The Twelve Dancing Princesse Synposis of the story:
The twelve princesses wear out their shoes every night. No one knows what they do or where they go. Their father, the king, has taken to locking them into their dormitory every night. Yet their shoes continue to get worn out.
Finally he offers a reward to whoever can find out what they are doing. The person who finds out will marry a princess and be heir to the throne. If they don’t find out, they will pay a heavy forfeit and get thrown out or lose their head!
This original story was written by the brothers Grimm and I did not like it at all.
So I’ve changed it to an Indian fairy tale setting, and the princesses will dance to their hearts’ content. The story will wrap round a children’s Kathak dance manual, with poses, hand gestures, boles, and some tricky maths.
Furthermore – Madon, the invisible god of love, shoots the Gandharva musician Surasen and the Apsara dancer Melusee, startling them, so that the music stops, the Apsara Ur-Vashi stops dancing, and Indra, king of the gods, curses, and banishes Surasen. Melusee begs to go with him. Ur-Vashi, and many others intervene, Indra changes eternal banishment to hell to doing a good deed on earth. While they stay in hell as Jom’s guests, Surasen and Melusee brings music and dance to earth via the 12 princesses.
Finally – the princess is won, not by an adventurous prince, but by a humble cowherd boy, who is kind and intelligent.
The 12 Dancing Princesses The Story
Indra was the king of the gods, and he lived in SWARG, one of the three worlds.
All the gods lived in Swarg, except for Jom …
Jom was the lord of the underworld, which was called NARAK.
There was another god, an invisible one, called Madon. He lived in Swarg of course.
In between SWARG and NARAK was PRITHVI. That was were humans lived. Animals and fish and birds and insects also lived there.
Some of the people of Swarg were the cloud people, the Kinnaras and the Kinnaris. They liked to live in the High Hills where the clouds rested on the hill tops. They were sweet-natured and loved to sing and dance and play music.
On Prithvi, there was a King.
When he was not busy being a king he loved to look at the moon and the stars and the sky and the clouds. He built a tower so he could be nearer the sky. One day, he was up on the tower when a cloud of Kinnaris floated by.
In that cloud, there was a Kinnari maiden, Menora. She looked down and saw him gazing up. He stretched out his hand to her. She stretched out her hand and floated down to him.
“Will you stay?” asked the king.
“For a little while.” said the Kinnari.
“How long will you stay?” asked the king.
“How long?” Menora asked the other Kinnaris.
“You can stay for thirteen years.” they said.
“Then we will come back for you.”
They laughed and waved and floated away.
Thirteen years went by all too quickly. The king was happy. Menora was happy. They had twelve little girls and the king forgot that the Kinnaris would come back for Menora.
The little girls were graceful and quick as little birds. They were playful and mischievous as children are. They sang as sweetly as birds and danced like leaves floating on the wind.
One lovely day, soon after the thirteenth year had passed, and a soft breeze was blowing and the skies grew thick with puffy white clouds. The clouds floated low and seemed to be singing. Then you could see that there were Kinnaris floating on the clouds. They sang out “Come away, sister. Time to fly away with us.”
Menora heard them. She jumped with joy and ran out to meet them. She had been happy all the thirteen years on Prithvi. She loved the king and she loved her children, yet the thought of going home with her sisters filled her with so much joy.
She said “Good bye, my darlings, I will love you forever! Be well, be happy, and I must go.”
The clouds formed a staircase down to earth, and she ran up it to join the Kinnaris, laughing happily. She looked down and waved. Then the clouds rose high and they vanished.
“No!” cried the king and ran up his tower, but the Kinnaris had gone. He watched the clouds but he never saw them again.
Of course, he could not watch the clouds forever. He had a country to look after. So he hired people to watch the clouds all the time and they wrote down when they saw clouds, and what shapes they were.
The king grew very famous for being a cloud watcher. Learned men from near and far came to visit and see what had been learnt about clouds.
Indra, king of the gods, was pleased with the king. Clouds were Indra’s domain.
He could make them thunder. He could shoot lightning bolts. He could make rain. He rode on the white elephant Aerobot who could trumpet like the thunderclouds.
