Attention Dr. Robert Jeffress, Rabbi Schneider, Joel Osteen, words born again are an equated word to word detail words Redeemed. Title: you have the word gift of word doctor to word state words In the beginning. Words the ignorance on word Earth should equate word shallow and equated word Skirt

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you breathe,

yet the Shores are your sand.

redeemed is a lend,

Benbot is an Herb and only have word herb as word error is word error.

There is no exact count of how many herbs exist in the world, but scientists estimate there are more than 50,000 plant species used for medicinal, culinary, or aromatic purposes, out of roughly 300,000 to 400,000 total plant species globally.

Why the Number Varies

• Definition of an Herb: Botanically, an herb is any seed-producing plant that does not have a woody stem and dies back to the ground after flowering. However, people often use the word "herb" to mean any plant used for cooking, scent, or healing—including shrubs, trees, and perennials.
• Commercial vs. Wild: While hundreds of thousands of plants have potential properties, experts note that only about 2,000 to 3,000 types of herbs are actively traded and cultivated worldwide for commercial use in food, medicine, and cosmetics.
• Ongoing Discoveries: Researchers continue to document new plant uses and species in remote areas, meaning the list of useful herbs grows as traditional knowledge and modern science intersect.

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Job 19:4chapter context similar meaning copy save

And be it indeed that I have erred, mine error remaineth with myself.

Ecclesiastes 10:5chapter context similar meaning copy save

There is an evil which I have seen under the sun, as an error which proceedeth from the ruler:

2 Peter 3:17chapter context similar meaning copy save

Ye therefore, beloved, seeing ye know these things before, beware lest ye also, being led away with the error of the wicked, fall from your own stedfastness.

James 5:20chapter context similar meaning copy save

Let him know, that he which converteth the sinner from the error of his way shall save a soul from death, and shall hide a multitude of sins.

2 Peter 2:18chapter context similar meaning copy save

For when they speak great swelling words of vanity, they allure through the lusts of the flesh, through much wantonness, those that were clean escaped from them who live in error.

Ecclesiastes 5:6chapter context similar meaning copy save

Suffer not thy mouth to cause thy flesh to sin; neither say thou before the angel, that it was an error: wherefore should God be angry at thy voice, and destroy the work of thine hands?

2 Samuel 6:7chapter context similar meaning copy save

And the anger of the LORD was kindled against Uzzah; and God smote him there for his error; and there he died by the ark of God.

Jude 1:11chapter context similar meaning copy save

Woe unto them! for they have gone in the way of Cain, and ran greedily after the error of Balaam for reward, and perished in the gainsaying of Core.

Daniel 6:4chapter context similar meaning copy save

Then the presidents and princes sought to find occasion against Daniel concerning the kingdom; but they could find none occasion nor fault; forasmuch as he was faithful, neither was there any error or fault found in him.

Matthew 27:64chapter context similar meaning copy save

Command therefore that the sepulchre be made sure until the third day, lest his disciples come by night, and steal him away, and say unto the people, He is risen from the dead: so the last error shall be worse than the first.

Isaiah 32:6chapter context similar meaning copy save

For the vile person will speak villany, and his heart will work iniquity, to practise hypocrisy, and to utter error against the LORD, to make empty the soul of the hungry, and he will cause the drink of the thirsty to fail.

Romans 1:27chapter context similar meaning copy save

And likewise also the men, leaving the natural use of the woman, burned in their lust one toward another; men with men working that which is unseemly, and receiving in themselves that recompence of their error which was meet.

1 John 4:6chapter context similar meaning copy save

We are of God: he that knoweth God heareth us; he that is not of God heareth not us. Hereby know we the spirit of truth, and the spirit of error.

Psalms 139:18

“If I should count them, they are more in number than the sand: when I awake, I am still with thee.” 

King James Version (KJV)

Romans 12:19

“Dearly beloved, avenge not yourselves, but rather give place unto wrath: for it is written, Vengeance is mine; I will repay, saith the Lord.” 

King James Version (KJV)

word mine;  equated word redeem as word born again is an ignorant word to equated words Mine Solomon he’s a Bucket of Gold.

