KCAL 9 And The Supermoon

CREDIT: CBS

I was watching the KCAL 9 news at 10 p.m. They had a report on the super moon. (yawn)

But then Serene Branson said this:

And they say that with the full moon like that, that if you’re feeling a little tired, a little sluggish, that it’s because of the pull. Just like how the moon has an effect on the tides, it has an effect on us, because we’re mostly water. And that’s when the crazies come out.

Despite what Bill O’Reilly thinks, the tides have a well-known cause. The tides are due to the difference in the strength of the gravitational force on opposite sides of the earth. 

There is no measurable effect on the moon’s gravitational field on us. UCLA astronomer George Abell calculated that a mosquito on your arm would exert a greater gravitational force on you than the moon.

As to the supposed lunar lunacy, that too was debunked long ago. 

I thought that maybe KCAL meteorologist Amber Lee might correct her, but no. That got me to thinking about Lee’s credentials. She has a bachelor’s degree in communications and a master’s in journalism. No degree but a certificate in  meteorology through Mississippi State University’s Broadcast Meteorology Program. To earn this certificate, she had to pass an online exam consisting of 100 multiple choice questions. 

Getting Crankier - Part 2

Let's deal with some of Mr. Stojanowski's comments made on Getting Crankier.

Only the latitudinal movement is relevant to angular momentum.

But again, the latitudinal movement of Pangea, and its remnants, during the past 350 myrs is what is important, not just the dispersal movement after its breakup.

No. Any change in I, a body's moment of inertia (the distribution of its mass about a rotation axis), is relevant to angular momentum.

…it was the displacement of the core elements, an action which would increase the Earth’s AM to balance the reduction of AM from Pangea’s center of mass moving closer to the spin axis as it moved to a higher latitude.

… an action which would increase the Earth’s AM to balance the reduction of AM from Pangea’s center of mass moving closer to the spin axis as it moved to a higher latitude.

CREDIT: J. Stojanowski

Let's apply Mr. Stojanowski's hypothesis to the problem. In his work, he claims that the Earth's core was displaced by 1000 km in the equatorial plane. (see his Fig. 3 to the left). He also references a paper in Geophysical Research Letters* in which he claims they show movement of Pangaea's center of mass. More on the center of mass later. Figure 3(a) in this article (shown below) does show variation in a parameter the authors label D.  The authors are attempting to quantitatively estimate the "asymmetry of continental surface." To calculate D, the authors use the first moment of the distance to the equator with respect to the surface area. This is not the center of mass.

CREDIT: Petrelis et al.

However, let's use Mr. Stojanowski's assumption that the two are the same and apply the conservation of angular momentum to his model. See the previous article for a brief introduction to this principle. 

The first term on the left hand side of the equation below represents the core 1000 km from the Earth's axis in the equatorial plane.  The second term represents the Earth minus the core and the continents, and the third term is Pangaea. The term on the right hand side is Earth today.

We need a few more numbers before we can calculate.  The mass of the core is about 1/3 of the Earth's mass. We'll use Mr. Stojanowski's number of 1000 km for rc. The last quantity required is the distance from the axis to Pangaea.  Here we'll use his assumption that D is the center of mass. From Figure 3(a) in the Geophys. Res. Lett. article, D is about 100 km south of the equator. We use a bit of elementary geometry and trigonometry to find the distance from the axis to Pangaea; rp = 6370 km.

Plug away. In the meantime, let's recap.  I've used the conservation of angular momentum and Stojanowski's model and numbers. We find that the consequence of his model is that the Earth rotates once every 16.6 hours. This contradicts what we know the length of the day; then it was about 23 hours long.

His assumptions in his calculation are:

1. Pangea’s center of mass was located on the equator 250 myr.

2. Today, the continental crust is distributed uniformly across the globe.

Based on the above assumptions, in both cases, the center of mass of continental crust is on the equator. Therefore, the moment of inertia in both cases must be the same, meaning the angular velocity must also be the same to conserve AM.

