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The moon is roughly 25% the size of Earth, but is only 1.2% of Earth's mass. How is this possible?
The Moon’s average radius is about 0.2727 that of The Earth, which is where I guess you get the 25% from.
The volume of a sphere is given by:
[math]V=\dfrac{4}{3}\pi r^3\tag*{}[/math]
So (using units of one Earth radius):
[math]V_{\text{Eart[/math]
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The moon is roughly 25% the size of Earth, but is only 1.2% of Earth's mass. How is this possible?
The Moon’s average radius is about 0.2727 that of The Earth, which is where I guess you get the 25% from.
The volume of a sphere is given by:
[math]V=\dfrac{4}{3}\pi r^3\tag*{}[/math]
So (using units of one Earth radius):
[math]V_{\text{Earth}}=\dfrac{4}{3}\pi\tag*{}[/math]
and
[math]V_{\text{Moon}}=\dfrac{4}{3}\pi \hspace{1mm}0.2727^3\tag*{}[/math]
As we are only concerned about relative volume, we can cancel the [math]\frac{4}{3}\pi[/math] and get:
[math]\dfrac{V_{\text{Moon}}}{V_{\text{Earth}}}=0.2727^3\approx 0.0203\approx2\%\tag*{}[/math]
If we assume that the density of The Earth and The Moon are equal, then we are still off. However, allowing for the Earth being larger and therefore its core being more compacted by gravity, you would assume it to be more dense.
In fact the density of The Moon is only 0.606 of that of The Earth. Applying this to the 2% we had before and we get the OP’s figure of 1.2%.
Maybe this is easier with cubes. Consider two cubes, one of which has sides of [math]1 m[/math] and the other of which has sides of [math]4 m[/math] (your 25% ratio again). What are the respective volumes? Well they would be [math]1 m^3[/math] and [math]64 m^3[/math] respectively. So a quarter of the length of a regular solid implies one sixty-fourth of the volume. One sixty-fourth is also approximately 1.5%.
More broadly, the function [math]f(x)=x^3[/math] grows quite quickly. So:
[math]\begin{array}{lllll}f(1)&=&1&\text{a ratio of}&1:1\\f(10)&=&1,000&\text{a ratio of}&1:100\\f(100)&=&1,000,000&\text{a ratio of}&1:10,000\end{array}[/math]
and so on.
Take a box and fill up that box with metal, such as iron. then check it’s mass. After that, fill up the same box with plastic and measure it’s mass. There would be a huge difference. The mass does NOT depend on size. It depends on what it is made of.
Earth’s diameter is 7,918 miles (12,742 kilometers) and the Moon’s diameter is 2.158 Miles (3,474 kilometers). By reading these numbers, you think the
Take a box and fill up that box with metal, such as iron. then check it’s mass. After that, fill up the same box with plastic and measure it’s mass. There would be a huge difference. The mass does NOT depend on size. It depends on what it is made of.
Earth’s diameter is 7,918 miles (12,742 kilometers) and the Moon’s diameter is 2.158 Miles (3,474 kilometers). By reading these numbers, you think the moon is 4 times smaller. Yes, the diameter is 4 times smaller but that does NOT make the whole moon 4 times smaller. Moon is even more smaller.
Look at the above cube picture. The big cube is 8 inches high and 8 inches wide. The small black cube at the right, is 2 inches high and 2 inches wide. By reading the number 2 and 8, you understand the big cube is 4 times big...
Where do I start?
I’m a huge financial nerd, and have spent an embarrassing amount of time talking to people about their money habits.
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Where do I start?
I’m a huge financial nerd, and have spent an embarrassing amount of time talking to people about their money habits.
Here are the biggest mistakes people are making and how to fix them:
Not having a separate high interest savings account
Having a separate account allows you to see the results of all your hard work and keep your money separate so you're less tempted to spend it.
Plus with rates above 5.00%, the interest you can earn compared to most banks really adds up.
Here is a list of the top savings accounts available today. Deposit $5 before moving on because this is one of the biggest mistakes and easiest ones to fix.
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Because Math.
The size of an object is measured by its diameter, which is the distance from one side to the other through the center. The diameter of the moon is 3,476 kilometers (2,159 miles), while the diameter of Earth is 12,742 kilometers (7,917 miles). If you divide the moon's diameter by Earth's diameter, you get 0.2725, which means the moon is about 27% the size of Earth.
The mass of an object is measured by how much matter it contains, which depends on its density and volume. The density of an object is how tightly packed its atoms are, and the volume of an object is how much space it oc
Because Math.
The size of an object is measured by its diameter, which is the distance from one side to the other through the center. The diameter of the moon is 3,476 kilometers (2,159 miles), while the diameter of Earth is 12,742 kilometers (7,917 miles). If you divide the moon's diameter by Earth's diameter, you get 0.2725, which means the moon is about 27% the size of Earth.
The mass of an object is measured by how much matter it contains, which depends on its density and volume. The density of an object is how tightly packed its atoms are, and the volume of an object is how much space it occupies. The density of the moon is 3.34 grams per cubic centimeter (3.34 g/cm3), while the density of Earth is 5.51 grams per cubic centimeter (5.51 g/cm3) . This means that Earth's atoms are more tightly packed than the moon's atoms. The volume of the moon is 2.1968 x 1010 cubic kilometers (2.1968 x 1010 km3) , while the volume of Earth is 1.08321 x 1012 cubic kilometers (1.08321 x 1012 km3). This means that Earth occupies much more space than the moon.