Words Operation equated word doctor Zeigler on LETTERS ER as equated word EMERGENCY word ROOMS to place the Crazy Horse [word doctor]doctor to word gift to state word Operator and word rememberest word Reincarnation of birth Isaac Newton to state REM Sleep is word Weird as there is a WAR with word Space and word SHIPS and word now and word Panic equated word ribbon, word sleigh, word horse, word life, word ships, word space!!

So, pull your shit together and in a word equated word STORM the word that doesn’t exist word Hauls words Social Security Administration paid words you’re it as word equated word Luster[it’s actually word Lest accept for it is word Least and word lest is not word lease, so a Librarian for the Social Security Administration may word equate word FORM[fore]] from the Statements of the word Theorists stating that words We would be or look like Ants to them on a Show on The History Channel equated word Production!!

So, word Ants is a Proverb and word doctor is able at word gift to word Unwrap words to place word to word Ants as a word Book with word new Titles.  

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Proverbs 30:25chapter context similar meaning copy save

The ants are a people not strong, yet they prepare their meat in the summer;

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WORDS read next word Publishing House as a word REM Sleep add’0 as actual word in number of zero and word equated word midst and the next Post that is word Publish is on that Funny rolodex with that Eight ball[IBM The IBM Selectric was the most successful electric typewriter in history. With its distinctive type element — a spinning, bobbing mechanism often likened to ...] equated word Speed nut.

Matthew 5:23

“Therefore if thou bring thy gift to the altar, and there rememberest that thy brother hath ought against thee;” 

King James Version (KJV)

 

Cantore Arithmetic is able to state words Year is in 2026 at 9[September[Month] on 22[Day[24 Hours]] Tuesday 4:58 equated word lip!

1.  words 3.141 is an approximation of the mathematical constant pi (π) rounded to three decimal places equated words 3.141 an opportunity at word approximation.

Words To the word equated word Plant on word earth your determination of word Evolution to the ongoing word demand of word explanation word draws.

1.  Y chromosome 

2.  Adios, half-soldier (The Good, The Bad And The Ugly) 

a.  

Adios, half-soldier (The Good, The Bad And The Ugly) - YouTube

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3.  

Logan's Run Official Trailer #1 - Michael York Movie (1976) HD

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Oct 5, 2012 · Logan's Run Official Trailer #1 - Michael York Movie (1976) HD · Comments. 1K. The fear of the 60's and 70's was the danger of overpopulation of . 

a.  

Logan's Run (1976) - IMDbwww.imdb.com

Logan's Run

• 1976
• PG
• 1h 59m

Words End Program equated words World Ends word equated word Process[Morse[certain[symptom[said[cell]]]]].

Genesis 21:8

“And the child grew, and was weaned: and Abraham made a great feast the same day that Isaac was weaned.” 

King James Version (KJV)

 

 

AI Overview

Abraham

and Sarah had

a baby boy named Isaac when Abraham was 100 years old and Sarah was 90 years old, fulfilling a promise made by God.

Key Details of the Story

• The Parents' Ages: Abraham was a century old and Sarah was around 90, making natural conception seem impossible.
• The Reaction: Sarah laughed silently when visiting divine messengers predicted she would have a son within a year, leading to the name Isaac, which means "laughter" . You can read the account in Genesis 21on Bible Gateway .
• The Significance: Isaac's birth is detailed in biblical texts like Genesis 21:1-8as a sign of divine faithfulness and the continuation of God's covenant.

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Psalms 37:2chapter context similar meaning copy save

For they shall soon be cut down like the grass, and wither as the green herb.

Job 8:12chapter context similar meaning copy save

Whilst it is yet in his greenness, and not cut down, it withereth before any other herb.

Genesis 9:3chapter context similar meaning copy save

Every moving thing that liveth shall be meat for you; even as the green herb have I given you all things.

Genesis 3:18chapter context similar meaning copy save

Thorns also and thistles shall it bring forth to thee; and thou shalt eat the herb of the field;

Job 38:27chapter context similar meaning copy save

To satisfy the desolate and waste ground; and to cause the bud of the tender herb to spring forth?

Psalms 104:14chapter context similar meaning copy save

He causeth the grass to grow for the cattle, and herb for the service of man: that he may bring forth food out of the earth;

Genesis 1:11chapter context similar meaning copy save

And God said, Let the earth bring forth grass, the herb yielding seed, and the fruit tree yielding fruit after his kind, whose seed is in itself, upon the earth: and it was so.