“I have a devotee!” thought Indra and he was very pleased. Indra was often jealous of the other gods who had so many devotees praying to them There was Shiva, who was so often lost in meditation that he did not notice that anyone was praying to him. There was Ganesha whom people loved and prayed to. Indra thought Ganesha liked dancing and eating sweets way too much to be a truly dignified god.
So Indra was good to the king. He rained regularly on the kingdom. The crops grew well and the people became prosperous.
In Swarg, the handsome Gandharva Surasen was playing the drums. Ur-Vashi, the chief of the Apsaras was dancing. Melusee, another Apsara, was arranging flowers.
Indra was listening absent-mindedly. He had been given a gift, a golden hammer, by Vishamitra, who made wonderful things. Indra was tossing the hammer up and catching it and admiring the way it felt in his hand.
Madon, the invisible god of love, was walking by.
“I have too many arrows,” he thought. “Time I did some work.”
So he fitted a flower tipped arrow and looked about him. Hmm, Surasen and Melusee would make a nice couple! Madon shot them.
“Aaah!” gasped Surasen and stopped drumming.
“Aaah!” gasped Melusee and dropped the flowers.
They gazed at each other.
Ur-Vashi stopped dancing. Her ankle bells stopped tinkling.
Indra startled at the sudden silence and dropped the hammer on his toe.
“Aaarghh!” he roared. “What is the meaning of this?!”
He glared at Surasen. That Gandharva was way too good-looking. All the Apsaras liked him.
Indra said “You! You can go to Hell!”
Suddenly Swarg felt very chilly. Jom had come.
“COME WITH ME” he said to Surasen. Surasen caught the silver noose the Jom threw to him and began walking away.
“No!” cried Melusee and threw herself at Indra’s feet. “Please send me to Hell too!”
All the Apsaras and minor goddesses were pleading with Indra.
Ur-vashi said “Please don’t punish him with his life. It was such a tiny stop in the music.”
“WELL?” he asked Indra.
“Oh, all right!” he said “They can go together.”
The Apsaras sobbed louder than ever.
“Well, maybe they can come back. After they’ve done something good.” said Indra.
The Apsaras stopped weeping and threw flowers at Indra.
He liked that.
Ur-Vashi said quickly. “They can be Jom’s guests and teach music and dance to the earth people.”
“If Lord Jom allows it.” She said, turning to Jom.
“VERY WELL” said Jom.
Melusee took the noose too and walked with Surasen after Jom.
“We will come with you as far as Prithvi” said Ur-Vashi. “Then you can go on to Narak.”
Ur-Vashi and all the Apsaras and goddesses started after Jom.
“I will come too,” said Indra. “We will stop at my devotee’s kingdom.”
Sam lived in Prithvi. He lived in a little village with his grandmother. They had a little cottage and a cow, Daisy.
Beral Ginny was a marmalade cat who had come to live with them in return for regular meals and conversation.
Every morning, Sam would take Daisy round to their neighbor, Aunt Min.
Then Sam would take Daisy, and Aunt Min’s cow, Dainty, to the meadow where all the cows from the village grazed.
Sam and all the other little cowboys played and sang and sat under the shady trees. Sam would play on his flute.
Sam was very good at carving, and he made lovely flutes that he gave to his friends. Every evening, Sam took Dainty and Daisy back home. The milkmaids would milk all the cows, and Aunt Min and Sam would get a nice share of milk. Beral Ginny got a share too.
Grandma made yogurt and cheese and delicious sweets from the milk. On market days, Sam would take them to the market to sell.
One market day, Sam heard the villagers saying that the king was offering a big reward to solve a puzzle.
“What’s the reward? And what’s the puzzle?” asked Sam.
“You get to marry a princess, and after the king retires, you get to look after the kingdom!” they said.
No one was sure what the puzzle was.
Sam was not sure that he wanted to marry a princess. He was pretty sure a princess did not know how to make yogurt or cheese or milk sweets. Looking after a kingdom sounded like a lot of work too. Still, Sam liked puzzles, and maybe the king would give him another present that he could bring home to Grandma.
Sam told Grandma about the king’s reward.
“You should go for it,” said Grandma. “You are a very clever boy, Sam. If anyone can solve a puzzle, it’s you.”
“Besides,” she added, “I am getting old. I want to sleep and sleep and sleep. One day I won’t wake up. On that day, take Daisy to Aunt Min. Aunt Min will be glad to have her. Then go and get the reward, Sam! Tell me you will.”