Yes, I did assume in Getting Crankier that the center of mass stays on the equatorial plane. However, as I clearly showed in my first attempt, the moment of inertia is not the same over 250 million years. There I modeled Earth 250 mya as a sphere and a object (Pangaea) located 6371 km from the axis. And my calculation clearly demonstrates that the angular velocity must change as a result of conserving momentum.

I mentioned above that I would say something about the Earth's center of mass, but I ran across another blog that has dealt with this issue quite well. Ed Brayton** blogged at Dispatches from the Creation Wars, and on Dec. 27, 2010, guest blogger W. Kevin Vicklund wrote New Explanation for Dinosaur Extinction? Revisited. He shows how bad Mr Stojanowski's figure of 1000 km is for the core offset. The short version is that if the Earth is to rotate about its axis then the Earth's center of mass must remain at the Earth's geometric center. Mr. Stojanowski's model doesn't do that. If the core moved as he claims, the Earth would have precessed like crazy.

Yes, surface gravity at the poles is less than at the equator based on difference in distance to the Earth’s center of mass. This is evident from the inverse square law (relative to distance) postulated by Newton. It’s exactly why surface gravity on Pangea changed when the Earth’s core elements moved off-center and away from Pangea, moving the Earth’s center of mass further away from Pangea.

No. The effect is due to the centrifugal term in Newton's 2nd law as I explained in the previous post. If you want to use Newton's law of universal gravitation to find the magnitude of the gravitational field near the Earth's surface, here's what you do.

The polar radius is 6357 km, and the equatorial one is 6378 km, only 0.3% larger. Use these to calculate the gravitational field, and you will quickly see that the equatorial field is only 0.6% smaller. Mr. Stojanowski may counter that his model yields a value 8% smaller for Pangaea, but as I and Mr Vicklund have shown, that core motion he postulates violates what we know about the Earth's rotation.

Mr Stojanowski.  Should you reply once again, I ask that you back up any claims with physics, mathematics, and numbers.

*Plate tectonics may control geomagnetic reversal frequency, F. Pétrélis, J. Besse, J.-P.Valet, Geophysical Research Letters, vol. 38, issue 19, October 2011.

**I highly recommend Ed Brayton's Dispatches from the Culture Wars.

Getting Crankier

Mr. Anonymous, who may or not be John Stojanowski, left two comments on my recent post, Feeling Cranky. To recap, Mr. Stojanowski has a hypothesis that the dinosaurs became extinct because the gravitational field of the Earth increased and that increase was caused by movement of the Earth's core accompanied by the shifting of the planet's crust.

The first comment:

Notice how he slyly calls into question my credentials, but I'll let that go. I do know how angular momentum works, and I seriously question Mr. Anonymous's understanding, not just of angular momentum, but of the meaning of the word latitudinally.

Watch this animation of the spreading of Pangaea.

There seems to some movement of the underlying tectonic plates northward and southward (latitudinal motion), but the greatest change in seen longitudinally; that is eastward and westward.

Be that as it may, let's examine our understanding of angular momentum which is conventionally denoted not by AM but by

Angular momentum is conserved, that is, it stays the same, when there are no unbalanced torques acting on the object. Mathematically it can expressed thusly,

Here's an excellent example of this principle. 

Here when the figure skater starts her spin she is spinning relatively slowly.  Then as she pulls her arms and leg in, she spins much faster. The Greek letter omega in the equation above represents the spin rate. The I in the equation is called the moment of inertia and describes how the mass is distributed around the rotation axis.  When the skater pulls her arm in, she is distributing her mass closer to the spin axis, and her rotation rate increases. There's no "compensating action." 

I can show with a simple model how the spreading of Pangaea could affect the length of the day. First, let's suppose the entire supercontinent is located at the equator. Second, let me suppose that the continental crust is now uniformly distributed across the globe. [Note: those simplifications are not necessary; they just make the work relatively easy to follow and make the calculations possible to do in a minute or two.]