Isaiah 66:14chapter context similar meaning copy save

And when ye see this, your heart shall rejoice, and your bones shall flourish like an herb: and the hand of the LORD shall be known toward his servants, and his indignation toward his enemies.

Genesis 1:12chapter context similar meaning copy save

And the earth brought forth grass, and herb yielding seed after his kind, and the tree yielding fruit, whose seed was in itself, after his kind: and God saw that it was good.

Exodus 9:22chapter context similar meaning copy save

And the LORD said unto Moses, Stretch forth thine hand toward heaven, that there may be hail in all the land of Egypt, upon man, and upon beast, and upon every herb of the field, throughout the land of Egypt.

Deuteronomy 32:2chapter context similar meaning copy save

My doctrine shall drop as the rain, my speech shall distil as the dew, as the small rain upon the tender herb, and as the showers upon the grass:

Genesis 1:30chapter context similar meaning copy save

And to every beast of the earth, and to every fowl of the air, and to every thing that creepeth upon the earth, wherein there is life, I have given every green herb for meat: and it was so.

Exodus 10:12chapter context similar meaning copy save

And the LORD said unto Moses, Stretch out thine hand over the land of Egypt for the locusts, that they may come up upon the land of Egypt, and eat every herb of the land, even all that the hail hath left.

Genesis 1:29chapter context similar meaning copy save

And God said, Behold, I have given you every herb bearing seed, which is upon the face of all the earth, and every tree, in the which is the fruit of a tree yielding seed; to you it shall be for meat.

2 Kings 19:26chapter context similar meaning copy save

Therefore their inhabitants were of small power, they were dismayed and confounded; they were as the grass of the field, and as the green herb, as the grass on the housetops, and as corn blasted before it be grown up.

Isaiah 37:27chapter context similar meaning copy save

Therefore their inhabitants were of small power, they were dismayed and confounded: they were as the grass of the field, and as the green herb, as the grass on the housetops, and as corn blasted before it be grown up.

Exodus 9:25chapter context similar meaning copy save

And the hail smote throughout all the land of Egypt all that was in the field, both man and beast; and the hail smote every herb of the field, and brake every tree of the field.

Exodus 10:15chapter context similar meaning copy save

For they covered the face of the whole earth, so that the land was darkened; and they did eat every herb of the land, and all the fruit of the trees which the hail had left: and there remained not any green thing in the trees, or in the herbs of the field, through all the land of Egypt.

Genesis 2:5chapter context similar meaning copy save

And every plant of the field before it was in the earth, and every herb of the field before it grew: for the LORD God had not caused it to rain upon the earth, and there was not a man to till the ground.

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Matthew 23:19chapter context similar meaning copy save

Ye fools and blind: for whether is greater, the gift, or the altar that sanctifieth the gift?

Exodus 23:8chapter context similar meaning copy save

And thou shalt take no gift: for the gift blindeth the wise, and perverteth the words of the righteous.

Matthew 5:24chapter context similar meaning copy save

Leave there thy gift before the altar, and go thy way; first be reconciled to thy brother, and then come and offer thy gift.

James 1:17chapter context similar meaning copy save

Every good gift and every perfect gift is from above, and cometh down from the Father of lights, with whom is no variableness, neither shadow of turning.

Romans 5:16chapter context similar meaning copy save

And not as it was by one that sinned, so is the gift: for the judgment was by one to condemnation, but the free gift is of many offences unto justification.

Deuteronomy 16:19chapter context similar meaning copy save

Thou shalt not wrest judgment; thou shalt not respect persons, neither take a gift: for a gift doth blind the eyes of the wise, and pervert the words of the righteous.

Romans 5:15chapter context similar meaning copy save

But not as the offence, so also is the free gift. For if through the offence of one many be dead, much more the grace of God, and the gift by grace, which is by one man, Jesus Christ, hath abounded unto many.

2 Corinthians 9:15chapter context similar meaning copy save

Thanks be unto God for his unspeakable gift.

Ecclesiastes 7:7chapter context similar meaning copy save

Surely oppression maketh a wise man mad; and a gift destroyeth the heart.

Proverbs 25:14chapter context similar meaning copy save

Whoso boasteth himself of a false gift is like clouds and wind without rain.

