# How is Earth's gravity modelled?

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The Earth does not have a defined geometric shape. Then how do space scientists who want to put a satellite in orbit model the gravitational field of Earth? Do they assume a single object with minute variations from sphericity, or as a combination of multiple objects of defined shapes? Or, are there different ways of doing it right?

Quick answer for now; the Earth's field has been more and more carefully measured by precise tracking of satellites over time. It stared with very careful visual tracking/timing and interferometrically tracking and recording the Doppler shift of the radio signals from late 1950's satellites like Sputnik and Vanguard and then many many others over the years, then on to pairs of satellites that track each others' distance GRACE and GRACE-FO in order to build an Earth Gravitational Model.

It's expressed as a bunch of coefficients of spherical harmonics. The monopole term is $$GM$$ the standard gravitational parameter, there is no dipole moment since the center is defined as the Earth's center of mass, and the quadrupole moment is expressed using $$J_2$$ and $$J_{22}$$, the first of which represents Earth's oblateness which is roughly a 0.1 % effect in low Earth orbit and is what makes Sun-synchronous and Molniya orbits possible.

The spherical harmonics of a given published model only work outside of (essentially) all of Earth's mass. Very near the Earth's surface (as opposed to in orbit) you would have to correct them for the shell of the mass of the atmosphere above you which is no longer affecting you as well as nearby mountain tops that rise above you.

## How is Earth's gravity modelled? - Astronomy

The Earth constantly deforms as it undergoes dynamic phenomena, such as earthquakes, post-glacial rebound and water displacement in its fluid envelopes. These processes have different spatial and temporal scales and are accompanied by mass displacements, which create temporal variations of the gravity field. Since 2002, satellite missions such as GOCE and GRACE provide an unprecedented view of the spatial and temporal variations of the Earth's gravity field. Gravity models built from these data are essential to study the Earth's dynamic processes.

The gravity field and its time variations are usually modelled using spatial spherical harmonics functions averaged over a fixed period, as 10 days or 1 month. This approach is well suited for modeling global phenomena. To better estimate gravity variations related to local and/or transient processes, such as earthquakes or floods, and take into account the trade-off between temporal and spatial resolution resulting from the satellites sampling, we propose to model the gravity field as a four-dimensional quantity using localized functions in space and time.

For that, we first design a four-dimensional multi-scale basis, well localized both in space and time, by combining spatial Poisson wavelets with an orthogonal temporal wavelet basis. In such approach, the temporal resolution can be adjusted to the spatial one. Then, we set-up the inverse problem to model potential differences between the twin GRACE satellites in 4D, and propose a regularization using prior knowledge on the water cycle signal amplitude. We validate our 4D modelling method on a synthetic test over Africa, using synthetic data on potential differences along the orbits constructed from a global hydrological model.

A perspective of this work is to apply it on real data, in order to better model and understand the non-stationnary gravity field variations and associated processes at regional scales.

In General Relativity you can have a force of gravity, but it is an inertial force in non-inertial coordinates, rather than an interaction over distance like in Newton's model of gravity. And conversely, you can reformulate Newtonian gravity using spacetime geometry.

Summary:: Looking for a definitive answer to pedantic arguments about whether gravity is a force or not.

In Einstein's theory, gravity is caused by the warping of spacetime. This leads some people to object to gravity being referred to as a force.

However, to me it is correct to say that a paperweight resting on a desk is exerting a force on the desk (and vice versa). Is this a correct statement at every level of physics- that, whatever the cause of gravity, forces are being exerted in this situation?

Several aspects of gravity in General relativity simply do not fit well into the model of a force, at least not the sort of force that a paperweight exerts.

My favorite example are gravitational time dilation, and the Shapiro effect (gravitational time delay, see for instance the wiki article by the same name).

Your question, ultimately, has no simple, single answer. Let's look at your scenario of a paperweight resting on a desk.

In Newtonian mechanics there are two forces acting on the paperweight: gravity acting downwards and, a force from the desk acting upwards. The two forces are equal and opposite, resulting in the paperweight remaining at rest.

In General Relativity there is only one force on the paperweight: the force from the desk. Because of the shape of spacetime around the Earth the natural path of the paperweight is towards the centre of the Earth. It requires a force from the desk to prevent the paperweight following that path and keep it at rest relative to the Earth.