Now here's the data (1):

Now we can plug in all the numbers and calculate what the Earth's the rotation rate should have been 250 million years ago.

You can see that the rotation rate is less than it is today by a factor of 0.995.  We conclude then that that day should have been 1.005 times longer than now - about 7 1/2 minutes.

Oops.  We know that 350 million years ago, one day lasted less than 23 hours.(2) Mr. Stojanowski's angular momentum hypothesis disastrously gives the wrong direction of change.

By the way, Mr. Anonymous, I am not a geologist, so can you explain what effect your oscillating core would have on the convection currents in the mantle, and what effect those changing currents would have had on driving plate tectonics?

The second comment:

Again with questioning my credentials. Oh well. Rotational dynamics is usually covered in an undergraduate third year classical mechanics course. All physicists learn early in their career how to do physics in a rotating reference frame.  Here's what we derive, essentially Newton's 2nd law in a rotating reference frame.(3)

One consequence of this is that the Earth is not spherical, but it bulges outward at the equator, and we drop something it drops straight down, perpendicular to the Earth's Surface.  However, straight down is not the same as pointing to the center of the Earth.  

Mr. Anonymous is curiously unaware of the size of the Earth's rotation rate.  He appears to say that the Earth has a high spin rate. As I can show from Newton's 2nd Law, the rotation of the Earth has about a 0.05% effect. The gravitational field is about 0.05% larger at the poles than it is at the equator.

If Mr. Anonymous cares to respond again, perhaps he would be so kind as to provide some mathematical and physical details. I think I'm qualified enough to handle them.

1. The numerical data can be found in any physics, astronomy, or geology book with the exception of the continental mass.  That estimate comes from Mass and Composition of the Continental Crust Estimated Using the CRUST2.0 Model , Peterson, B. T.; Depaolo, D. J., American Geophysical Union, Fall Meeting 2007, abstract #V33A-1161.  Any introductory physics text will have a chapter or two on rotational dynamics at this level.

2. See for example, this article at Scientific American.
3. For those you have completed an introductory calculus-based physics sequence, as well as a differential equations course, see a standard classical mechanics textbook such as Symon's Mechanics, or Thorton and Marion's Classical Dynamics of Particles and Systems. Graduate level students can consult Goldstein's Classical Mechanics.

Feeling Cranky?

crank |kraNGk|

noun

an eccentric person, esp. one who is obsessed by a particular subject or theory [New Oxford American Dictionary]

I present three people I have come across in my journey through the World Wide Web. I'll let you be the judge as to their eccentricity.

1. John Stojanowski

Back in February, I wrote a post about former Oakland A star Jose Canseco and his musings on the strength of gravity and the size of the dinosaurs. One month later, someone left a comment:

Mr. Canseco apparently has read my theory, 'The Gravity Theory of Mass Extinction', which explains how surface gravity changed. The theory posits that when a supercontinent such as Pangea moves latitudinally, the core elements move off-center to maintain the Earth's conservation of angular momentum.

Therefore, Mr. Canseco cannot claim that this is his theory.

If interested, visit a summary of the theory: http://www.dinoextinct.com/page13.pdf.

While I can't be sure Mr. Stojanowski left the comment, the person does write "my theory."

Let's examine his speculations.

The Gravity Theory of Mass Extinction (GTME) [1] is a theory that explains the causation of mass extinction events throughout the history of the Earth. It also posits the reason for dinosaur gigantism, flood basalt volcanism, rapid changes in marine eustatic sea level, the Earth’s geomagnetic reversals and geomagnetic secular variation. The theory asserts that all of these phenomena are linked together. The foundation of the theory is the assertion that the Earth’s core elements (i.e., inner core, outer core and the densest part of the lower mantle), under certain conditions, can be displaced from their current Earth-centric position. [emphasis in the original]

CREDIT: John Stojanowski

Here's the crux of his thoughts.  As Pangaea split, the core of the core shifted from a off-center position to where it is today - at the center of the Earth.  The initial displacement of the core, he claims, would result in a smaller gravitational field on the supercontinent and allowing the evolution of gigantism among certain reptilian species. He further posits that the motion of the core to the center with the resulting increase in the gravitational field is the major cause of the extinction of the dinosaurs.