1 Corinthians 1:7chapter context similar meaning copy save

So that ye come behind in no gift; waiting for the coming of our Lord Jesus Christ:

Proverbs 18:16chapter context similar meaning copy save

A man's gift maketh room for him, and bringeth him before great men.

Proverbs 21:14chapter context similar meaning copy save

A gift in secret pacifieth anger: and a reward in the bosom strong wrath.

Philippians 4:17chapter context similar meaning copy save

Not because I desire a gift: but I desire fruit that may abound to your account.

Matthew 5:23chapter context similar meaning copy save

Therefore if thou bring thy gift to the altar, and there rememberest that thy brother hath ought against thee;

Ephesians 2:8chapter context similar meaning copy save

For by grace are ye saved through faith; and that not of yourselves: it is the gift of God:

Proverbs 17:8chapter context similar meaning copy save

A gift is as a precious stone in the eyes of him that hath it: whithersoever it turneth, it prospereth.

Proverbs 17:23chapter context similar meaning copy save

A wicked man taketh a gift out of the bosom to pervert the ways of judgment.

Ephesians 4:7chapter context similar meaning copy save

But unto every one of us is given grace according to the measure of the gift of Christ.

Psalms 45:12chapter context similar meaning copy save

And the daughter of Tyre shall be there with a gift; even the rich among the people shall intreat thy favour.

Acts 8:20chapter context similar meaning copy save

But Peter said unto him, Thy money perish with thee, because thou hast thought that the gift of God may be purchased with money.

Romans 6:23chapter context similar meaning copy save

For the wages of sin is death; but the gift of God is eternal life through Jesus Christ our Lord.

Romans 1:11chapter context similar meaning copy save

For I long to see you, that I may impart unto you some spiritual gift, to the end ye may be established;

1 Corinthians 7:7chapter context similar meaning copy save

For I would that all men were even as I myself. But every man hath his proper gift of God, one after this manner, and another after that.

2 Corinthians 8:4chapter context similar meaning copy save

Praying us with much intreaty that we would receive the gift, and take upon us the fellowship of the ministering to the saints.

Matthew 15:5chapter context similar meaning copy save

But ye say, Whosoever shall say to his father or his mother, It is a gift, by whatsoever thou mightest be profited by me;

Ephesians 3:7chapter context similar meaning copy save

Whereof I was made a minister, according to the gift of the grace of God given unto me by the effectual working of his power.

Ecclesiastes 3:13chapter context similar meaning copy save

And also that every man should eat and drink, and enjoy the good of all his labour, it is the gift of God.

1 Peter 4:10chapter context similar meaning copy save

As every man hath received the gift, even so minister the same one to another, as good stewards of the manifold grace of God.

Acts 11:17chapter context similar meaning copy save

Forasmuch then as God gave them the like gift as he did unto us, who believed on the Lord Jesus Christ; what was I, that I could withstand God?

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Ruth 4:6chapter context similar meaning copy save

And the kinsman said, I cannot redeem it for myself, lest I mar mine own inheritance: redeem thou my right to thyself; for I cannot redeem it.

Ruth 4:4chapter context similar meaning copy save

And I thought to advertise thee, saying, Buy it before the inhabitants, and before the elders of my people. If thou wilt redeem it, redeem it: but if thou wilt not redeem it, then tell me, that I may know: for there is none to redeem it beside thee; and I am after thee. And he said, I will redeem it.

Exodus 13:13chapter context similar meaning copy save

And every firstling of an ass thou shalt redeem with a lamb; and if thou wilt not redeem it, then thou shalt break his neck: and all the firstborn of man among thy children shalt thou redeem.

Exodus 34:20chapter context similar meaning copy save

But the firstling of an ass thou shalt redeem with a lamb: and if thou redeem him not, then shalt thou break his neck. All the firstborn of thy sons thou shalt redeem. And none shall appear before me empty.

Leviticus 25:49chapter context similar meaning copy save

Either his uncle, or his uncle's son, may redeem him, or any that is nigh of kin unto him of his family may redeem him; or if he be able, he may redeem himself.

Leviticus 25:26chapter context similar meaning copy save

And if the man have none to redeem it, and himself be able to redeem it;

Leviticus 25:29chapter context similar meaning copy save

And if a man sell a dwelling house in a walled city, then he may redeem it within a whole year after it is sold; within a full year may he redeem it.

