# Moon and tides (tide on the moon instead of earth)

#### andytran

Hi

There is a queston in my physics book that kept me thinking but still can't find a solution...

here is the question: The Moon is observed to keep the same side facing the Earth at all times. If the Moon had oceans, how much time would elapse between it's high tides?

since we know that tides on earth is caused by the moon gravitional pull. this creates two bulge on the earth, one facing the moon and the other is on the other side of the earth.. these bulges are the causes of high tides on earth.. we kno the period elapse between each high tides is due to the rotation of the earth and the orbiting moon.. since the earth rotates once every 24h, it's correct to say that the period for each high tides is 12h. however, the moon orbiting the earth (or more correctly the center point of gravity) caused the bulges to rotate as well but much smaller than the earth rotation... every 12 the moon orbit 6 degree around the earth, therefore the bulges also rotation 6 degree or about 25 minutes... so we concluded that the period of high tides on earth is 12 hours and 25 minutes...

Now as for tides on the moon,the two bulges created by the earth gravitional pull, one facing the earth the other is on the far side of the moon. since the same ocean is facing the earth, it is safe to say that the period doesn't exist, the high tides always stay in the same place. but would the earth's orbit around the center point of gravity betweeen the earth and the moon effect the moon tides? i kno the center point is located inside the earth, but if the moon orbits around this center point of gravity has an effect on earth high tides period then the earth should do the same too rite? even tho is significantly smaller......

i'm kinda confused so please help...(sorry for the slopppy writing

thx

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#### russ_watters

Mentor
It could be a trick question: the Sun also causes tides. So, 14.5 days.

#### andytran

14.5 days due to the earth's orbiting the center of gravity and the sun? and how do you get 14.5 days?
thx

#### Janus

Staff Emeritus
Gold Member
Originally posted by andytran
14.5 days due to the earth's orbiting the center of gravity and the sun? and how do you get 14.5 days?
thx
14.5 days is 1/2 the synodic month. ( it is actually closer to 14.76 days.) this is the time it takes for the Moon to go from full moon to new moon. (or from the from a view point on the moon, 1/2 the time it takes for the sun to travel from zenith to zenith.

But even if we to ignore the Sun's effect, there would still be a variation of tide height on the the moon, due to the fact that the moon travels in an eliptical rather than circular orbit. This causes two effects.

The first is simply due to the fact that this causes the moon to vary in distance from the Earth, thus varying the strength of the tidal force exerted on the moon. This will cause the tidal bulges to "throb" in and out a little.

The second is due to Librations. This casues the moon to not present the exact same face to the Earth at all times.

As the moon orbits the Earth in its eliptical orbit, it has to speed up and slow down at perigee and apogee. The moon's rotation rate however remains constant. Thus over the course of a revolution, the Moon's rotation alternately speed's ahead and lags behind of its revolution. From the point of view of the Earth, it is like the moon is swinging slightly back and forth aorund its axis. Thus the tidal bulge, which always points towards the Earth, will roam back and forth a few degrees over the course of a Lunar orbit.

Now these variations follow the period of the Moon's sidereal month. (the time it takes for the moon to apparently travel from fixed star to fixed star.)

This period is 27.32 days.

The variation due to the distance of the moon takes place over the whole period, while the libration period completes a cycle every 1/2 period or 13.66 days. This would bur successive "high" tides 13.66 days apart , with the the high tides alternating in height.

To get a complete picture, you would then have to factor in the effect of the Sun's tides with its 14 .76 day period.

#### LURCH

Originally posted by russ_watters
It could be a trick question: the Sun also causes tides. So, 14.5 days.
Just to add, if it's not a trick question, the answer is "never". The same side of the faces the Earth all the time, so there would be no tide.

#### andytran

[q]Just to add, if it's not a trick question, the answer is "never". The same side of the faces the Earth all the time, so there would be no tide.[/q]

that's what i thought too, since the high tides remain in the same place, the period wouldn't exist...

btw this question is from first level physics course in my University.

Janus:

Since your answer is 14.76 days and without the sun's effect it's 13.66 days, so the sun's effect adds 1.1 days to the period..
but how do you get 1.1days for the sun's effect on the moon...

ps. thx for ur explaination

#### Nereid

Staff Emeritus
Gold Member
Originally posted by LURCH
Just to add, if it's not a trick question, the answer is "never". The same side of the faces the Earth all the time, so there would be no tide.
Or, saying the same thing in a slightly different way, there is a 'permanent' tide, more or less facing the Earth (and a slightly smaller one on the opposite side), so from the POV of someone on the Moon, there would be no rising and falling of water.

The Sun tides and libration would cause some apparent rising and falling of the maria level. Can anyone estimate what the height of each tidal effect would be, approximately, assuming no local effects (e.g. embayments in the lunar oceans)?

#### Janus

Staff Emeritus
Gold Member
Originally posted by andytran
[q]Just to add, if it's not a trick question, the answer is "never". The same side of the faces the Earth all the time, so there would be no tide.[/q]

that's what i thought too, since the high tides remain in the same place, the period wouldn't exist...

btw this question is from first level physics course in my University.

Janus:

Since your answer is 14.76 days and without the sun's effect it's 13.66 days, so the sun's effect adds 1.1 days to the period..
but how do you get 1.1days for the sun's effect on the moon...

ps. thx for ur explaination
Imagine that you are sitting above the earth-moon system looking down. You are using the stars as a fixed background, so they don't move from your perspective. now draw two line from the center of the Earth out to the moon's orbit. One line joins to a fixed star and the other with the sun. Starting off we'll assume that these lines are pointing in the same direction (the star is directly behind the sun) and the moon starts out on this line.

After 27.32 days the moon will have returned to the fixed star line. This is the sidereal month that the librations follow. But during this time, the Earth will have traveled some 27° along in its orbit, which means that the sun line will have moved this much, so the moon will have to continue in its orbit for another 1.1 days to return to it. This is the synodic month the solar tides follow. This means that the solar tide will have a slighty different period than the libration tide, causing an additional varitation in the heights of the tidal bulge.

The same thing happens on Earth with the difference in period between the Lunar tide and Solar tide. The Solar tide has a period of 12 hrs (1/2 a solar day) , While, as you pointed out, the Lunar tide has a period of about 12 1/2 hours. (12 hr, 27 min, 21 sec to be more exact.)

As a result, the Solar and Lunar tides drift in and out of "phase" with each other, somtimes pulling together, and sometimes foghting each other. This is why high and low tides vary from day to day in height. the greatest extremes are during new and full moons and the least during the first and last quarter.

Most likely, like Lurch said, your physics text doesn't expect you to take libration or solar tides into consideration, so the answer that they are looking for is that there is no tide change.

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