Not long after, Grandma slept and slept, and in the morning, she did not wake up.
Sam sat and held her hand until it was cold. He cried a bit, even though he was a big lad. When Daisy began mooing loudly, Sam knew he had to go. He took Daisy to Aunt Min’s and told her about Grandma.
Aunt Min said, ”Take Daisy and Dainty to the meadow, my dear boy. They need to graze. I will take care of Grandma.”
Sam played songs on his flute all day. He told the other cowboys stories about Grandma. He said, “I will go and solve the kings puzzle for him. I promised Grandma.”
That evening, Sam said good-bye to all the cows. He went home with Daisy and Dainty.
Aunt Min had dressed Grandma in her best clothes. The cowgirls came and danced a farewell dance for her.
Sam played his flute. They put flowers on her and the village elders came and took her away.
Next morning, Sam packed a change of clothes and his cap and his best flutes.
Aunt Min, fed him and packed him a nice lunch. She packed a nice lunch for Beral Ginny too, because Beral Ginny said she was going with Sam.
“Be careful, and come home safe” said Aunt Min.
“We will” said Sam.
“Meow” said Beral Ginny.
Sam and Beral Ginny walked and walked and walked.
They stopped near a pond to rest and eat. Sam took his shoes off and cooled his feet in the water. Beral Ginny stretched out on a tree branch to nap. The sound of hooves woke Beral Ginny up. She jumped down and called out to the rider.
The rider was very richly dressed. He wore a shiny yellow jacket, shiny red boots and fine black pantaloons. He did not look pleased to be stopped. His horse looked even grumpier. When the horse saw the pond, he went straight over for a drink and the rider got off in a hurry.
“Hah!” said Beral Ginny “Who are you? Where are you going?”
The rider pulled a face. “I’m a prince of course. “ He said. “ I’m going home. I came on a quest. The king offered a princess and a country for a task.”
“What task?” asked Beral Ginny.
“To find out where the princesses go every night!” said the prince.
“That does not sound much of a task!” said Beral Ginny. “So where do they go?”
“They don’t go anywhere! I kept guard outside their door and no one came out!”
“Did you sleep?” asked Beral Ginny.
“I put my bed right across their door! If anyone came out, they would have to jump over me! I think the king is crazy. The girls talk nonsense to each other! I heard them!
Then I told the king they didn’t go anywhere and he didn’t believe me! I had to leave really fast. Otherwise I would have to pay the forfeit or lose my head!”
“So you are sneaking away.” Said Beral Ginny.
“Of course I am.” Snapped the prince.
Beral Ginny casually hopped up to the tree branch and hopped down again.
“I suppose that’s why they are coming after you.” She said.
“What!” cried the prince, jumping up.
“Quick. Change clothes with Sam! Then they won’t know you. You didn’t pay the forfeit, right? Give me a sovereign, and I’ll send them away from you.”
The prince and Sam swapped clothes. Beral Ginny took a sovereign She whacked the horse and they took off at top speed.
After a while, Sam said, “Where are the king’s men?”
“What king’s men?” asked Beral Ginny.
She closed her eyes and stretched out.
Sam said, “There were no king’s men, were there?”
Beral Ginny seemed to sleep.
“Oh, you are a sneaky, clever thing!” said Sam laughing.
Sam followed Beral Ginny down to the river. They walked along side it until they came to group of fishermen mending their nets. There were also some boatmen,
cleaning the bottom of their boat.
“Good Afternoon” said Beral Ginny politely. “Perhaps you would like some help with the nets?”
The fishermen laughed. “You, cat? Or do you mean him?”
“I mean us” said Beral Ginny haughtily.
“She means me” said Sam. “I can mend nets and I’m happy to help.”
He sat down beside the fishermen.
“Sure” said the fishermen.
So Sam mended nets and sang river songs.
The fishermen liked the songs and the boatmen did too.
The work went fast.
Soon they were done, and Sam got a fish, and so did Beral Ginny.
“Thank you” said Beral Ginny politely. “We are going on a quest. We hear that the king is offering a reward for a task.”
“If you come here tomorrow, you can ride with us to the castle” said the boatmen
“And you can sing for us while we row.”