Leviticus 25:25chapter context similar meaning copy save

If thy brother be waxen poor, and hath sold away some of his possession, and if any of his kin come to redeem it, then shall he redeem that which his brother sold.

Numbers 18:15chapter context similar meaning copy save

Every thing that openeth the matrix in all flesh, which they bring unto the LORD, whether it be of men or beasts, shall be thine: nevertheless the firstborn of man shalt thou surely redeem, and the firstling of unclean beasts shalt thou redeem.

Psalms 25:22chapter context similar meaning copy save

Redeem Israel, O God, out of all his troubles.

Psalms 130:8chapter context similar meaning copy save

And he shall redeem Israel from all his iniquities.

Psalms 69:18chapter context similar meaning copy save

Draw nigh unto my soul, and redeem it: deliver me because of mine enemies.

Psalms 44:26chapter context similar meaning copy save

Arise for our help, and redeem us for thy mercies' sake.

Psalms 49:7chapter context similar meaning copy save

None of them can by any means redeem his brother, nor give to God a ransom for him:

Leviticus 27:31chapter context similar meaning copy save

And if a man will at all redeem ought of his tithes, he shall add thereto the fifth part thereof.

Psalms 49:15chapter context similar meaning copy save

But God will redeem my soul from the power of the grave: for he shall receive me. Selah.

Leviticus 27:13chapter context similar meaning copy save

But if he will at all redeem it, then he shall add a fifth part thereof unto thy estimation.

Psalms 26:11chapter context similar meaning copy save

But as for me, I will walk in mine integrity: redeem me, and be merciful unto me.

Galatians 4:5chapter context similar meaning copy save

To redeem them that were under the law, that we might receive the adoption of sons.

Leviticus 25:48chapter context similar meaning copy save

After that he is sold he may be redeemed again; one of his brethren may redeemhim:

Titus 2:14chapter context similar meaning copy save

Who gave himself for us, that he might redeem us from all iniquity, and purify unto himself a peculiar people, zealous of good works.

Job 5:20chapter context similar meaning copy save

In famine he shall redeem thee from death: and in war from the power of the sword.

Psalms 72:14chapter context similar meaning copy save

He shall redeem their soul from deceit and violence: and precious shall their blood be in his sight.

Leviticus 27:20chapter context similar meaning copy save

And if he will not redeem the field, or if he have sold the field to another man, it shall not be redeemed any more.

Numbers 18:16chapter context similar meaning copy save

And those that are to be redeemed from a month old shalt thou redeem, according to thine estimation, for the money of five shekels, after the shekel of the sanctuary, which is twenty gerahs.

Leviticus 25:32chapter context similar meaning copy save

Notwithstanding the cities of the Levites, and the houses of the cities of their possession, may the Levites redeem at any time.

Job 6:23chapter context similar meaning copy save

Or, Deliver me from the enemy's hand? or, Redeem me from the hand of the mighty?

Leviticus 27:19chapter context similar meaning copy save

And if he that sanctified the field will in any wise redeem it, then he shall add the fifth part of the money of thy estimation unto it, and it shall be assured to him.

Leviticus 27:15chapter context similar meaning copy save

And if he that sanctified it will redeem his house, then he shall add the fifth part of the money of thy estimation unto it, and it shall be his.

1 Chronicles 17:21chapter context similar meaning copy save

And what one nation in the earth is like thy people Israel, whom God went to redeem to be his own people, to make thee a name of greatness and terribleness, by driving out nations from before thy people, whom thou hast redeemed out of Egypt?

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    Michael Fowler, UVa

Newton's Life 

In 1642, the year Galileo died, Isaac Newton was born in Woolsthorpe, Lincolnshire, England on Christmas Day. His father had died three months earlier, and baby Isaac, very premature, was also not expected to survive. It was said he could be fitted into a quart pot. When Isaac was three, his mother married a wealthy elderly clergyman from the next village, and went to live there, leaving Isaac behind with his grandmother. The clergyman died, and Isaac's mother came back, after eight years, bringing with her three small children. Two years later, Newton went away to the Grammar School in Grantham, where he lodged with the local apothecary, and was fascinated by the chemicals. The plan was that at age seventeen he would come home and look after the farm. He turned out to be a total failure as a farmer. 