I might lean towards saying gravity is not a real force, but can be modelled as a force - as it is in Newtonian mechanics.

PS If you understand Newtonian mechanics and General Relativity, then this is not a question to get worked up about. Only non-physicists, I suggest, think it's an important question.

The paperweight is free-falling on a geodesic towards the center of the Earth and the desk is exerting a force pushing back against that motion, impeding the movement of the weight. In Newtonian physics, you have to say that the weight is exerting an equal and opposite force, but in GR, that's not the case.

EDIT: I wrote this reply before there were others but somehow neglected to hit "post"

And I agree w/ @jbriggs444 that you are concerned about words, not physics. Pick your model (Newton or GR) and be happy.

Your question, ultimately, has no simple, single answer. Let's look at your scenario of a paperweight resting on a desk.

In Newtonian mechanics there are two forces acting on the paperweight: gravity acting downwards and, a force from the desk acting upwards. The two forces are equal and opposite, resulting in the paperweight remaining at rest.

In General Relativity there is only one force on the paperweight: the force from the desk. Because of the shape of spacetime around the Earth the natural path of the paperweight is towards the centre of the Earth. It requires a force from the desk to prevent the paperweight following that path and keep it at rest relative to the Earth.

I might lean towards saying gravity is not a real force, but can be modelled as a force - as it is in Newtonian mechanics.

PS If you understand Newtonian mechanics and General Relativity, then this is not a question to get worked up about. Only non-physicists, I suggest, think it's an important question.

## Making sense of astronomical misconceptions

Shortly after posting my last blog, I was abducted by aliens who flew me to Thermoman‘s home planet of Ultron where I was taught secrets of the universe. Having just returned, I will now enlighten you with a new blog.

Now, I know that no one reading this will believe that, but I am amazed sometimes at the things people will believe. Some of it is simply unlikely, such as the idea that Earth is being visited by aliens from other worlds. This is certainly not impossible, but for various reasons it is deemed unlikely by most scientists and in any event there is no good physical evidence to support it.

And then there are other beliefs that simply fly in the face of established fact, such as the absurd idea that the Earth is hollow or that the Apollo astronauts never really landed on the moon. Add to those ideas the belief in a non-existant planet Nibiru, or in the idea that a real but harmless Comet Elenin was a spaceship or a doomsday object.

Leaving TV commercials and all manner of advertising aside, there are many other basic facts and concepts of science that people believe that are flat out wrong. Read on, to find three examples.

The moon is smaller than Earth and contains less mass. So its gravity is weaker, only 17% the force of gravity at Earth’s surface. Astronauts in space experience weightlessness because they are in free fall around the Earth, moving at the same rate at their spacecraft.

1. Many people erroneously believe that there is no gravity on Earth’s moon. Sometimes they justify this belief by claiming that since there is no gravity in space and the moon is in space, then there logically must be no gravity on the moon. Unfortunately, this is an illogical mash-up of misunderstood concepts. Any object with mass has gravity, and missions to the moon have proved beyond doubt that gravity does indeed operate there, just as it operates everywhere else.

2. Some mistakenly believe there is no gravity in space generally. Gravity pervades the entire universe – holds stars, planets and galaxies together – and is impossible to escape. People get the idea that there is no gravity in space when they see astronauts floating in the space station or International Space Station (ISS). But neither the astronauts nor their spacecraft are free of gravity, ever. In fact for near-Earth missions, astronauts are subject a force of gravity 98 to 99 percent as strong as it is on Earth’s surface! The fact that they are falling around the Earth at the same rate as the spacecraft makes them seem weightless relative to things around them.

Images of the sun on July 4, 2008 (left) and January 2, 2009. The January image is very slightly larger. This minor difference has virtually no bearing on the seasons. Image via SOHONASA Solar & Heliospheric Observatory.

