Which Is Denser?
Which of the following celestial objects, on average, is denser?
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3 solutions
Well that was a clever deduction. This accounts for the fact the time of peak tides changes over the days in sync with the lunar orbit. If the sun had the greater pull, then the time of peak tides would hover around noon and midnight consistently.
Bro I didn't understand , can you explain in more easy way
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Okay, understanding this involves 2 parts, the first about the gravitational pull of "spherical bodies", and the second about the tides.
1) Because of the inverse square law of gravity, given two spherical bodies of the same density will exert the same gravitational force if they both have the same angular size, i.e., e.g., one could be twice as far away and twice as large in diameter, and yet both will exert he same force----if their densities are the same. However, the force is directly proportional to the density, for a given distance to and diameter of a spherical body.
2) Let's imagine that the moon has the density of an air balloon. Then tides around the world will more or less peak around noon or midnight, i.e., "in line with the earth and the sun". What most people find hard to understand about tides caused by gravitational attraction is that no only water is "pulled" towards the sun, it's also "pulled" away from the sun on the other side. Furthermore, because of local "underwater geography", times of arrival of tides may be delayed. Nevertheless, the peaks will tend to be around noon or midnight, if the moon had much less density than the sun.
Because peak tides clearly follow the lunar calendar, i.e., "where the moon is at the time", the moon is effectively out-pulling the sun. Which makes sense anyway, because the sun is mostly a gaseous ball, while the moon is solid rock. The sun has enormous pull simply because it is so huge.
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I have a confusion regarding the first part. According to you, the gravitational field's intensity should be same if the angular size. Same angular size implies same ratio of radius of the celestial body and its distance from us. And if density is same ratio of mass of body to cube of its radius. But to prove that the gravitational field is same, we must prove that the ratio of mass to the square of distance from us is same. I am unable to do it.
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@Manish Mayank – yeah, you're right, the mass is a cube function of its size. I'll pull the numbers together and have another look at this, why should the moon have a greater pull. The moon does have a density greater than the sun, but we need to look at the numbers.
Okay, this is interesting. Here are the relevant figures
7.35 x 10^22 kg----Mass of moon
3340 kg/km^3---Density of moon
3473 km---Diameter of moon
384390 km---Distance moon to Earth
1.989 x 10^30 kg----Mass of sun
1410 kg/km^3---Density of sun
1.39 x 10^6 km---Diameter of sun
1.496 x 10^8 km---Distance moon to sun
110.65---ratio of Distance to moon / Diameter of moon
107.52---ratio of Distance to sun / Diameter of sun
Hence, nice solar eclipses!
2.701 x 10^7---ratio of Mass of sun / Mass of moon
2.701 x 10^7---ratio of (Density of sun x cube of Diameter sun) /
(Density of moon x cube of Diameter of moon)
Check---good agreement, density figures are correct
6.089 x 10^15---Mass of moon / square of Distance to moon
1.029 x 10^18---Mass of sun / square of Distance to sun
In other words, the sun should still exert a greater force on Earth than the moon, in spite of the moon's greater density. Oh, well, let this be a teaching moment---always check the numbers! Now I have to look at the tidal charts and figure out what's going on.
No, tides don't depend on how strong is gravitational force but on how steeply it decreases with distance. So, you can't find density relation from tides at-least.
We can also determine by which material it was created.sun is gaseous and the moon is of soil or organic material.so gaseous matter about the low density so sun is of low density than the moon...but does it matter the angular velocity to find the density also rather the difference in radius of moon and sun is different...
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We should be careful in thinking that just because a star is "gaseous" it's necessarily less dense than the moon, because of extreme gravitation in the interior of stars.
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so which part to be called a denser part...of the star .is it center or side part?
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@A Former Brilliant Member – The center of the star. In rare cases, stars can directly form a black hole at its center without even firs going through a supernova stage.
@Sharky Kesa g = [4/3 (pi)R d G] where d is density of the object and "g" is acceleration due to gravity. G is gravitational constant . As this equation indicates that g is directly proportional to density (d) . That means more the value of g , greater will be the density . As we know that "g" for earth is more than "g" for moon . Hence , earth is more denser than moon.
Can't we take the point density is proportional to mass?
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@Dhrutik Cool Density = mass/volume Therefore mass is directly proportional to density.
Let by on average density,its mean Consider the sun and the moon subtend both with same angle in the sky,which will obvious same time a solar eclips. both the sun and moon influence tides but the moons influence is larger. i conclude that moon is denser than sun through gravitational formulae
i.e. F = G m 1 m 2 / r 2
The fact that the volume of sun and moon are in the same proportion as cube of distance from the earth.
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Influence is not decided by gravitational force but by the difference of its value at the centre of earth on surface. First read something about tides then comment.
Sun is actually a huge mass of plasma. Solid moon is obviously denser than a ball of hydrogen or helium. Thus moon is denser than sun.
The sun loses mass by time, eventually no sun.
We can determine this easily. Firstly, note the angular sizes of the Sun and the Moon are the same (This is why we get Total Solar Eclipses), and the tides made by the Moon on Earth are greater than the tides made by the Sun. These two bits of information give us sufficient evidence to prove the density of the Moon, on average, is greater than that of the Sun.