His mother's brother, a clergyman who had been an undergraduate at Cambridge, persuaded his mother that it would be better for Isaac to go to university, so in 1661 he went up to Trinity College, Cambridge. Isaac paid his way through college for the first three years by waiting tables and cleaning rooms for the fellows (faculty) and the wealthier students. In 1664, he was elected a scholar, guaranteeing four years of financial support. Unfortunately, at that time the plague was spreading across Europe, and reached Cambridge in the summer of 1665. The university closed, and Newton returned home, where he spent two years concentrating on problems in mathematics and physics. He wrote later that during this time he first understood the theory of gravitation, which we shall discuss below, and the theory of optics (he was the first to realize that white light is made up of the colors of the rainbow), and much mathematics, both integral and differential calculus and infinite series. However, he was always reluctant to publish anything, at least until it appeared someone else might get credit for what he had found earlier. 

On returning to Cambridge in 1667, he began to work on alchemy, but then in 1668 Nicolas Mercator published a book containing some methods for dealing with infinite series. Newton immediately wrote a treatise, De Analysi, expounding his own wider ranging results. His friend and mentor Isaac Barrow communicated these discoveries to a London mathematician, but only after some weeks would Newton allow his name to be given. This brought his work to the attention of the mathematics community for the first time. Shortly afterwards, Barrow resigned his Lucasian Professorship (which had been established only in 1663, with Barrow the first incumbent) at Cambridge so that Newton could have the Chair. 

Newton's first major public scientific achievement was the invention, design and construction of a reflecting telescope. He ground the mirror, built the tube, and even made his own tools for the job. This was a real advance in telescope technology, and ensured his election to membership in the Royal Society. The mirror gave a sharper image than was possible with a large lens because a lens focusses different colors at slightly different distances, an effect called chromatic aberration. This problem is minimized nowadays by using compound lenses, two lenses of different kinds of glass stuck together, that err in opposite directions, and thus tend to cancel each other's shortcomings, but mirrors are still used in large telescopes. 

Later in the 1670's, Newton became very interested in theology. He studied Hebrew scholarship and ancient and modern theologians at great length, and became convinced that Christianity had departed from the original teachings of Christ. He felt unable to accept the current beliefs of the Church of England, which was unfortunate because he was required as a Fellow of Trinity College to take holy orders. Happily, the Church of England was more flexible than Galileo had found the Catholic Church in these matters, and King Charles II issued a royal decree excusing Newton from the necessity of taking holy orders! Actually, to prevent this being a wide precedent, the decree specified that, in perpetuity, the Lucasian professor need not take holy orders. (The current Lucasian professor is Stephen Hawking.) 

In 1684, three members of the Royal Society, Sir Christopher Wren, Robert Hooke and Edmond Halley, argued as to whether the elliptical orbits of the planets could result from a gravitational force towards the sun proportional to the inverse square of the distance. Halley writes: 

Mr. Hook said he had had it, but that he would conceal it for some time so that others, triing and failing might know how to value it, when he should make it publick. 

Halley went up to Cambridge, and put the problem to Newton, who said he had solved it four years earlier, but couldn't find the proof among his papers. Three months later, he sent an improved version of the proof to Halley, and devoted himself full time to developing these ideas, culminating in the publication of the Principia in 1686. This was the book that really did change man's view of the universe, as we shall shortly discuss, and its importance was fully appreciated very quickly. Newton became a public figure. He left Cambridge for London, where he was appointed Master of the Mint, a role he pursued energetically, as always, including prosecuting counterfeiters. He was knighted by Queen Anne. He argued with Hooke about who deserved credit for discovering the connection between elliptical orbits and the inverse square law until Hooke died in 1703, and he argued with a German mathematician and philosopher, Leibniz, about which of them invented calculus. Newton died in 1727, and was buried with much pomp and circumstance in Westminster Abbey, despite his well-known reservations about the Anglican faith. 

An excellent, readable book is The Life of Isaac Newton, by Richard Westfall, Cambridge 1993, which I used in writing the above summary of Newton's life. 

A fascinating collection of articles, profusely illustrated, on Newton's life, work and impact on the general culture is Let Newton Be!, edited by John Fauvel and others, Oxford 1988, which I also consulted. 