To calculate the mass of an object, you multiply its density by its volume. The mass of the moon is 7.35 x 1022 kilograms (7.35 x 1022 kg) , while the mass of Earth is 5.9724 x 1024 kilograms (5.9724 x 1024 kg). If you divide the moon's mass by Earth's mass, you get 0.0123, which means the moon is only 1.2% of Earth's mass.
So, how is it possible that the moon is roughly 25% the size of Earth, but only 1.2% of Earth's mass? It's because the moon has a much lower density than Earth, which means its atoms are more loosely packed and it contains less matter per unit volume. In other words, the moon is like a big ball of cotton candy, while Earth is like a solid rock.
From NASA:
- Mass ratio: 0.0123:1 Moon:Earth
- Volume ratio: 0.0203:1 Moon: Earth
- Equatorial radius ratio: 0.2725 Moon: Earth
So I suppose the question is: what do you mean by size? The volume ratio is not a great deal different. The Moon is overall less dense than the Earth, but not dramatically so.
If you mean by ‘size’ the radius, then, indeed, the radius of the Moon is 27% that of the Earth. But from the radius we calculate the volume, which will be approximately 4/3πr³ in each case—only approximately, because neither are exactly spherical.
Let’s take r=1 and r=0.25, and do this calculation for the
Footnotes
From NASA:
- Mass ratio: 0.0123:1 Moon:Earth
- Volume ratio: 0.0203:1 Moon: Earth
- Equatorial radius ratio: 0.2725 Moon: Earth
So I suppose the question is: what do you mean by size? The volume ratio is not a great deal different. The Moon is overall less dense than the Earth, but not dramatically so.
If you mean by ‘size’ the radius, then, indeed, the radius of the Moon is 27% that of the Earth. But from the radius we calculate the volume, which will be approximately 4/3πr³ in each case—only approximately, because neither are exactly spherical.
Let’s take r=1 and r=0.25, and do this calculation for the respective volumes. We can cancel out the 4/3π in each case, because they are the same.
- 1³=1
- 0.25³=0.015625.
So, there’s no mystery here. If by size you mean ‘radius’, then it makes complete sense that the Moon’s volume is 2% of the Earth’s. It’s somewhat less dense, but this shouldn’t surprise us very much.
Footnotes
The moon's size and mass relative to Earth can be explained through its density and composition. While the moon has a diameter of about 3,474 kilometers (roughly 27% of Earth's diameter), its mass is much lower—about 1/81 of Earth's mass. Here's how this is possible:
- Volume vs. Mass: The volume of the moon is significantly less than that of Earth, which is why its size can be larger in terms of diameter while having a much lower mass. The volume of a sphere is calculated using the formula [math]V = \frac{4}{3} \pi r^3[/math]. Even a relatively small difference in radius can lead to a large difference in vol
The moon's size and mass relative to Earth can be explained through its density and composition. While the moon has a diameter of about 3,474 kilometers (roughly 27% of Earth's diameter), its mass is much lower—about 1/81 of Earth's mass. Here's how this is possible:
- Volume vs. Mass: The volume of the moon is significantly less than that of Earth, which is why its size can be larger in terms of diameter while having a much lower mass. The volume of a sphere is calculated using the formula [math]V = \frac{4}{3} \pi r^3[/math]. Even a relatively small difference in radius can lead to a large difference in volume.
- Density: Density is defined as mass per unit volume. The moon has a lower average density (about 3.34 grams per cubic centimeter) compared to Earth (about 5.52 grams per cubic centimeter). This lower density suggests that the moon is composed of lighter materials than Earth, which is primarily made up of heavier elements like iron and nickel in its core.
- Composition: The moon's surface is predominantly made up of silicate rocks and minerals, which are less dense than the metallic composition of Earth's core and mantle. The differences in composition lead to lower overall mass despite a significant volume.
- Formation: The leading theory for the moon's formation is the Giant Impact Hypothesis, which posits that the moon formed from the debris of a massive collision between a Mars-sized body and the early Earth. This impact may have ejected lighter materials into orbit, contributing to the moon's lower density and mass.
In summary, the moon's relatively large size compared to its mass is due to its lower density and different composition, which result from its unique formation history and the materials that constitute it.
It is a simple calculation.
Moon is actually about 27% in radius compared to Earth, not volume.
Mass = Density * Volume
First we will compare volumes and then density.
For spherical bodies:
Volume = 4/3 * π * (r)^3 [where r is the radius of the body]
If we compare the volumes of Moon ([math]V_{m}[/math]) and Earth ([math]V_{e}[/math]) assuming
[math]R_{m}[/math] (radius of Moon) = 0.27*[math]R_{e}[/math] (radius of Earth):
[math]V_{m}[/math] = 4/3 * π * ([math]R_{m}[/math])^3 = 4/
It is a simple calculation.
Moon is actually about 27% in radius compared to Earth, not volume.
Mass = Density * Volume
First we will compare volumes and then density.