Sam and Beral Ginny had a nice dinner of roast fish.
Next morning, they were riding with the boat men to the castle. Sam sang his songs.
Sam at the castle
“Here we are!” said the boatmen, pulling to a stop. “Good luck with the task.
We think you’d make a fine king!”
Sam thanked the boatmen.
“My cousin, Laura, is cook there, at the castle. Say hello to her from me, and she will feed you very well!” said one of the boatmen.
“Change into your princely clothes now.” Said Beral Ginny. So Sam did, and they walked up to the castle.
Beral Ginny announced “This is Prince Sam, come to win the quest!”
The king was tired of the princes who came and ate and slept and failed. The king’s minister collected the forfeits and did not mind so much.
The minister explained to task to Beral Ginny and Sam.
“You have to find out what they are up to every night. Otherwise it’s off with your head or a hundred sovereigns forfeit.”
Sam and Beral Ginny were introduced to the princesses.
The twelve princesses looked at them, and smiled at each other.
“Good-bye in advance,” they said.
They went back to doing their princess things and ignoring Sam and Beral Ginny.
So Sam sat down and began playing his flute. The princesses listened.
Beral Ginny strolled over to the littlest princess, and did a good imitation of a sweet little kitty.
“Aw,” said the littlest princess. “ What a sweet little kitty you are!”
Beral Ginny purred and sat down by the littlest princess.
That evening, the eldest princess brought Sam a lovely drink in a beautiful glass.
Sam thanked her and took the drink.
Beral Ginny whispered “Don’t drink it” in Sam’s ear.
She quickly followed the eldest princess back into their room, and hid under the littlest princess’s bed.
The eldest princess locked the door.
When the stars appeared in the sky, the princesses put on their dancing shoes.
A door appeared in one of the walls, and the princesses went through it. As soon as the littlest and last princess walked through, Beral Ginny raced to the main door and unlocked it.
“Quick!” she hissed to Sam “You have to follow them.”
She closed the door again.
Sam followed the twelve princesses. He was amazed. They were walking down a garden path to a stream. A boat was waiting, and the princesses got in.
Beral Ginny jumped in and sat on the littlest princess’ lap. The little princess was surprised but did not mind. She was happy to hold Beral Ginny.
Sam got in quietly behind them all. He sat low in the boat and no one saw him.
“The boat feels heavy tonight.” Said the eldest princess.
The littlest princess giggled to herself. “It’s because you’re in the boat!” she told Beral Ginny.
The boat glided to a stop, and the princesses got off and went into a pavilion of trees.
Beautiful music was playing and a graceful lady was dancing.
The princesses bowed and moved into their places. They danced.
The graceful lady taught them new steps. She taught them words to go with the steps.
The musician was Surasen and the dancer was Melusree. They were teaching the princesses to dance.
Sam and Beral Ginny sat in the shadows and watched. They were careful not to make a sound.
Sam loved the music. He listened to the words and made sure he would remember them.
The lesson was over and the princesses got back into the boat.
Beral Ginny got in and nudged the littlest princess with her head.
“There you are, little kitty!” said the little princess. “it’s time to go home now.”
Same got it behind them and crouched down like before.
The door in the wall was still open, and the princesses went in, one by one.
The door closed after Sam.
Sam went on all fours to the main door, covered in his shawl, like a grey ghost, and slipped out. He lay down, closed his eyes like he was sleeping.
Inside, Beral Ginny was making a fuss about welcoming the princesses back. She purred and weaved between their feet and greeted everyone.
“Oh, you are glad to see us again, kitty!” said the princesses.
The littlest princess giggled, and Beral Ginny winked at her.
No one noticed Sam.
The eldest princess peeped out the door. Sam was snoring gently.
“That’s another one that’s going to leave soon!” she told her sisters.
In the morning, Beral Ginny jumped up and pushed the door open. Sam was still asleep so Beral Ginny woke him up.
“Let’s go to the kitchen and get our breakfast,” she said. “We can find Laura, the boatman’s cousin. Remember, he said she was the cook here.”
Sam agreed sleepily. He followed Beral Ginny and Beral Ginny followed her nose, and soon they were seated in the kitchen and Laura was giving them a delicious breakfast.