How does Mr. Stojanowski explain the core shift? He thinks that it was produced by the accumulation of the continental crust on one side of the planet. I won't go into all the gory details, but this situation is why your car tires must be balanced.  If the mass of the tire and wheel is not uniformly distributed, the tire will wobble. Your mechanic adds small weights to the rim to prevent this. I'll omit the physical and the mathematical details, and simply state that the largest possible change to the gravitation field is about 1%.  On a side note, the astronauts in the International Space Station orbit 200 miles above the Earth and experience a gravitation field that is only 2.5% smaller.

2. Steven Christ

Oh, where do I begin with Steven Christ. He is a proponent of the Hollow Earth. The Earth is hollow, and we live on the inside. You have to see for yourselves.

The Earth You Live IN...prt 1

If this video is not enough, just go to YouTube and search for his name. Want more after that. Visit his website missteribabylonestar.

3. Louis Savain

I ran across Louis on the creationist website Darwin's God. I commented on Photosynthesis Relies on Quantum Coherence: When Will They Cry Uncle?

Louis replied with typical creationist flair.

So I became intrigued.  A quick Google and I found his blog Rebel Science. Wow!  Louis is some sort of computer guy who has dreams of revolutionizing computer science.  In his ebook How to Solve the Parallel Program Crisis, he claims the the problem with the computer industry is using "the Turing Machine as the de facto computing model in the last century." His answer is "to switch to a non-threaded, non-algorithmic, synchronous (deterministic), reactive and implicitly parallel model."

However, I am not going to take issue with his programming; it's his physics that is… Hmmm, how do I put this politely? Oh, yes. Eccentric.

Louis takes issue with Newton's 1st law of motion, "an object at rest stays at rest and an object traveling in a straight line at a constant speed will continue in that uniform motion unless acted upon by an unbalanced, external force." Newton's 1st law is superstition according to Louis. 

Then he takes on the entire physics community. "I claimed that the physics community’s understanding of motion is fundamentally flawed, on a par with the flat earth hypothesis."

What truly lifts Louis above the rest is his insistence that motion is impossible, and he proves it.

Why is motion in spacetime impossible? It has to do with the definitions of space and time and the equation of velocity v = dx/dt. What the equation is saying is that, if an object moves over any distance d x, there is an elapsed time d t. Since time is defined in physics as a parameter for denoting change (evolution), the equation for velocity along the time axis must be given as v = dt/dt which is self-referential. The self-reference comes from having to divide dt by itself. dt/dt always equals 1 because the units cancel out. This is of course meaningless as far as velocity is concerned.

It is not only not right, it is not even wrong.*

The velocity is defined to be the rate of change of an object's position, but Louis makes a mistake here that I have never seen a student make in my 24 years as a professional physicist. He is seriously confused about what a variable is and what an axis on a graph represents. The equation for velocity along the time axis? Louis doesn't seem to realize that motion along the time axis is simply an object at rest at the origin, that is dx = 0.  0/dt = 0. 

I bet if Louis runs across this blog, he'll call me stupid. Or worse.

Reply to stereox112.
CREDIT: Louis Savain

*For an interesting physics anecdote, see the Wikipedia entry.

Baby Pictures

A baby picture of the universe!

http://www.nasa.gov/mission_pages/planck/multimedia/pia16873.html

This is a map of the cosmic microwave background (CMB), the leftover radiation of the Big Bang, made by the Planck mission of the European Space Agency.    This light was emitted when the universe was 380,000 years old. 

There's a number of AWESOME results here.