For spherical bodies:
Volume = 4/3 * π * (r)^3 [where r is the radius of the body]
If we compare the volumes of Moon ([math]V_{m}[/math]) and Earth ([math]V_{e}[/math]) assuming
[math]R_{m}[/math] (radius of Moon) = 0.27*[math]R_{e}[/math] (radius of Earth):
[math]V_{m}[/math] = 4/3 * π * ([math]R_{m}[/math])^3 = 4/3 * π * (0.27*[math]R_{e}[/math])^3 = 0.0197 * (4/3 * π * ([math]R_{e}[/math])^3) = 0.0197 * [math]V_{e}[/math]
So the Volume of moon ~ 1.97% of Volume of Earth
Density of moon ([math]D_{m}[/math]) = 3.34 g/cc
Density of Earth ([math]D_{e}[/math]) = 5.51 g/cc
Comparing mass:
[math]M_{m}[/math] = [math]D_{m}[/math] * [math]V_{m}[/math]
[math...
Earth has an iron core of liquid magma. Very heavy. The moon is basically just compressed sand and is much smaller. Here's an actual photo.
Earth has an iron core of liquid magma. Very heavy. The moon is basically just compressed sand and is much smaller. Here's an actual photo.
I once met a man who drove a modest Toyota Corolla, wore beat-up sneakers, and looked like he’d lived the same way for decades. But what really caught my attention was when he casually mentioned he was retired at 45 with more money than he could ever spend. I couldn’t help but ask, “How did you do it?”
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Mos
I once met a man who drove a modest Toyota Corolla, wore beat-up sneakers, and looked like he’d lived the same way for decades. But what really caught my attention was when he casually mentioned he was retired at 45 with more money than he could ever spend. I couldn’t help but ask, “How did you do it?”
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Because volume is proportional to the cube of the radius. So, at [math]\frac{1}{4}[/math] the radius, we should expect the moon to be about [math](\frac{1}{4})^3 = \frac{1}{64}[/math] times the volume of the Earth, and, consequently, about [math]\frac{1}{64}[/math] times Earth’s mass.
The moon, it turns out, it a bit less dense than the Earth, so when we factor in density it reduces to about 1/81.
Sadly, the author has used trigger language to get hits. The answerers get bent out of shape criticizing the ambiguity of “size.” Guess what. That’s intentional. All these angry answers and comments are generating revenue for this Qwhora.
Learn to spot these kinds of questions. Check the log and look at the question to answer ratio of the asker. Then don’t answer them when they are insincerely and intentionally deceptive. in fact block them too if this bothers you.
Sadly, the author has used trigger language to get hits. The answerers get bent out of shape criticizing the ambiguity of “size.” Guess what. That’s intentional. All these angry answers and comments are generating revenue for this Qwhora.
Learn to spot these kinds of questions. Check the log and look at the question to answer ratio of the asker. Then don’t answer them when they are insincerely and intentionally deceptive. in fact block them too if this bothers you.
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To word “size” needs to be disambiguated here: it is the diameter of the Moon that is 25% that of the Earth. Bearing in mind that the volume of an object is proportional to the cube of the radius and that the radius of the Earth is about 4 times that of the moon, this implies that the Earth’s volume is 4*4*4=64 times larger than that of the Moon. This means, assuming both objects have similar density, that the mass of the Moon would be 1/64, or 1.6%, that of the Earth. We can, however, expect that the Earth would have an overall higher density than the Moon because of its larger gravity, so th
To word “size” needs to be disambiguated here: it is the diameter of the Moon that is 25% that of the Earth. Bearing in mind that the volume of an object is proportional to the cube of the radius and that the radius of the Earth is about 4 times that of the moon, this implies that the Earth’s volume is 4*4*4=64 times larger than that of the Moon. This means, assuming both objects have similar density, that the mass of the Moon would be 1/64, or 1.6%, that of the Earth. We can, however, expect that the Earth would have an overall higher density than the Moon because of its larger gravity, so that would make the Moon a bit lighter than the 1.6% value calculated above.
Size & mass are two different things.
(See how the smaller object has higher mass)
It’s all about material molecules & density.
Size & mass are two different things.
(See how the smaller object has higher mass)
It’s all about material molecules & density.
The volume of a sphere of radius r is [math]\frac{4}{3}\pi r^3[/math].
So if a second sphere has 1/4 the radius of the first sphere, it has a volume [math](1/4)^3 = 1/64 \approx 1.56\%[/math] that of the first sphere. Now account for the difference in the average density of the material and you get the 1.2% figure.
Simple answer: the theory most agreed upon for the moon’s creation has a very large object (a protoplanet) slamming into Earth and knocking a large amount of Earth’s crust and some of the other object back into space as debris. That crustal material is less dense (less massive than the core of Earth.) Eventually most of that material orbiting Earth coalesced into what is now our moon.
This method of creation for the moon resulted in an object smaller that the one it came from and lighter, less massive. You can test this by making a slushy snowball with rocks in it and throw it at a snow man. So
Simple answer: the theory most agreed upon for the moon’s creation has a very large object (a protoplanet) slamming into Earth and knocking a large amount of Earth’s crust and some of the other object back into space as debris. That crustal material is less dense (less massive than the core of Earth.) Eventually most of that material orbiting Earth coalesced into what is now our moon.
This method of creation for the moon resulted in an object smaller that the one it came from and lighter, less massive. You can test this by making a slushy snowball with rocks in it and throw it at a snow man. Some of the slush and snow will splatter back from the impact, but most of the rocks will become in-bedded into the snowman.