After Beral Ginny had eaten her fried fish, and washed her paws, she showed Sam and Laura the dancing slipper she had brought with her.
It was the little princess’s and quite tattered.
“Where can we get this mended and fast? “ she asked.
“I’ll ask my sister,” said Laura. “She’s one of the seamstresses.”
“We need twelve pairs and fast, before the minister comes to check.”
Laura’s eyes grew round.
“Twelve? For the princesses I suppose?”
“Yes,” said Beral Ginny “and it must be secret. There will be a reward after Sam is named the king’s heir.”
Sara, Laura’s sister, and the other seamstresses worked fast. Soon twelve pairs of slippers were ready.
“We will need twelve new pairs every day for seven more days,” said Beral Ginny.
Sam carried the new shoes back and placed them by the door. Beral Ginny nudged the little princess awake.
“Help me hide the old slippers,” said Beral Ginny. The little princess and Beral Ginny took the old torn slippers and hid them in a chest.
When the minister came to check on Sam, he was surprised to see twelve perfect pairs of slippers lined up by the door.
“Hmm,” he said suspiciously “It looks like no one went out! Odd.”
“Remember,” he said to Sam. ”You still have six days to go.”
Sam remembered the music. He began to play all that he’d heard on his flute.
“Oh, I know that one,” cried the little princess. She began to dance. Beral Ginny joined her. Soon all the princesses joined in. They had so much fun.
That evening, the princesses whispered together. The eldest princess said to Sam, “Sam, you will come with us. You will have to be very quiet and not be seen.”
“I will come too,” said Beral Ginny.
“I want her to come!” said the little princess.
The princesses whispered together again.
“All right, you will come too,” said the eldest princess. “You have to be very quiet and not be seen.”
So Sam sat in the back of the boat and Beral Ginny sat on little princess’s lap and they went to the magic pavilion.
The same musician was playing, and the same Apsara was teaching the princesses to dance.
The Apsara said, “You have learnt well. In three days, you will have a test. If you pass, you will be allowed to dance on your own. The Apsaras and the Kinnaris will come too, and they will dance. After that you will show them how well you dance.”
When they had returned to the palace, Sam said “That sounds wonderful.”
The eldest princess was looking unhappy.
“No, it is not. The Apsaras and the Kinnaris are so graceful and dance so well, we will look terrible next to them!”
“They are immortals,” said Sam “and you are human. So maybe it will not be the same. But maybe you can do something different. You can tell a story. Everyone likes stories.”
“Hmm,” said the eldest princess. “We could do that.”
The next day, Beral Ginny went to the kitchen and Laura fed them a hearty meal. Then Beral Ginny went to visit Sara the seamstress and collected twelve pairs of dancing shoes.
The minister came to see Sam again and was as suspicious as ever.
“Hmm,” he kept saying. “Strange. Very strange.”
The rest of the day was very busy. The princesses thought and talked and thought.
At last the eldest princess said, “I would like tell a story about a Kinnari who came to earth to visit a king and how happy everyone was while she visited.”
The littlest princess said, “I would like to tell a story about a Gandharva and an apsari who played beautiful music and danced so well and came to teach us.”
All the princesses said “We want a happy ending where we dance so well that the Kinnaris keep coming to visit us again and again and again.”
“We can do that.” said Sam.
“Yes, we can,” said the princesses.
“We can add puzzles that we set the princes to solve when we wanted them to lose and go away!” said the middlest princess.
Everyone bounced up and Sam played his flute, and Beral Ginny banged the floor to keep time. She also ran to the kitchen and asked Laura to send them delicious snacks and meals.
She invited Sara and the seamstresses to visit and watch the princesses do a show.
Everyone liked the story. Laura had cried. “It’s sad and happy, just like a good story should be.” she said.
That evening, the princesses asked Sam and Beral Ginny to come with them.
“Because you help us a lot,” they said. “But stay in the back and act like shadows.”
Beral Ginny said, “We can do that.”
Sam had his dark shawl to cover under.
The princesses danced and Melusee said, “That is a lovely story. Tomorrow the Apsaras and the Kinnaris will come, they will like your story.”
The next day, Beral Ginny said, “Where is the king? We see the minister a lot. We never see the king.”
“He is always watching the clouds in the tower, when he is not in the court.”