1. The colors represent small fluctuations in the temperature of the radiation, about 1 part in 100,000 or 0.001%.  Since the average temperature is a mere 2.73 K (2.73 degrees above absolute zero), the fluctuations are roughly 0.00003 K.  To put this in perspective, imagine setting your oven to 350ºF and it never varies by more than 0.008ºF.

2. This light was created just 80,000 years after the universe was cool enough for neutral hydrogen atoms to form.

I couldn't find any baby pictures,
but here I am when I'm about
10% of my current age.

3. It provides the best estimate for the age of the universe.  13.82 billion years.

4. The universe is 4.9% normal matter (protons, neutrons, and electrons for the most part.) Dark matter makes up 26.8% and dark energy 68.3%.

5. The universe is amazingly uniform, isotropic in the physicist's lingo. But there is a tiny difference in the size of the fluctuations in one half of the sky as compared to the other half.  Intriguing!

6. This picture represents the universe when it was just 0.00002750 of its present age.  Let's compare this to one of my students who say is 20 years old; this student was only 5 hours at 0.00002750 of 20 years.    

Flying Aircraft Carriers: Physics and Engineering in The Avengers

CREDIT: Marvel Studios

I saw the Avengers on Memorial Day.  Awesome movie, and if you've read one of my early blog posts, Transformers 3 - Dark of the Moon, you might guess I sometimes think about physics during the movie.  One thing that caught my attention was the flying aircraft carrier.  What would it take to make one fly?

Thanks to Wikipedia, I found some specifications for a modern US navy supercarrier.  They are 333 meters long (1,092 ft) and 78 meters wide (260 ft), and its displacement is 100,000 long tons which is equal to 224,000,000 pounds and 101,600,000 kg.  It is powered by two nuclear power reactors that provide 190 megawatts.

Now for science!

There was a shot in the movie when two of their fans were shut down and the ship was plummeting.  The altimeter read between 17 and 18,000 ft.  So I will begin by assuming they were cursing at 30,000 ft.  This is also where many commercial flights travel.  I will also assume that it takes about 30 minutes to reach cruising altitude.

CREDIT: Marvel Studios

Now I can estimate the acceleration.  Kinematics, the study of motion, says that for a body initially at rest, the acceleration is given by

Plugging in gives a value of 0.006 m/s/s.  For you non-students of physics, this means that for every minute, the carrier goes almost 1 mph faster.

Now for Isaac Newton.  To produce this acceleration, Professor Newton says that unbalanced forces have to act on the carrier.  Newton's 2nd law:

Here I will have to use the ship's displacement as its mass.  The displacement measures how much water an object pushes out of the way.  Rather than trying to calculate the ship's mass, I'll take the shortcut.  The total unbalanced force is about 570,000 Newtons.

There will be two forces acting on the ship - the thrust and the gravitational force (commonly referred to as the weight).  The thrust has to be 570,000 Newtons larger than the weight.  We can find the weight by multiplying the mass by the gravitational field (9.8 N/kg).  Therefore the thrust is approximately 10,000,000,000 Newtons.

The total energy used in both speeding up the ship and raising it can be found by multiplying the thrust by the distance.  

Since power is the rate at which energy is converted, we can take the energy and divide by 30 minutes.  To raise SHIELD's ship requires 5,000,000,000 Watts; that's 5.0 gigawatts!  Earlier I noted that the 2 reactors aboard a US carrier provide 190 megawatts, SHIELD needs 52 nuclear reactors.

Now for those fans providing the thrust.  To try to calculate the thrust of a ducted fan, one needs an extensive knowledge of fluid dynamics and aeronautical engineering plus a powerful computer.  I'll take the quick path to the answer.

With a 0.16 second Google search of "thrust fan specifications", the first result was for Ventry Solutions, Inc.  They sell a 24 inch ventilation fan that supplies 108 Newtons of thrust.  I'll scale that up for the ducted fans seen in the movie.  