Keep reading and commenting. Together we learn.
Well first, let's unpack "The Moon is 1/4 the size of the Earth."
Luna, Earth's sole Moon, has a radius (on average) of 1737 miles, which is 27.3% of Earth's. So it's 1/4 of the way across, or around, the Moon compared to the Earth. But that means that the Moon's volume, which depends on the cube of the radius, is only 2% of Earth's. So is the Moon 1/4 the size of the Earth, or 1/50? Depends on how you look at it.
Moreover, gravity depends not only on the Moon's size, but also on its mass -- how much stuff is in the Moon. And the Moon doesn't weigh as much as the Earth: the Moon is, on average,
Well first, let's unpack "The Moon is 1/4 the size of the Earth."
Luna, Earth's sole Moon, has a radius (on average) of 1737 miles, which is 27.3% of Earth's. So it's 1/4 of the way across, or around, the Moon compared to the Earth. But that means that the Moon's volume, which depends on the cube of the radius, is only 2% of Earth's. So is the Moon 1/4 the size of the Earth, or 1/50? Depends on how you look at it.
Moreover, gravity depends not only on the Moon's size, but also on its mass -- how much stuff is in the Moon. And the Moon doesn't weigh as much as the Earth: the Moon is, on average, made of lighter rocks than the Earth is. (We think that the Moon was made in a collision between the Earth and a now-destroyed planet called Theia, with the Moon made of the upper and lighter layers of both worlds.) The Moon's density is 3.34 g/mL, which is three-fifths of Earth's. So even though the Moon has 2% of Earth's volume, it only has 1.2% of Earth's mass.
Gravity weakens with less mass, but grows stronger by the square of the radius. An object the size of the Earth, but with the mass of the Moon, would have 1.2% as much gravity. An object the size of the Moon, but with the mass of the Earth, would have 13 times as much gravity (1 divided by .273 squared). And 1.2% of 13 is.... 1/6.
The moon is 25% the RADIUS of Earth.
ie a measurement of ONE dimension.
Mass on the other hand relates to volume which is a THREE dimensional measurement.
25% cubed is 1.5%.
Pretty close to 1.2%.
The difference results from Earth’s greater gravity squeezing more material into the same volume of space, making Earth denser.
The ratio of the mass of the Earth to the moon is about 81 : 1
The ratio of their diameters is about 3.67 : 1
The ratio of their volumes is about 49 : 1
And finally, the density of the Earth is about 5.51 g/cm^3, while that of the Moon is about 3.34 g/cm^3, or about 1.65 : 1. Note that 1.65 x 49 is 81.
The Moon and the Earth are not made of the same stuff in the same proportions. That is different than saying they don't contain the same stuff, they do. A major difference is that the Earth is about one third Iron, while the Moon is believed to only be about 3.5% Iron. Interestingly, while t
The ratio of the mass of the Earth to the moon is about 81 : 1
The ratio of their diameters is about 3.67 : 1
The ratio of their volumes is about 49 : 1
And finally, the density of the Earth is about 5.51 g/cm^3, while that of the Moon is about 3.34 g/cm^3, or about 1.65 : 1. Note that 1.65 x 49 is 81.
The Moon and the Earth are not made of the same stuff in the same proportions. That is different than saying they don't contain the same stuff, they do. A major difference is that the Earth is about one third Iron, while the Moon is believed to only be about 3.5% Iron. Interestingly, while the Earth is about 30% Oxygen, the moon is about 60% Oxygen. Iron is considerably denser than Oxygen. Put another way, we have a large Iron core. The Moon does not.
Others have covered the radius-vs.-volume argument, so I won’t reiterate that. Clearly the Moon is also somewhat less dense than the Earth. Why is that?
I believe there are two reasons.
Firstly, the Earth’s mass (and therefore gravity) compresses the material it’s made of far more than the Moon’s meagre gravity would.
Secondly - lava tubes and pumice. The Moon had a volcanic history before it cooled. Long suggested, there is now solid evidence of the existence of lava tubes riddling the Moon’s crust. This is very exciting for the prospect of human colonisation, as it solves both the accommodation
Others have covered the radius-vs.-volume argument, so I won’t reiterate that. Clearly the Moon is also somewhat less dense than the Earth. Why is that?
I believe there are two reasons.
Firstly, the Earth’s mass (and therefore gravity) compresses the material it’s made of far more than the Moon’s meagre gravity would.
Secondly - lava tubes and pumice. The Moon had a volcanic history before it cooled. Long suggested, there is now solid evidence of the existence of lava tubes riddling the Moon’s crust. This is very exciting for the prospect of human colonisation, as it solves both the accommodation and radiation shielding issues, and - if there is indeed water ice in the lava tubes, as has been suggested - also oxygen, water and rocket fuel. In addition, active vulcanism tends to lead to formation of low-density rock foams like pumice.
Put together, these ought to explain the lower density.
Mostly it is because volume behaves as a linear distance cubed and [math]\left(\frac14\right)^3=\frac1{64}\approx1.6\%[/math]
But also the Moon's mean density is only about [math]60\%[/math] that of Earth (which has a much denser iron core than the basalt rock that makes up most of the Moon).
The Moon isn’t as dense. Whilst it has a similar structure in terms of layers, the Moon’s mantle is far larger as a proportion of its volume than Earth’s is.