3. Some wrongly believe Earth’s seasons are caused by our distance from the sun. They think Earth is farther from the sun in winter and closer in summer. At least this bears a little logic, because the Earth does vary slightly in distance to the sun through the year, and it is natural and logical to think that the Earth would be warmer when we are closer to the sun. However, if the sun-Earth distance variation fueled seasonal changes, then Northern Hemisphere winters would be hot and summers cold. In fact, the Earth is about 3 million miles closer to the sun in early January than in early July! What does cause the seasons? The Earth is tilted on its axis, pointing more or less toward Polaris, the North Pole star. As the Earth orbits the sun, this tilt causes the planet to nod toward the sun in June, and away from it in December. The upshot to this is that the sun’s height in the sky varies, which in turn affects the amount of sunshine any given location receives and hence the overall temperatures. The Northern Hemisphere is tilted away from the sun in winter and receives less sunshine.

Our modern era is not alone in holding astronomical misconceptions. The early astronomers believed in a geocentric cosmology. That is, they thought Earth was the center of the universe, because we cannot feel Earth move under us. It seems natural that this big, massive Earth would be stationary while those little twinkling lights circle around us. Seems natural … but isn’t true.

My point is that we need to look at everything and ask why we believe what we believe.

I’d be interested in learning of misconceptions you have heard (or perhaps been guilty of), regarding astronomy, space or physical science in general. Comments?

## How strong is the force of gravity on Earth?

The Geoid 2011 model, based on data from LAGEOS, GRACE, GOCE and surface data. Credit: GFZ

Gravity is a pretty awesome fundamental force. If it wasn't for the Earth's comfortable 1 g, which causes objects to fall towards the Earth at a speed of 9.8 m/s², we'd all float off into space. And without it, all us terrestrial species would slowly wither and die as our muscles degenerated, our bones became brittle and weak, and our organs ceased to function properly.

So one can say without exaggerations that gravity is not only a fact of life here on Earth, but a prerequisite for it. However, since human beings seem intent on getting off this rock – escaping the "surly bonds of Earth", as it were – understanding Earth's gravity and what it takes to escape it is necessary. So just how strong is Earth's gravity?

To break it down, gravity is a natural phenomena in which all things that possess mass are brought towards one another – i.e. asteroids, planets, stars, galaxies, super clusters, etc. The more mass an object has, the more gravity it will exert on objects around it. The gravitational force of an object is also dependent on distance – i.e. the amount it exerts on an object decreases with increased distance.

Gravity is also one of the four fundamental forces which govern all interactions in nature (along with weak nuclear force, strong nuclear force, and electromagnetism). Of these forces, gravity is the weakest, being approximately 1038 times weaker than the strong nuclear force, 10 36 times weaker than the electromagnetic force and 10 29 times weaker than the weak nuclear force.

As a consequence, gravity has a negligible influence on matter at the smallest of scales (i.e. subatomic particles). However, at the macroscopic level – that of planets, stars, galaxies, etc. – gravity is the dominant force affecting the interactions of matter. It causes the formation, shape and trajectory of astronomical bodies, and governs astronomical behavior. It also played a major role in the evolution of the early universe.

Artist’s impression of the effect Earth’s gravity has on spacetime. Credit: NASA

It was responsible for matter clumping together to form clouds of gas that underwent gravitational collapse, forming the first stars – which were then drawn together to form the first galaxies. And within individual star systems, it caused dust and gas to coalesce to form the planets. It also governs the orbits of the planets around stars, of moons around planets, the rotation of stars around their galaxy's center, and the merging of galaxies.

Universal Gravitation and Relativity

Since energy and mass are equivalent, all forms of energy, including light, also cause gravitation and are under the influence of it. This is consistent with Einstein's General Theory of Relativity, which remains the best means of describing gravity's behavior. According to this theory, gravity is not a force, but a consequence of the curvature of spacetime caused by the uneven distribution of mass/energy.

The most extreme example of this curvature of spacetime is a black hole, from which nothing can escape. Black holes are usually the product of a supermassive star that has gone supernova, leaving behind a white dwarf remnant that has so much mass, it's escape velocity is greater than the speed of light. An increase in gravity also results in gravitational time dilation, where the passage of time occurs more slowly.

For most applications though, gravity is best explained by Newton's Law of Universal Gravitation, which states that gravity exists as an attraction between two bodies. The strength of this attraction can calculated mathematically, where the attractive force is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

Artist’s impression of the frame-dragging effect in which space and time are dragged around a massive body. Credit: einstein.stanford.edu

On Earth, gravity gives weight to physical objects and causes the ocean tides. The force of Earth's gravity is the result of the planets mass and density – 5.97237 × 10 24 kg (1.31668×10 25 lbs) and 5.514 g/cm 3 , respectively. This results in Earth having a gravitational strength of 9.8 m/s² close to the surface (also known as 1 g), which naturally decreases the farther away one is from the surface.

