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Why are their two high tides?

6 Answers
I know it is a common misconception that high tide is caused by the pull of the moon. Instead tides are caused by different accelerations of the earth toward the moon. If this is true then why do we get a high tide when the earth and moon are in opposition as well as inferior conjunction?
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The tide induced by the Moon is based on the difference in the distances of two antipodal points of the Earth from the Moon. Thus, the Moon simultaneously induces a high tide at both the point closest to the Moon and farthest from the Moon. Likewise, the tide induced by the Sun is also based the difference in the distances of two antipodal points of the Earth from the Sun. Thus, the tide induced by the Sun is maximal at the points of the Earth closest to and farthest from it. When the Sun and Moon are aligned in a full moon or a new moon, the tide induced by the Sun is maximized at the same antipodal points where the Moon induces a high tide, thereby increasing the magnitude of the high tide at each antipodal point.

Keep in mind that the distance between two points is the absolute value of the difference in their coordinates. Thus, if points P and Q are antipodal points of the Earth, the difference in the distances of P and Q from the Moon is maximized twice during each orbit of the Moon around the Earth - once when the distance from P to the Moon is minimized and the distance from Q to the Moon is maximized and once when the distance from P to the Moon is maximized and the distance from Q to the Moon is minimized. When that difference is maximized, high tides occur at both points P and Q. Thus, points P and Q experience high tides twice during each lunar orbit of the Earth (which takes about 24 h 50 min). It also means that a high tide occurs at point P (respectively, Q) when the Moon is nearest to P (respectively, Q) and when it is farthest from P (respectively, Q). The same principle applies to the tides induced by the Sun. Therefore, the Sun has the same effect on the tides during a full moon as it does during a new moon.

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F

Gravity varies inversely with the square of the distance between two objects. Thus, the Moon exerts a greater force on the side of the Earth that is closer to it than the side that is opposite from it. Ocean tides are caused by the difference in the gravitational pull of the Moon on opposite sides of the Earth.

Suppose you are in a fixed location and that a woman is located on the opposite side of the Earth from you. As the Moon rotates around the Earth, the difference in the distances between you and the woman on the opposite side of the Earth varies sinusoidally. When you are farthest from the Moon, she is closest to the Moon. As the Moon rotates, you move closer to the Moon, and she moves away from it. After a 90 degree rotation, the difference in your distances from the Moon diminishes to zero, inducing a low tide at both your location and hers. As the Moon continues to rotate, your distance from the Moon continues to decrease while her distance from the Moon continues to increase. After another 90 degree rotation, you are now at the point of the Moon's rotation when you are closest to the Moon and she is farthest from it, inducing a high tide at both her location and yours. As the Moon continues to rotate around the Earth, your distance from the Moon increases while hers decreases until after a third 90 degree rotation the difference in your distances from the Moon again diminishes to zero, inducing low tides at both your locations. Finally, the Moon completes its orbit around the Earth so that you are farthest from it and she is closest to it, which induces high tides at both your locations.

Since the Moon rotates around the Earth in approximately 24 hours and 50 minutes, you experience high tides 12 hours and 25 minutes apart. Consequently, you experience high tides nearly twice a day.

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Thank you for the clarification.

The Sun does have an influence on tides. However, the difference in distances of the near and far sides of the Earth from the Sun is small compared to the distance of the Earth from the Sun, so the magnitude of the ocean tides induced by the Sun is smaller than that induced by the Moon. When the Earth, Moon, and Sun are aligned (during a full moon, when the Earth is between the Sun and the Moon, or a new moon, when the Moon is between the Earth and the Sun), the tides due to the Sun and Moon coincide, increasing the magnitude of both high and low tides (a phenomenon known as a spring tide). The highest spring tide occurs when the Sun and Moon are closest to the Earth. At times other than a full moon or a new moon, the tides produced by the Sun partially cancel those caused by the Moon. The cancellation is greatest when the Moon is halfway between a full moon and a new moon, producing both high and low tides of smaller magnitude (a phenomenon known as a neap tide). The greatest cancellation occurs during a neap tide when the Sun is closest to the Earth and the Moon is farthest from the Earth.

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Thanks again Forbie89 I appreciate your dedication to help me understand this principal. I hate to be a pesky student but I have one last question. I am looking in a mechanics book that explains the tides and the have a picture of the Earth with arrows at different locations representing the acceleration at that point relative to the acceleration at the center of the Earth. The point closest to the moon has an arrow pointing towards the moon. The point farthest from the moon has an arrow pointing away from earth, and the poles have arrows pointing in towards the center of earth. It seems to me though that the acceleration of the center of the Earth has a greater magnitude during a new moon than during a full moon. During the new moon the forces of the moon and sum combine to create a larger acceleration. If the tides are due to accelerations relative to the acceleration of the center of the Earth, then why are the tides the same when the acceleration of the center of the Earth is different?

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Alright, so if tides are caused by a gravitational acceleration due to the moon and sun, then why would the tide during a full moon be as large as a tide during a new moon. When there is a new moon the gravitational acceleration of points on earth should be directed toward the moon and sun in a constructive interference. However during a full moon wouldn't the gravitational acceleration caused by the sun and the moon be destructive? I am really having trouble wrapping my head around this.

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Thank you for replying Forbie89

I already understand how the moon alone generates the tides. The problem I am struggling with happens when you factor in the sun. Namely, why is there a high tide when the moon is between the Earth and the sun, and why is there also a high tide when the Earth is between the moon and the sun?

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