Earth, in fact, is the densest planet
(along with Mercury).The Moon, however, has a density of 3.34 grams per cubic centimetre - less than any of the first four planets.
Footnotes
The Moon isn’t as dense. Whilst it has a similar structure in terms of layers, the Moon’s mantle is far larger as a proportion of its volume than Earth’s is.
Earth, in fact, is the densest planet
(along with Mercury).The Moon, however, has a density of 3.34 grams per cubic centimetre - less than any of the first four planets.
Footnotes
Earth’s density is 5g/cm^3 and the Moons is around 3g/cm^3.
Yes the Moon’s mass is 81 times less than the Earth’s, but it’s radius is around 1/4 (actually 0.272) - so on the surface of the Moon you are actually a lot closer to the center of gravity compare to being on the surface of the Earth.
The Gravity at the surface of a body is :
[math]g = \frac{Gm}{r^2}[/math]
[math]g_m = \frac{G \cdot \frac{m_e}{81}}{(r_e *0.272)^2}[/math]
[math]g_m = \frac{G \cdot m_e}{81} \cdot \frac{1}{0.0743 \dot (r_{e}^2)}[/math]
[math]g_m = \frac{G \cdot m_e}{r_{e}^2} \cdot \frac{1}{81*0.0743}[/math]
[math]g_m = g_e \cdot \frac{1}{6}[/math]
so the Moon’s gravity at the surface is appro
Earth’s density is 5g/cm^3 and the Moons is around 3g/cm^3.
Yes the Moon’s mass is 81 times less than the Earth’s, but it’s radius is around 1/4 (actually 0.272) - so on the surface of the Moon you are actually a lot closer to the center of gravity compare to being on the surface of the Earth.
The Gravity at the surface of a body is :
[math]g = \frac{Gm}{r^2}[/math]
[math]g_m = \frac{G \cdot \frac{m_e}{81}}{(r_e *0.272)^2}[/math]
[math]g_m = \frac{G \cdot m_e}{81} \cdot \frac{1}{0.0743 \dot (r_{e}^2)}[/math]
[math]g_m = \frac{G \cdot m_e}{r_{e}^2} \cdot \frac{1}{81*0.0743}[/math]
[math]g_m = g_e \cdot \frac{1}{6}[/math]
so the Moon’s gravity at the surface is approximately 1/6’s of the gravity of the Earth’s at the surface of the Earth.
My assumption is that the mass of the moon is 1.0445×10^23kg and the surface gravity on the moon around 2.57 m/s^2.
Because
1. Density of solid all over the universe is same.
2. The ratio between solid, liquid and gas are almost same.
3. The orbit of the moon fixed by the gravitational force between the earth and the moon, therefore the orbital radius of the moon and it's mass ...
The gravity on the surface of a body depends on its mass - but also on its radius.
Remember - gravity follows an “inverse square law” - since the moon is only about a quarter the size of Earth - (0.27 to be more exact) - when you’re standing on the Moon, you’re roughly 4 times closer to the center than you are when you’re considering the Earth.
That makes gravity 13.7 times stronger (1/(0.27 x 0.27)) than it would be if the moon had the same diameter as Earth. With 81 times less mass, the overall surface gravity is 13.7/81 times Earth’s gravity - which I’m relieved to discover is 1/5.9 that of E
The gravity on the surface of a body depends on its mass - but also on its radius.
Remember - gravity follows an “inverse square law” - since the moon is only about a quarter the size of Earth - (0.27 to be more exact) - when you’re standing on the Moon, you’re roughly 4 times closer to the center than you are when you’re considering the Earth.
That makes gravity 13.7 times stronger (1/(0.27 x 0.27)) than it would be if the moon had the same diameter as Earth. With 81 times less mass, the overall surface gravity is 13.7/81 times Earth’s gravity - which I’m relieved to discover is 1/5.9 that of Earth…about 1/6th of a ‘g’.
(Yeaaaahhhhh! Math works!)
If the moon were the same density as the earth, its mass relative to earth would be proportional to its volume. The volume is 1/4 x 1/4 x 1/4 = 1/64 = 1.56% of the earth’s volume. Since the density is less than earth’s, the moon’s mass is 1.2% that of the earth.
Warning, math ahead.
Gravitational force is calculated with mass over the distance from the center squared, so the distance is the bigger factor. If the Moon were exactly one fourth the diameter of the Earth, that would make it 1/64th the volume. So we would expect the Moon to have 1/64th the mass. That's about 1.6% of the Earth's mass, not 1.2%. Close, but it's a little off.
If we use the accepted figure for the mass and work backwards, 1.2% of the mass divided by the approximate radius of 0.25 x 0.25 gets us 19.2% of the gravity, or almost one fifth. Pretty close, but still a little off.
The ra
Warning, math ahead.
Gravitational force is calculated with mass over the distance from the center squared, so the distance is the bigger factor. If the Moon were exactly one fourth the diameter of the Earth, that would make it 1/64th the volume. So we would expect the Moon to have 1/64th the mass. That's about 1.6% of the Earth's mass, not 1.2%. Close, but it's a little off.
If we use the accepted figure for the mass and work backwards, 1.2% of the mass divided by the approximate radius of 0.25 x 0.25 gets us 19.2% of the gravity, or almost one fifth. Pretty close, but still a little off.
The radius of the Moon is actually a little more than one forth, more like 0.27 the radius of Earth.