In addition, the force of gravity on Earth actually changes depending on where you're standing on it. The first reason is because the Earth is rotating. This means that the gravity of Earth at the equator is 9.789 m/s 2 , while the force of gravity at the poles is 9.832 m/s 2 . In other words, you weigh more at the poles than you do at the equator because of this centripetal force, but only slightly more.

Finally, the force of gravity can change depending on what's under the Earth beneath you. Higher concentrations of mass, like high-density rocks or minerals can change the force of gravity that you feel. But of course, this amount is too slight to be noticeable. NASA missions have mapped the Earth's gravity field with incredible accuracy, showing variations in its strength, depending on location.

Gravity also decreases with altitude, since you're further away from the Earth's center. The decrease in force from climbing to the top of a mountain is pretty minimal (0.28% less gravity at the top of Mount Everest), but if you're high enough to reach the International Space Station (ISS), you would experience 90% of the force of gravity you'd feel on the surface.

However, since the station is in a state of free fall (and also in the vacuum of space) objects and astronauts aboard the ISS are capable of floating around. Basically, since everything aboard the station is falling at the same rate towards the Earth, those aboard the ISS have the feeling of being weightless – even though they still weight about 90% of what they would on Earth's surface.

Earth's gravity is also responsible for our planet having an "escape velocity" of 11.186 km/s (or 6.951 mi/s). Essentially, this means that a rocket needs to achieve this speed before it can hope to break free of Earth's gravity and reach space. And with most rocket launches, the majority of their thrust is dedicated to this task alone.

Because of the difference between Earth's gravity and the gravitational force on other bodies – like the moon (1.62 m/s² 0.1654 g) and Mars (3.711 m/s² 0.376 g) – scientists are uncertain what the effects would be to astronauts who went on long-term missions to these bodies.

While studies have shown that long-duration missions in microgravity (i.e. on the ISS) have a detrimental effect on astronaut health (including loss of bone density, muscle degeneration, damage to organs and to eyesight) no studies have been conducted regarding the effects of lower-gravity environments. But given the multiple proposals made to return to the moon, and NASA's proposed "Journey to Mars", that information should be forthcoming!

As terrestrial beings, we humans are both blessed and cursed by the force of Earth's gravity. On the one hand, it makes getting into space rather difficult and expensive. On the other, it ensures our health, since our species is the product of billions of years of species evolution that took place in a 1 g environment.

If we ever hope to become a truly space-faring and interplanetary species, we better figure out how we're going to deal with microgravity and lower-gravity. Otherwise, none of us are likely to get off-world for very long!

## How is Earth's gravity modelled? - Astronomy

Present day changes in the ice volume in glaciated areas like Greenland will change the load on the Earth and to this change the lithosphere will respond elastically. The Earth also responds to changes in the ice volume over a millennial time scale. This response is due to the viscous properties of the mantle and is known as Glaical Isostatic Adjustment (GIA). Both signals are present in GPS and absolute gravity (AG) measurements and they will give an uncertainty in mass balance estimates calculated from these data types. It is possible to separate the two signals if both gravity and Global Positioning System (GPS) time series are available. DTU Space acquired an A10 absolute gravimeter in 2008. One purpose of this instrument is to establish AG time series in Greenland and the first measurements were conducted in 2009. Since then are 18 different Greenland GPS Network (GNET) stations visited and six of these are visited more then once. The gravity signal consists of three signals the elastic signal, the viscous signal and the direct attraction from the ice masses. All of these signals can be modelled using various techniques. The viscous signal is modelled by solving the Sea Level Equation with an appropriate ice history and Earth model. The free code SELEN is used for this. The elastic signal is modelled as a convolution of the elastic Greens function for gravity and a model of present day ice mass changes. The direct attraction is the same as the Newtonian attraction and is calculated as this. Here we will present the preliminary results of the AG measurements in Greenland. We will also present modelled estimates of the direct attraction, the elastic and the viscous signals.