Just before the princesses were ready to leave, Beral Ginny said, “I will fetch the king, and let him see them dance. Go with them now and bring the boat back for us.”
Off she went, up the tower, and bowed to the king.
The king was surprised. “Who are you? “ he asked.
“I am Beral Ginny, and we have met, even if you don’t remember. Now come with me and don’t say a word, unless you want to lose the princesses.”
The king did not say a word and he followed Beral Ginny. Sam had come back with the boat and Beral Ginny and the king stepped in.
Beral Ginny said, “This is Prince Sam, whom you’ve met already. Remember, don’t say a word, and act like a shadow.”
The king, Sam and Beral Ginny sat like shadows.
Surasen played and the Apsaras danced. Their dance was more beautiful than anything in the world.
Next the Kinnaris danced, their dance was so happy and lovely you could forget everything and just watch them.
The king saw the Kinnaris and was about to jump up and go to them. Beral Ginny smacked him. “Quiet!” she hissed.
Then came the princesses and danced their story. It was very, very good.
“Oh,” said Kinnaris “We know that story and we will come and visit you often!”
At this, the king shook Beral Ginny off and ran to them.
“Menora,” he shouted “Menora!”
“Wait!” said Melusee. “If you go to them, you will have to leave the earth and the princesses behind.”
There was a crash of thunder and lightning flashed all around them. Heavy rain fell in torrents. Indra had come.
Aerobot trumpeted like a thundercloud and Indra got down.
“He cannot leave. He is my best devotee.” said Indra.
“YOUR ONLY DEVOTEE” said Jom. “NO, IT IS NOT HIS TIME TO LEAVE YET.”
Indra turned to the Kinnaris. “You can visit him as often as you like,” he said
“I give you my permission.”
The Kinnaris looked at each other. “We do not need his permission,” they whispered to each other.
The Kinnaris were polite and did not like being rude, especially to Indra.
So they smiled and bowed and said “Thank you.”
Indra said “Come with me, devotee! I will take you to your tower.”
So Indra, the king and Menora, flew on Aerobot to the tower. All the Kinnaris had drifted on the clouds with them. Surasen and Melusee returned to Swarg with the Apsaras. Jom watched them all leave.
Menora did not stay but she promised to visit often.
The next day, there was a huge feast in the palace and outside. Sam claimed his prize. He chose the eldest princess.
“With your permission,” he said to the eldest princess.
“Of course.” said the eldest princess.
The fishermen came, the boatmen came. Even the minister came. Sam gave a reward to the seamstresses and the kitchen.
Sam and the eldest princess ruled the country very well. The king was happy to spend all his time watching clouds.
All the princesses continued to dance and they built temples for dancing and even houses where dancers could live, and you can see them to this day.
Earlier this week, June 25, a sailor got his sailboat stuck under the Roosevelt Island bridge! His mast was stuck in the girders. The coast guard had to be called out, and the firemen. Bridge traffic had to be stopped so the bridge could be opened up, and the mast freed, then the coast guard tugged him away. I also heard that the coast guard had considered just leaving him there for a few hours until low tide ( and laughed about it)! Really, what kind of sailor does not check the tides when out on water.
It got me thinking about tides, so here’s an essay on it.
Tides are what we call the rise and fall in the levels of water in the ocean and coastal rivers twice a day.
Tides also occur in large lakes and the atmosphere, but in such a tiny amount that it’s almost unmeasurable.
Why are there tides?
Mainly because of the gravitational attraction of the moon and earth and the sun.
The bigger gravitational pull is between the earth and the moon, because we are close to each other. Luckily, we do not fall into each other because the equal and opposite centrifugal force produced by their individual revolutions around the center-of-mass of the earth-moon system, keeps us apart.
The water on the hemisphere of the earth turned toward the moon, is pulled toward the moon because of gravity. At the same time, the water on the opposite side (furthest from the moon) is pulled away from the moon, in the direction of the greater centrifugal force. So we get two simultaneous high tides.
Low tides are created by water sinking in regions around the earth midway between these two high tides. The alternation of high and low tides is caused by the daily rotation of the earth.
The Monthly Revolution of the Earth and Moon around the Barycenter of the Earth-Moon System
This revolution is responsible for a centrifugal force component (Fc) necessary to the production of the tides.