So if we use both those figures, we get 1.2% ÷ 0.27 x 0.27, which is 16.4% for the Moon’s gravity, or just about one sixth that of Earth.
It's just math.
OP: “How is the Moons gravity 1/6th of Earth’s, when the Moon is 1/4 the diameter of Earth, only 1.2% of the Earth's mass and 60% as dense?”
The moon is thought to be made up of accreted debris left over by an ancient collision between proto-earth and a planet, named (Theia?) - spelling may need correction.
Astrogeologists have done echo-sounding of the Moon's interior and found that some areas are less dense, leading scientists to believe or hypothesize that large molten clumps may have come together, leaving gaps in the interior.
Other research suggests that the bulk material of the moon is less dense than on earth.
I have a suspicion what you mean but in the way it is stated it is wrong. The gravitational pull of the moon versus the pull of the earth is in the same ratio as the mass of the moon versus the mass of the earth. That applies to any same distance from the mass center of the two bodies. Example: if you are in a place 20000 km away from the mass center of the moon the gravitational pull of the moon is 1.2% as strong as the gravitational pull of the earth when you are in a place that is 20000 km away from the mass center of the earth.
What you probably meant was why is the surface gravity of the m
I have a suspicion what you mean but in the way it is stated it is wrong. The gravitational pull of the moon versus the pull of the earth is in the same ratio as the mass of the moon versus the mass of the earth. That applies to any same distance from the mass center of the two bodies. Example: if you are in a place 20000 km away from the mass center of the moon the gravitational pull of the moon is 1.2% as strong as the gravitational pull of the earth when you are in a place that is 20000 km away from the mass center of the earth.
What you probably meant was why is the surface gravity of the moon 16% of the surface gravity of the earth when the moon has only 1.2% of the mass of earth? The answer is because the distance from the mass center of the moon to the surface of the moon is not the same as the distance from the mass center of the earth to the surface of the earth and the pull of gravity is dependent on the distance to the mass center.
The surface of the earth is roughly 3.6 times away from the mass center of the earth compared to the distance of the mass center of the moon to the surface of the moon. As gravity is proportional to the square of the distance this would mean if the earth had the same mass of the moon but keeps its size the surface gravity of the earth would be only 1/13 of the surface gravity of the moon. If you put the numbers back in considering the difference of distances you get that the surface gravity of the moon is 13 * 1.2% ~ 16% of the surface gravity of the earth which is what is to be expected from how gravity works.
Size is an imprecise word. It’s better to say radius, diameter or volume, in this case volume would be the sensible metric, and that’s only 2% of Earth’s volume. Volume is proportional to the radius cubed, so 1/4th the radius would be 1/64th the volume.
Additionally, the moon is made from the the relatively lightweight material from Earth’s crust, it lacks an iron core like Earth, and is thus much less dense.
Just to clarify one point: gravity among natural objects does not depend significantly on the density of one area or another, only total mass and distance.
One of Newton’s great discoveries is that gravity on the surface of a spherically symmetric body has no dependence whatever on the distribution of mass with depth. High or low density regions can be central, close to the surface, or an arbitrary mix. It does not matter.
For mass M, radius r, the force of gravity at the surface is proportional to the acceleration
g = GM / r^2 = 9.8 meters / sec ^2 for the earth, and
for the moon: 1.62 meters / s
Just to clarify one point: gravity among natural objects does not depend significantly on the density of one area or another, only total mass and distance.
One of Newton’s great discoveries is that gravity on the surface of a spherically symmetric body has no dependence whatever on the distribution of mass with depth. High or low density regions can be central, close to the surface, or an arbitrary mix. It does not matter.
For mass M, radius r, the force of gravity at the surface is proportional to the acceleration
g = GM / r^2 = 9.8 meters / sec ^2 for the earth, and
for the moon: 1.62 meters / sec ^2. The ratio between them about 6.
Here are the numbers: The radius r of the earth is 3959 miles, of the moon 1080 miles.
The mass M of the earth is 81 times that of the moon, the radius 3.666 times the moon, radius squared 13.4 times. So the ratio of g values (and the force of gravity) is as M/r^2 = 81 / 13.4 = 6.
The moon is roughly 1/4 the diameter of the Earth’s diameter. That is 1/64th the size when using size to mean volume as most people do. That is 1.56% the size of the Earth. So if its mass is 1.2% of the Earth’s mass that is understandable as gravity is crushing the matter on Earth into a smaller volume. The moon has a tiny fraction of the Earth’s gravity so it is expected to be less dense. That makes the 1.2% mass of the Earth seem about perfect.
No - the thing is that tidal effects of the moon (or the sun or any other body for that matter) depends on how much difference there is in the gravitational field from that body at the nearest and furthest parts of the Earth.
Since the moon is fairly close - the difference in the distance to the moon from the side of the Earth that’s closest to the side that’s furthest - is actually a fairly signif
No - the thing is that tidal effects of the moon (or the sun or any other body for that matter) depends on how much difference there is in the gravitational field from that body at the nearest and furthest parts of the Earth.
Since the moon is fairly close - the difference in the distance to the moon from the side of the Earth that’s closest to the side that’s furthest - is actually a fairly significant change.
The Moon is about 240,000 miles from the center of the Earth…but the Earth is 8,000 miles in diameter.