## Theories of Gravity

One way to think of the gravitational attraction between objects, expressed by the late theoretical physicist Jacob Bekenstein in an essay for CalTech, is as "long range forces that electrically neutral bodies exert on one another because of their matter content." That is, while objects may experience a force as a result of differences in electrostatic charge, gravity instead results in a force owing to sheer mass. Technically, you and the computer, phone or tablet you're reading this on exert gravitational forces on each other, but you and and your Internet-enabled device are so small that this force is virtually undetectable. Obviously, for objects on the scale of planets, stars, whole galaxies and even clusters of galaxies, it is a different story.

Isaac Newton (1642-1727), credited with being one of the most brilliant mathematical minds in history and one of the co-inventors of the field of calculus, proposed that the force of gravity between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. This takes the form of the equation:

where Fgrav is the gravitational force in newtons, m1 and m2 are the masses of the objects in kilograms, r is the distance separating the objects in meters and the value of the proportionality constant G is 6.67 × 10 -11 (N ⋅ m 2 )/kg 2 .

While this equation works superbly for everyday purposes, its value is diminished when the objects in question are relativistic, that is, described by masses and speeds well outside of typical human experience. This is where Einstein's theory of gravity comes in.

## NGSS Earth & Space Science Astronomy Lesson Plan #44 Gravity & Planet's Surface

This lesson plan includes a summary, list of resources, learning outcomes, the NGSS alignment for the lesson, lesson procedures, one Science Literacy Activity. The lesson plan also includes a discussion question and sample responses, assessment questions and answer keys.

Upon completion of this lesson, students will be able to:

• Explain how a planet’s gravity sets limits for the height of mountains on the planet.

• Describe how scientists define weight.

• Explain why we would feel lighter on Mars than on the Earth.

• Explain what a gravity anomaly is.

• Describe how NASA scientists study the gravity anomalies of Mars.

• Explain how the Earth’s rotation changes the Earth’s shape and affects the Earth’s gravity.

I will be adding more teaching resources to this lesson plan. Follow me to receive email notifications via TPT Inbox when new teaching resources are added to this lesson plan.

This lesson plan is also included in:

Please take a look at other collections of educational resources that I offer:

Terms of Use: Copyright © Irina Mullins. All rights reserved by the author. This product may be used by one teacher for educational purposes in one classroom only. Copying for more than one teacher, classroom, department, school, or school system is prohibited. This entire product, or any parts within this product, may not be electronically redistributed or posted to any website including teacher blogs or classroom blogs.

## Incredible Gravity Map of the Earth’s Seafloors

Map by NASA Earth Observatory/Joshua Stevens, using data from Sandwell, D. et al. (2014).

The picture above is not actually a map of the topography * (height variation) of the Indian Ocean seafloor, as much as it looks like it.

It’s actually a map of the change in the Earth’s gravity field across the Indian Ocean seafloor, and it’s so cool I can hardly stand it.

Why is it cool? For a lot of reasons. One is how it was made: using data from a bunch of different satellites, including Jason-1 and CryoSat-2. These satellites used various methods to determine their exact altitude above the sea surface at any given time. Since the orbits of the satellites are well known, variations in the altitude above the sea surface correspond to changes in the height of the surface. So, for example, if there’s a wave a meter high moving across the ocean, a satellite would measure its own altitude as being a meter lower, since the distance from the satellite to the top of the wave is one meter less than the average distance to the sea surface.

So how does this map the seafloor? Get this: If there’s a mountain under the ocean, then it has more gravity than the water around it (rock is denser than water, so it has more mass per cubic centimeter, which means it has more gravity than the same volume of water). This slight increase in gravity draws in water on the surface around it, piling it up on the surface—water is incompressible, so it doesn’t just flatten out. So when the satellite flies over a seamount, it sees a little bump in the sea surface.

If there’s a chasm or trench in the seafloor, then it has slightly lower gravity than the rock around it, so there’s a corresponding dip in the sea surface above it.

Mind you, these bumps are dips in the water are subtle: They may have a height of several meters, which sounds like a lot, but they’re spread out over a long distance, sometimes hundreds of kilometers. The slope of the water is incredibly small and difficult to measure, and this is complicated by currents, waves, chop, and the like. The satellites have to find that gently sloping trend up (in the case of seamounts) or down (in the case of trenches) despite all that noise. The only way to get good measurements is to take a lot of them, and then the noise that changes over time will cancel out. It’s like flipping a coin do it a few times and they might all come out heads, but do it a million times and you can be pretty sure you’ll get extremely close to half heads and half tails. **

This was the first thing to amaze me: Scientists can measure the sea surface height to incredible accuracy. The map is based on new techniques that improve over the old measurements by a factor of two or so.