Judging from the photo above, the fans have a diameter of about 40 meters (130 ft).  If - a very big if - the thrust is proportional to the diameter, then one fan can give 7100 Newtons.  Uh oh.  7100 Newtons per fan; 10,000,000,000 Newtons needed.  

14 million of them.

A Lesson on Wine and Physics

There's a field of physics engineering called statics.  It is concerned with the forces and torques acting on objects at rest.  If you want to build a bridge, you have to understand statics.

Here's an example of either poor engineering of store shelves or of incorrect loading of those shelves.

Now let the crying commence..

Your Elementary School Teachers Were Right. So were Copernicus, Galileo, Kepler, Newton, and Einstein.

We all learned that the that there are there are nine planets sometime in grade school. You may have used the mnemonic "My Very Educated Mother Just Served Us Nine Pizzas." There are now only eight, because astronomers decided that Pluto along with Ceres, Iris, and perhaps about 50 others are dwarf planets. So maybe we should memorize "My Very Educated Mother Just Served Us Nuts."

We also learned that these planets orbit the Sun. I bet none of us ever questioned how we know this. Why would we? It is established scientific fact, right?

So why would anyone think Galileo Was Wrong; The Church Was Right. This link is to a website that promotes Geocentrism, the idea that the Earth is not only the center of the solar system, but the center of the universe. I've been through this website looking for one thing - an explanation of orbits, because it's a straightforward calculation if you start with Newton's 2nd law and his law of universal gravitation. My students who have had PHY 211 can go back to Unit N of the text book and read chapters 12 and 13, and I can show anyone else who's interested how it works. [In the interest of scientific honesty, Mercury presents a small problem that took Einstein to solve.] So my challenge is that a geocentrist must be able to write a force law and derive a equation of motion for the planets that reproduce the orbits with the Earth as the force center.

Let's illustrate the problem:
Here's a Flash simulation of the heliocentric (Sun-centered) solar system. Only Mercury, Venus, Earth and Mars are shown. Press play and pay close attention to Mars. You see that Mars follows a nearly circular orbit as explained by Newton.

Now look at the Ptolemaic or geocentric (Earth-centered) solar system. Here Mars, Jupiter, Saturn, Uranus, and Neptune are shown. Again press play and pay attention to Mars. Press the circle button and the animation will trace out the orbit.

See the problem? [Again in the interest of scientific honesty, many of these geocentrism web sites don't use a purely Ptolemaic system, they use the Tychonic model where the Earth is the center, the Sun and the Moon orbit the Earth and the rest orbit the Sun. But the orbit problem among others remains.]

So why would anyone believe in a theory put to rest 400 years ago? Galileo Was Wrong; The Church Was Right goes to great lengths to couch its arguments in criticizing Einstein's theory of relativity and other physics, but when you examine closely their argument comes down to…

Because the Bible says so.

Here are the verses (from NIV) commonly used by geocentrists:

Joshua 10:12-13
12 On the day the LORD gave the Amorites over to Israel, Joshua said to the LORD in the presence of Israel: “Sun, stand still over Gibeon, and you, moon, over the Valley of Aijalon.” 13 So the sun stood still, and the moon stopped, till the nation avenged itself on its enemies, as it is written in the Book of Jashar. The sun stopped in the middle of the sky and delayed going down about a full day.

Ecclesiastes 1:5
5 The sun rises and the sun sets, and hurries back to where it rises.

Psalm 96:10
10 Say among the nations, “The LORD reigns.” The world is firmly established, it cannot be moved; he will judge the peoples with equity.

Psalms 104:5
5 He set the earth on its foundations; it can never be moved.

Isaiah 66:1
1 This is what the LORD says: “Heaven is my throne, and the earth is my footstool…

1 Chronicles 16:30
30 Tremble before him, all the earth! The world is firmly established; it cannot be moved.

Amos 8:9
9 “In that day,” declares the Sovereign LORD, “I will make the sun go down at noon and darken the earth in broad daylight.