So the distance from Moon to the point closest to the moon is about 3% less on the near side of Earth.
Because gravity decreases with range - that’s enough to produce a significant difference in the amount of gravity the Moon produces on the near and far sides of Earth - and that’s what causes tidal effects.
But if the Moon was 3 times further away (720,000 miles) then there would only be about a 1% difference between the two sizes.
The other part of this is that the force of gravity is proportional to one over the SQUARE of the distance - multiplied by the mass. So to have your THREE times heavier moon, it would have to be NINE times further away.
Then the difference in distance between the two sides of Earth would be m...
Although as you say, the moon is approximately 25% of the diameter of the earth, it's obviously a three dimensional object so it’ll be approximately a 64th of its volume. 25% of 25% of 25% = 1/64 or ~ 1.5%. Imagine that you have a cubic box 4 inches on each side. How many one inch cubes can you fit into it? 4 x 4 x 4 = 64.
It isn't as simple as “Body A weighs twice as much as B, hence A will exert twice as much gravitational force than B”
Rememeber, that according to Newton, the Gravitational force is directly proportionate to the mass of both bodies multiplied with each other BUT inversely proportionate to the radius between their respective centres squared.
Remember the /r^2. Make a hashtag out of it. #Remember2 :D
Anyways, take the gravitational theorem and plug some values in there, for both the earth and the moon. Take your own weight, do the calculations and see what you find. You will find that Moon has 16%
It isn't as simple as “Body A weighs twice as much as B, hence A will exert twice as much gravitational force than B”
Rememeber, that according to Newton, the Gravitational force is directly proportionate to the mass of both bodies multiplied with each other BUT inversely proportionate to the radius between their respective centres squared.
Remember the /r^2. Make a hashtag out of it. #Remember2 :D
Anyways, take the gravitational theorem and plug some values in there, for both the earth and the moon. Take your own weight, do the calculations and see what you find. You will find that Moon has 16% of Earth's gravity
Peace
It’s for the same reason that a person is lighter at high altitude and heavier near sea level: the distance from the center of the planetary body has quite a bit to do with it. Gravity is not just about mass, but also radius (distance from the center of gravity). If the Moon was exactly as big as Earth, but still 1.2% the mass, then it WOULD have just 1.2% of the gravitational pull.
I’ll try to keep this as math-free as possible, but of course some is required to explain the reasoning. I am not a mathematician or physicist, and anyone with some credentials can feel free to correct me if/where I
It’s for the same reason that a person is lighter at high altitude and heavier near sea level: the distance from the center of the planetary body has quite a bit to do with it. Gravity is not just about mass, but also radius (distance from the center of gravity). If the Moon was exactly as big as Earth, but still 1.2% the mass, then it WOULD have just 1.2% of the gravitational pull.
I’ll try to keep this as math-free as possible, but of course some is required to explain the reasoning. I am not a mathematician or physicist, and anyone with some credentials can feel free to correct me if/where I am wrong.
The following formula is the Universal Law of Gravitation (ooooo, capital letters for effect!)
[math]𝐹=𝐺𝑀𝑚/𝑅^2[/math]
In this example:
F = Force
G = The Gravitational Constant, which is important to know if you’re actually doing this calculation, but you don’t need to know for the purposes of this answer
M = Mass of the planet
m = Mass of you
R = Radius of the planet
You’ll notice that where M is situated, it is simply multiplied by G and m. But down below, the radius is squared!
So, then, you can really simplify that down to find the ratio of the Moon’s gravity to Earth’s gravity. You don’t really have to run the full equation twice; you can simply come up with an answer that will compare the two by swapping out M and R.
For M:
Earth’s mass is 81 times that of the Moon.
The Moon is 0.012 times the mass of Earth.
For R:
Earth’s radius is 3.666 times that of the Moon.
The Moon is 0.273 times that of Earth.
So place in those values, and you have 0.012/0.273^2. That comes out to 0.161011150022139, which is the ratio of the Moon’s gravitation to Earth’s. A little over 16%.
Acceleration due to gravity is not just about mass, it’s also about distance from the centre. The Moon’s equatorial radius is only approximately 27.3% of ours. Moreover acceleration due to gravity is proportional to mass divided by the square of the radius.
1.2% = 0.012 x that of the Earth.
27.3% = 0.273 x that of the Earth.
0.012/0.273^2 = approximately 0.16 which is nearly 1/6.
No.
The effect is gravity. But gravity changes as the inverse of the of square of the distance. So it is (1/3)^2 distance times 3 mass. So the gravitational effect will be 1/3 less gravitational effect on the Earth, and hence on the height of the lunar tides—the sun tides won’t change (noticeably). But the orbital period of the Moon will also change, and so will the timing of tidal effects.
You might think that that changing your specifications to moving the Moon by only the square root of 3 would make the effects ‘the same’. After all squaring √3 is 3, so 3/3 is back to 1. And that would equ
No.
The effect is gravity. But gravity changes as the inverse of the of square of the distance. So it is (1/3)^2 distance times 3 mass. So the gravitational effect will be 1/3 less gravitational effect on the Earth, and hence on the height of the lunar tides—the sun tides won’t change (noticeably). But the orbital period of the Moon will also change, and so will the timing of tidal effects.
You might think that that changing your specifications to moving the Moon by only the square root of 3 would make the effects ‘the same’. After all squaring √3 is 3, so 3/3 is back to 1. And that would equalize the gravitational attraction.
