 0.8-1 confi-dence index, ±20% for 0.6-0.8 confidenceindex, ±25% for 0.4-0.6 confidence index,±30% for 0.2-0.4 and ±35% for 0-0.2.

The final element of the graph is a the-oretical line to show how gravity may havevaried over time from 300 million yearsago up to the present day. It is interest-ing to note that this gravity line lies wellwithin the error bars of the calculated val-ues of gravity and even the estimates withthe lowest confidence index are still withinthe error bars. In general, life indicates thatgravity was less on the ancient Earth andhas slowly increased up to its present-dayvalue.


Fig. 8. A typical Expanding Earth reconstruction based on geological data.


Fig. 9. Earth’s changing gravity over time based on geological reconstructions of an Expanding Earth.

8. Implications for the expandingEarth

The magnetic recordings on the oceanfloor have been mapped to give a detailedaccount of the age of the Earth’s oceanfloor. By removing the ocean floor thatis known to be younger than a particu-lar age, it is possible to reconstruct an-cient Expanding Earth globes by rejoin-ing the remaining ocean floors. A numberof reconstructions have been produced byHilgenberg (1933), Vogel (2003), Hurrell(1994, 2011), Luchert (2003), Maxlow(2005) and many others. Fig.8 shows a typ-ical Expanding Earth reconstruction.

The estimates of ancient Earth’s re-duced gravity, indicated by the larger rela-tive scale of ancient life, can be comparedwith estimates of gravity for ConstantMass and Increasing Mass ExpandingEarth models. The force of the Earth’sgravity is:

F = G × M1 × M2/R2, (5)

where M1 and M2 are the masses of thetwo mutually attracting bodies, R is the dis-tance separating them and G is UniversalConstant of Gravity and the calculatedforce F is effectively the force of gravity.

For a Constant Mass Expanding Earthancient gravity would be about four timesthe present value which does not agreewith the results from ancient life. For an

Increasing Mass Expanding Earth gravitywould gradually increase over time as theEarth grew in diameter and mass so thisagrees with the gravity results from ancientlife.

This is a simplistic method of calculat-ing the force of gravity since it assumesthat the density of the ancient Earth isexactly the same as the present Earth. Itis much more probable that as the an-cient Earth grew larger in size and mass itwould become denser as its core becamemore compact due to the increasing surfacegravity (Hurrell 1994, 2003). This densityincrease can be estimated by plotting theknown variation of gravity against the ra-dius of other known celestial bodies, anda graph of changing gravity on the ancientEarth taking account of density variationsin the Earth’s core and mantle based onother celestial bodies is shown in Fig.9.

The Reduced Gravity Earth modelagrees most closely with an IncreasingMass Expanding Earth model rather thana Constant Mass Expanding Earth model.Estimates of ancient life’s gravity indicatethat Earth Expansion is due to mass in-crease.

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Author’s Biographical Notes: Stephen Hurrelllives near Liverpool in the UK where he has workedin mechanical engineering design positions forvarious companies. It was his role as a mechanicaldesign engineer at the UK’s Electricity ResearchCentre that first offered him his insight into howscale effects were pertinent to the biomechanicalproblems of the dinosaurs’ large size. Thesethoughts about dinosaurs as engineering structures,and the influence of scale effects, fostered thedevelopment of the Reduced Gravity Earth theoryand its implications for the Expanding Earth.

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Ancient Life’s Gravity and its Implications for the ...€¦ · the elephant’s legs are thicker still to sup-port its massive bulk. The elephant is near the upper size limit for