Map by NASA Earth Observatory/Joshua Stevens, using data from Sandwell, D. et al. (2014).

I got a fun surprise as I read more about this, too: A new unit to think about, called a “Gal,” which is short for “Galileo.” It’s a measure of acceleration, and is equal to one centimeter per second per second. What does that mean?

Gravity is a force that accelerates a mass. On the Earth’s surface, the strength of gravity is enough to accelerate a mass by about 10 meters per second every second. If you drop a rock, after one second it will fall at 10 meters per second (22 mph). After another second it will have accelerated to 20 meters/second (44 mph), and then after another to 30 meters/second (66 mph).

A Gal is an acceleration of 1 cm/s every second, so the strength of Earth’s gravity at the surface is roughly 1,000 Gals. (It varies a bit from place to place due to density differences in the ground, changes in latitude, and so on.)

OK, so what? Well, the maps of the seafloor need some sort of unit attached to them. They’re not really showing the heights of the mountains and the depths of the trenches, because there’s no way to directly measure that this way. They’re displaying the change in gravity. So the maps display this in Gals—actually in milliGals, 1/1000 th of a Gal. The darkest red parts of the map are an increase in strength of 90 mGals, and the darkest blue -90 mGals.

Again, this is phenomenal. A milliGal is one-millionth the strength of Earth’s surface gravity! But this is the sort of thing engineers and scientists can measure using the satellite data.

The result is a very detailed and accurate map of the seafloor, which has tremendous value. It can be used by ships and submarines to navigate, of course. But it also maps out where tectonic plates meet, and that has quite a bit of interest to geologists. In fact, a new feature was discovered using these maps: a microplate.

Map by NASA Earth Observatory/Joshua Stevens, using data from Sandwell, D. et al. (2014).

The crust of the Earth floats on the mantle below it and is broken up into a bunch of chunks called plates. These are pretty big, thousands of kilometers across. As they float, they move around very slowly, a couple of centimeters per year. They collide, grinding into each other, slipping past one another, or one sliding under another. This puts a lot of stress on the surrounding material, and can shear off parts of a plate to create a smaller microplate. Late last year, an oceanic microplate was discovered in the maps and was dubbed the Mammerickx microplate, after Jacqueline Mammerickx, who was a pioneer in seafloor mapping.

## Einstein's Gravity Protects Earth

By: Johannes Hirn June 29, 2009 12

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If the universe obeyed Newton's laws of gravity, there would be about a 60% chance that Mercury would head toward the Sun or Venus during the Sun’s lifetime. But according to a new study, corrections to Newton's laws using Einstein's theory of gravity (general relativity) lower these chances to about 1%. That’s good news, because if Mercury had a near miss with Venus or the Sun, it could wreak havoc on Earth.

Artist's concept of a collision between Venus and Earth.

J. Vidal-Madjar / IMCCE / CNRS

new study by Jacques Laskar and Mickael Gastineau (Paris Observatory, France), published in the June 11th issue of Nature.

For all of Jupiter’s mass, sending Mercury farther out than Venus requires an "alignment of planets" of sorts — a near-perfect geometry that physicists call a resonance — allowing a small effect to build up over time.

In the case of Jupiter and Mercury, the accidental matching is provided by the speed at which their elliptical orbits move around the Sun — the precession of their perihelia — which happens to be nearly synchronized. But the warping of space-time near the Sun predicted by general relativity introduces a slight mismatch, by speeding up Mercury’s precession. So the resonance is less likely to happen.

We can thank Einstein once more (and Laskar too) for informing us that Mercury has only a 1% chance of going out of whack. Laskar's estimate following Newtonian gravity was 60%. "[The Newtonian calculation] had to be wrong," says Jack Lissauer (NASA/Ames Research Center), arguing that, with such high probabilities, Mercury would already have hit Venus or the Sun during the past few billion years.