But orbital periods are more complex: T = 2π√(distance)^3/(G*(M1+M2)))
And using √3 for the distance doesn’t equalize T (the orbital period).
And what you learn from this is 1) orbital mechanics is not simple, and 2) math is fun!
The mass grows as the volume grows, and it grows in a cubic scale! If something is the double in one dimention it would be 8 times(2^3) bigger in volume! If the moon is 1/4 of Earth radius it should be 1/64 less in volume. Otherwise the composition of Moon is also lighter than Earth’s, that’s why it is 1/81 instead of 1/64!
The force of gravity is measured as the result of The mass of Objects attracted gravitationally, and the distance between those two objects. G(m1m2)/R2. We feel the effects of gravity all the time. The more mass you have, the greater the force of gravity affects you, as weight. The further away you are from the object gravitationally attracting you, the weaker the force of gravity is by the square
The force of gravity is measured as the result of The mass of Objects attracted gravitationally, and the distance between those two objects. G(m1m2)/R2. We feel the effects of gravity all the time. The more mass you have, the greater the force of gravity affects you, as weight. The further away you are from the object gravitationally attracting you, the weaker the force of gravity is by the square of the distance. R, in our case would be the distance we are from the center of the Earth. If you went really, really high up, like Mount Everest, or in an air plain, you would weigh a tiny bit less. If you went the distance of the radius of the Earth up, and somehow survived the vacuum, and found a platform to stand on, you would weigh 2R x 2R, or one fourth what you do on the surface of the Earth, 1R …
So take a diameter 1/4 that of Earth, the Force of Gravity would be 16 times greater, as you are 4 times closer to the source of gravity pull. But the mass of the object pulling you...
The difference in mass is a result of different density, the moon has a more solid structure with a molten inner core, on the other hand the Earth is mostly molten with the thin crust which we inhabit. The molten metal is much denser than the metal in a solid state, that would make up the mass difference being that mass =density *volume so the volume is only 4 times that of the moon but the density is what makes the difference.
The question is really interesting in a way that the prior answers have neglected.
Gravitational acceleration at the surface of an object is A=G*M/r^2. G is a constant, M is the mass of the object, and r is the radius of the object.
The mass of a spherical object is M=d*4/3*pi*r^3. If you plug this into the surface acceleration expression, you'll find that surface acceleration scales linearly with the radius of the object.
So the Moon is 3.67x smaller than the Earth but has 6x less gravity. That's because it's 1.65x less dense than Earth. How is that?
The Earth has an approximately Moon-sized meta
The question is really interesting in a way that the prior answers have neglected.
Gravitational acceleration at the surface of an object is A=G*M/r^2. G is a constant, M is the mass of the object, and r is the radius of the object.
The mass of a spherical object is M=d*4/3*pi*r^3. If you plug this into the surface acceleration expression, you'll find that surface acceleration scales linearly with the radius of the object.
So the Moon is 3.67x smaller than the Earth but has 6x less gravity. That's because it's 1.65x less dense than Earth. How is that?
The Earth has an approximately Moon-sized metal ball in the center, which is much denser than rock. For the moon to be so much less dense, it must be made of rock all the way through.
That means the moon came from a different source than Earth came from. It came from the outer part of the Earth, after the Earth had grown into a ball and the liquid metal had fallen into the center. Metaphorically it's a bit like Eve being made from a rib pulled from Adam's side.
The gravitational force between two objects depends on two factors: the mass of the objects and the distance between them. While it's true that the Moon is much smaller and less massive than the Earth, the distance between the center of the Moon and the center of the Earth also plays a crucial role in determining the gravitational force between them.
Although the Moon has only about 1.2% of the Earth's mass, its average distance from the Earth is approximately 384,400 kilometers (238,900 miles). This relatively close proximity helps compensate for its smaller mass, resulting in a gravitational
The gravitational force between two objects depends on two factors: the mass of the objects and the distance between them. While it's true that the Moon is much smaller and less massive than the Earth, the distance between the center of the Moon and the center of the Earth also plays a crucial role in determining the gravitational force between them.
Although the Moon has only about 1.2% of the Earth's mass, its average distance from the Earth is approximately 384,400 kilometers (238,900 miles). This relatively close proximity helps compensate for its smaller mass, resulting in a gravitational force that is about 1/6th the strength of Earth's gravity.
The Moon's density and diameter are not the primary factors affecting its gravitational force compared to Earth. Density is a measure of mass per unit volume, so even if the Moon is 60% as dense as Earth, its smaller size means it contains much less mass overall. Additionally, the Moon's diameter being one quarter that of Earth doesn't directly correlate to its gravitational strength.
Ultimately, it is the combination of the Moon's mass, its distance from Earth, and the universal law of gravitation that determines the observed strength of its gravitational pull.
=•••
Because it is much smaller than the earth, so you are closer to the centre on the surface of the moon. The radius of the earth is 6378 km and the moon is 1737, so the surface gravity will by 0.012 * (6378/1737)^2, bearing in mind the inverse square law for gravitational attraction. This comes out to 15.6 %.
The Earth is the densest planet in the Solar system and the Moon is less bulky than 25%. I don’t recall how many Moons can fit inside the Earth, but the 1.2% should give us a ballpark figure.