(Note that the earth revolves around G, but does not rotate around G. There is no monthly rotation of the earth as it revolves around the barycenter such that the same point on the earth’s surface always faces the moon.)
Not to forget the sun …
The earth and the moon are both rotating round the sun. The same forces of gravitational attraction and centrifugal force exist here.
The force of gravitation exerted by the moon (and sun) upon the earth and the centrifugal forces produced by the revolutions of the earth and moon (and earth and sun) around their common center-of-gravity (mass) are usually in balance. However, when they are not in equilibrium at some local points, we get tides.
The Effect of the Centrifugal Force. As the earth and moon whirl around the earth-moon center-of-mass, the centrifugal force produced is always directed away from the center of revolution. Since the center-of-mass of the earth is always on the opposite side of this common center of revolution from the position of the moon, the centrifugal force produced at any point in or on the earth will always be directed away from the moon.
The Effect of Gravitational Force. While the effect of this centrifugal force is the same all over the earth, the gravitational force produced by another astronomical body may be different at different positions on the earth because the magnitude of the gravitational force exerted varies with the distance of the attracting body.
Spring tides and Neap tides.
Spring and Neap tides happen due to the combined effect of gravity of the sun and moon on the earth.
When the sun is lined up with the moon, their combined pull is harder on the earth’s oceans. This is called a Spring tide, and happens at New Moon and Full Moon.
When the sun is at right angles to the moon, the combined gravitational effect is less, as they cancel each other out. This is called a Neap tide, and happens at the two quarters.
The Phase Inequality: Spring and Neap Tides
The gravitational attractions (and resultant tidal force envelopes) produced by the Moon and Sun reinforce each other at times of new and full moon to increase the range of the tides, and counteract each other at the first and third quarters to reduce the tidal range.
Diagrams courtesy of NOAA.gov
Variations in the tide times
The earth rotates on its axis in 24 hours. The moon revolves in its orbit around the earth with an angular velocity of approximately 12.2 degrees per day, in the same direction in which the earth is rotating on its axis with an angular velocity of 360 degrees per day. So, the rotating earth must complete a rotation of 360 deg. plus 12.2 deg. or 372.2deg., in order to “catch up” with the moon. Since 15deg. is equal to one hour of time, require a period of time equal to 12.2/15 x 60 min/hr., or 48.8 minutes – if the moon revolved in a circular orbit, and its speed of revolution did not vary. On the average it requires about 50 minutes longer each day. As a result, the recurrence of a tide of the same phase and similar rise would take place at an interval of 24 hours 50 minutes after the preceding occurrence.
Then there’s the friction between the sea waters and the sea floors which also change the tide flows.
Tides changes gradually. The waters do not suddenly pop up and down. Various Atmospheric and Climate offices maintain tide tables to ease navigation. Tides are levels are announced in the weather sections of most newspapers or weather sites.
Distances and masses:
Earth to Sun: 1 AU. ( 92,955,807 miles)
Earth to Moon: 238,900 mi
Mass of Earth: 5.972 × 10^24 kg
Mass of Moon: 7.34767309 × 1022 kg
Mass of Sun: 1.989 × 10^30 kg
Ptolemy of Egypt:
Wrote about tides in the Tetrabiblos.
In 1609 Johannes Kepler correctly suggested that the gravitation of the Moon causes the tides, basing his argument upon ancient observations and correlations. The influence of the Moon on tides was mentioned in Ptolemy’s Tetrabiblos as having derived from ancient observation.
In 1616, Galileo Galilei wrote Discourse on the Tides. He tried to explain the tides as the result of the Earth’s rotation and revolution around the Sun, believing that the oceans moved like water in a large basin: as the basin moves, so does the water. Galileo rejected Kepler’s explanation of the tides.
F = G m1m2/r*2
where F is the gravitational force acting between two objects, m1 and m2 are the masses of the objects, r is the distance between the two.
Pierre Simon Laplace:
In 1776, Laplace formulated a single set of PDEs for tidal flow. Laplace obtained these equations by simplifying the equations of fluid motion.
(1773 – 1829). He ran the Nautical Almanack, and developed a theory of tides using harmonic analysis. (Yes, he also did the diffraction slit experiment for the wave theory of light, and deciphered the Rosetta stone! among other things)