Micah 3:6
6 Therefore night will come over you, without visions, and darkness, without divination. The sun will set for the prophets, and the day will go dark for them.

Jeremiah 15:9
9 The mother of seven will grow faint and breathe her last. Her sun will set while it is still day; she will be disgraced and humiliated. I will put the survivors to the sword before their enemies,” declares the LORD.

If you read this literally, then I guess it's clear that the Earth is stationary and the Sun moves.

Now for the irony. Answers in Genesis, a creationist site, finds geocentrism embarrassing. The site goes to great lengths to debunk geocentrism. But Ken Ham, the founder of Answers in Genesis, is the man who built the Creation Museum in Petersburg, KY. The museum has Adam and Eve and says T. Rex ate coconuts. He is also building Ark Encounter near Cincinnati, OH that will also feature dinosaurs.

What do you think is Ken Ham's reason for believing in creation?

Transformers 3 - Dark of the Moon

Saturday night I went to see Transformers 3 - Dark of the Moon. Did I like it? Well, it was loud and I was out of the house for three hours.

As I was watching it though, I began to wonder about some physics (SPOILER ALERT) when Sentinel Prime began transporting the remains of Cybertron. So I said to myself, "Self. What sort of gravitational effects would that have on the Earth?"

Let's start with Cybertron. I will need to find its mass. So I'll need its radius and an estimate of its density. I need an image to make measurements, but I couldn't find an image from the movie, so working from memory, I made one. It appeared to me that Cybertron would be much bigger than the Earth. By the time Earth was saved, my estimate is that about 1/16 of Cybertron (by volume) had been transported. Then the Transformers' planet had a radius five times larger than Earth's. Since the war had destroyed much of Cybertron, only the cubic structural elements were left, so instead of a solid, we have a lot of empty space. Judging from the width of the structural beams, I'd judge that 105/125 of the planet is empty.

Now for geometry. The volume of a sphere is

The radius of the Earth is about 6400 km. So the volume of the transported Cybertron is approximately 2 X 10^22 cubic meters.

We can get from the mass from the density and the volume. Aluminum has a density 2700 kg/m^3, steel has a density of 7500 kg/m^3, and 4500 kg/m^3 for titanium. Now maybe the Transformers are using graphene for their structures, but doesn't their technology look metal-based and not organic? So I'll use the density of titanium as an average value. Plugging in the numbers yields for Cybertron's mass 1 X 10^26 kg. Yikes! Seventeen times more mass than the Earth.

Before I start with the gravitational effects, I need an estimate of how far Cybertron is from Earth. It wasn't very far - maybe 1 Earth radius away; that's 6400 km (4000 miles).

The biggest effect would be that the Earth would in effect become a moon of Cybertron; technically though, they would be a planetary binary system. Binary systems orbit about their common center of mass. If we calculate the center of mass, (it's okay to think center of gravity) it would be located 470 km beneath the surface of Cybertron,

How long would it take for the Earth to orbit Cybertron? Just under 8 minutes. Let's start with Newton's 2nd law of motion. Substitute Newton's law of universal gravitation, and the expressions for the centripetal acceleration and the speed of an object in circular motion. Now solve for the period.

Night time every 4 minutes.

Now let's consider the tides. Tides occur because of the Moon, the Sun, and the Earth's rotation. The major effect is called the principal lunar semidiurnal constituent and is due to the Moon. In short the Moon's gravitational pull is slightly larger on the side of the Earth nearer the Moon than on the far side; physicists call this a gravitational gradient.

So all I have to calculate is the gravitational force on opposite sides of the Earth and subtract the two to estimate the gradient. I find that Cybertron's gradient is three hundred million times stronger than the Moon's. I wouldn't be living near any large body of water.

It's a good thing Optimus Prime is on our side.

P.S. I noticed that when Decepticons came through the portal, they maintained their motion. That's what Newton's first law of motion would demand. But when the transportation of cCybertron occurred, it didn't maintain its motion. Violation!!!