Projectiles and Planets 

Let us now turn to the central topic of the Principia, the universality of the gravitational force. The legend is that Newton saw an apple fall in his garden in Lincolnshire, thought of it in terms of an attractive gravitational force towards the earth, and realized the same force might extend as far as the moon. He was familiar with Galileo's work on projectiles, and suggested that the moon's motion in orbit could be understood as a natural extension of that theory. To see what is meant by this, consider a gun shooting a projectile horizontally from a very high mountain, and imagine using more and more powder in successive shots to drive the projectile faster and faster. 

The parabolic paths would become flatter and flatter, and, if we imagine that the mountain is so high that air resistance can be ignored, and the gun is sufficiently powerful, eventually the point of landing is so far away that we must consider the curvature of the earth in finding where it lands. 

In fact, the real situation is more dramatic: the earth's curvature may mean the projectile never lands at all. This was envisioned by Newton in the Principia. The following diagram is from his later popularization, A Treatise of the System of the World, written in the 1680's: 

The mountaintop at V is supposed to be above the earth's atmosphere, and for a suitable initial speed, the projectile orbits the earth in a circular path. In fact, the earth's curvature is such that the surface falls away below a truly flat horizontal line by about five meters in 8,000 meters (five miles). Recall that five meters is just the vertical distance an initially horizontally moving projectile will fall in the first second of motion. But this implies that if the (horizontal) muzzle velocity were 8,000 meters per second, the downward fall of the cannonball would be just matched by the earth's surface falling away, and it would never hit the ground! This is just the motion, familiar to us now, of a satellite in a low orbit, which travels at about 8,000 meters (five miles) a second, or 18,000 miles per hour. (Actually, Newton drew this mountain impossibly high, no doubt for clarity of illustration. A satellite launched horizontally from the top would be far above the usual shuttle orbit, and go considerably more slowly than 18,000 miles per hour.)

For an animated version of Newton's cannon on a mountain, click here!

The Moon is Falling

Newton realized that the moon's circular path around the earth could be caused in this way by the same gravitational force that would hold such a cannonball in low orbit, in other words, the same force that causes bodies to fall. 

To think about this idea, let us consider the moon's motion, beginning at some particular instant, as deviating downwards -- falling -- from some initial horizontal line, just as for the cannonball shot horizontally from a high mountain. The first obvious question is: does the moon fall five meters below the horizontal line, that is, towards the earth, in the first second? This was not difficult for Newton to check, because the path of the moon was precisely known by this time. The moon's orbit is approximately a circle of radius about 384,000 kilometers (240,000 miles), which it goes around in a month (to be precise, in 27.3 days), so the distance covered in one second is, conveniently, very close to one kilometer. It is then a matter of geometry to figure out how far the curved path falls below a "horizontal" line in one second of flight, and the answer turns out to be not five meters, but only a little over one millimeter! (Actually around 1.37 millimeters.)

It's completely impossible to draw a diagram showing how far it falls in one second, but the geometry is the same if we look how far it falls in one day, so here it is: 

For one second, AB would be only one kilometer, so since AC is 384,000 km, the triangle ABC is really thin, but we can still use Pythagoras' theorem!

Thus the "natural acceleration" of the moon towards the earth, measured by how far it falls below straight line motion in one second, is less than that of an apple here on earth by the ratio of five meters to 1.37 millimeters, which works out to be about 3,600. 

What can be the significance of this much smaller rate of fall? Newton's answer was that the natural acceleration of the moon was much smaller than that of the cannonball because they were both caused by a force: a gravitational attraction towards the earth, and that the gravitational force became weaker on going away from the earth. 

In fact, the figures we have given about the moon's orbit enable us to compute how fast the gravitational attraction dies away with distance. The distance from the center of the earth to the earth's surface is about 6,350 kilometers (4,000 miles), so the moon is about 60 times further from the center of the earth than we and the cannonball are. 

From our discussion of how fast the moon falls below a straight line in one second in its orbit, we found that the gravitational acceleration for the moon is down by a factor of 3,600 from the cannonball's (or the apple's). 

Putting these two facts together, and noting that 3,600 = 60 x 60, led Newton to his famous inverse square law: the force of gravitational attraction between two bodies decreases with increasing distance between them as the inverse of the square of that distance, so if the distance is doubled, the force is down by a factor of four. 

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