Example of long-term evolution of the planetary orbits: Mercury (white), Venus (green), Earth (blue), Mars (red). Time is indicated in thousands of years (kyr). (a) In the vicinity of the current state, the orbits become distorted under the influence of planetary perturbations, but without allowing close encounters or collisions. (b) In about 1% of cases, the orbit of Mercury may be distorted enough to allow a collision with Venus or the Sun in less than 5 billion years. (c) In one of the trajectories, the eccentricity of Mars increases sufficiently to allow for a close encounter or collision with Earth. (d) This leads to a destabilization of the terrestrial planets and collision between Venus and Earth.

A neat report here. If Mercury orbited the Sun for 1E+9 years, that could involve > 4E+9 revolutions and over 4.5 billion years > 18E+9. Ruling out the Newtonian calculation because it does not fit with 4.5 billions years is an interpretation. Could this also be interpreted that the planets simply have not been orbiting the Sun for billions of years?

In working with Laplace-Lagrange (LL) secular theory, we used to talk about the long-term instability inherent in all planetary systems and the likelihood that Mercury would most probably one day slam into the Earth. You don't know how good it is to hear that that probability has been reduced down to only 1%. Thank you, Albert Einstein!

I always did like that guy!

This is an interesting article but the "what ifs" are so pervasive and overwhelming that they don't really mean anything at all. Of course, any theories that predict a 60% chance or a 1% chance of something happening in the extreme past or future never affect reality at all but only describe someone's faulty perceptions of reality.
So. it may be best not to thank the theorists who generate all this smoke and mirrors but rather the ONE who designed and built it all in the first place.

Clearly Laskar needs to calm down and stop jumping about before he dooms us all.

I've played with GravitySimulator a bunch. If you run it too fast or your computer is too slow, various mathematical errors can creep into your calculations. It doesn't do relativity, anyway, that would just slow it down too much. I think Renu Malhotra is right about a previous collision giving Mercury an eccentric orbit the object was formed in the Sun/Mercury L4 or L5 point and plunged into the Sun, the other L5 or L4 object formed Caloris Basin. It's become apparent that other solar systems generally have larger planets than ours, if you replace the masses of the gas giants of our solar system with 10 Jupiter masses, the Solar System falls apart immediately. This might be a partial answer to the Fermi Paradox ("If there are aliens, where are they?"). It's best to carefully construct simulations to answer generalized situations.

In reference to Michael Emmert's comments, exoplanet.eu website shows 353 exoplanets. The table indicates 146 have semi-major axis 1-8 AU, the average mass is a little more than 4 Jupiters, average semi-major axis 2.26 AU and average eccentricity is 0.3087. 102 of the 353 listed are apparently hot Jupiters. This configuration here could make for some chaos at home.

Regarding the first comment by Rod-It's very unlikely. General relativity has been proven extremely reliable and the other lines of evidence(geology, radiometric dating, etc.) indicate an Earth that is about 4.5 byo. Also, Big Bang cosmology has much evidential support. This is not necessarily in conflict w/Christian scripture(assuming that is where you are coming from). reasons.org

Grant Miller, interesting points raised. A problem I see is that radiometric ages cannot be shown to represent true orbital revolutions around the Sun, only circular reasoning supports the interpretation. Case in point, Mercury needs some 18 billion revolutions to experience 4.5 billion years of radiometric dating.

As far as I'm concern, we'll all humans would be gone before this would ever happen. We just won't live that long.

"We can thank Einstein.." for clarifying the law, but he did not write it.

In reference to Michael Emmert and Rod's comments, one should not forget that the current sample of exoplanets cannot be assumed to be representative of all planetary systems in the sun's neighbourhood, or indeed the rest of the universe. This is simply because the methods used to detect exoplanes are strongly biased to detecting planets with relatively large masses which orbit close to their parent star. If our models of planet formation are correct (and there is currently no real fundamental reason to believe that they are not) there will be plenty of planetary systems out there that resemble our solar systems. However, our current techniques are simply not sensitive enough to detect these.

## Watch the video: How Does Gravity Work? (May 2022).

1. Giollabuidhe

Absolutely agrees with you. In this something is I seem this the good idea. I agree with you.

2. Kenos

Let's be.

3. Tygolrajas

Wise objects, says)

4. Arnatt

And indefinitely it is not far :)