<h1>Your Earth mass is off by a factor of 1000</h1>
<p>As @planetmaker has pointed out, the mass of the earth is <span class="math-container">$6$$⋅$$10^{24}$</span> kg, instead of <span class="math-container">$6$$⋅$$10^{27}$</span>.</p>
<p>Second, <span class="math-container">$km^{3}$</span> and <span class="math-container">$m^{3}$</span> are different things. <span class="math-container">$km^{3}$</span> is off <span class="math-container">$m^{3}$</span> by a factor of 1 billion (<span class="math-container">$1km^{3}$</span>=<span class="math-container">$10^9m^{3}$</span>).</p>
<p>Correct your calculations using these factors. If calculations are correct, you should obtain <span class="math-container">$1.08321 × 10^{21}$$m^3$</span> as your correct answer.</p>

CC BY-SA 4.0
2023-06-18T11:52:24.673Z
2023-06-18T11:52:24.673Z
Arcturus
<p>I'm having trouble with this and am unsure what I'm doing wrong. Let's use Earth as an example.</p>
<p>Earth has a mass of <a href="https://www.google.com/search?q=earth%27s%20mass" rel="nofollow noreferrer">5,972,168,000,000,000,000,000,000 (5.97E+27) kg</a> and a density of <a href="https://www.google.com/search?q=earth%27s%20density" rel="nofollow noreferrer">5513.4 kg/m3 or 5.5134 g/cm3</a>.</p>
<p>Volume = mass / density.</p>
<p>The calculation gives me a result of 1,086,109,090,909,090,000,000,000.00 (1.09E+24) m3. However, the Earth's volume is
<a href="https://en.wikipedia.org/wiki/Earth" rel="nofollow noreferrer">1,083,210,000,000,000.00 m3</a>. That's a 1 billion times difference.</p>
<p>Is there a discreprancy with the units <a href="https://worldbuilding.stackexchange.com/questions/125543/given-the-mass-and-composition-of-a-planet-can-one-determine-what-the-radius-sh">this question advised to always use kg and m2</a>?</p>

CC BY-SA 4.0
2023-06-17T20:13:47.470Z
Earth's volume from wikipedia is $1.0832 \times10^{12} $ km, not $1.0832 \times10^{12} $  m. Correct this error and you'll see you calculated approximately the right answer the first time.
Connor Garcia
CC BY-SA 4.0
2023-06-17T20:53:34.187Z
I cannot correct the volume as this is the value I'm trying to calculate from the forumla. I can only change the mass or density. I can however fix my reference to know what the value should be, so thank you for pointing that out.
Harry Korone
CC BY-SA 4.0
2023-06-18T00:29:44.127Z
Your Earth mass is off by a factor 1000, that's jupiter mass. The mass of earth is is $6\cdot 10^{24}$kg.
planetmaker
<earth><mathematics>
Whis my planetary volume formula wrong? (volume = mass/density)
Harry Korone
# Whis my planetary volume formula wrong? (volume = mass/density)

(Asked by: username_0 on 2023-06-17)

I'm having trouble with this and am unsure what I'm doing wrong. Let's use Earth as an example.

Earth has a mass of [5,972,168,000,000,000,000,000,000 (5.97E+27) kg](https://www.google.com/search?q=earth%27s%20mass) and a density of [5513.4 kg/m3 or 5.5134 g/cm3](https://www.google.com/search?q=earth%27s%20density).

Volume = mass / density.

The calculation gives me a result of 1,086,109,090,909,090,000,000,000.00 (1.09E+24) m3. However, the Earth's volume is
[1,083,210,000,000,000.00 m3](https://en.wikipedia.org/wiki/Earth). That's a 1 billion times difference.

Is there a discreprancy with the units [this question advised to always use kg and m2](https://worldbuilding.stackexchange.com/questions/125543/given-the-mass-and-composition-of-a-planet-can-one-determine-what-the-radius-sh)?

**Tags:** earth, mathematics

> **Comments:**
> **username_1**: Earth's volume from wikipedia is $1.0832 \times10^{12} $ km, not $1.0832 \times10^{12} $  m. Correct this error and you'll see you calculated approximately the right answer the first time.  
> **username_0**: I cannot correct the volume as this is the value I'm trying to calculate from the forumla. I can only change the mass or density. I can however fix my reference to know what the value should be, so thank you for pointing that out.  
> **username_2**: Your Earth mass is off by a factor 1000, that's jupiter mass. The mass of earth is is $6\cdot 10^{24}$kg.  

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## 1 answers

### Answer by username_3 on 2023-06-18. Score: 2

# Your Earth mass is off by a factor of 1000

As @username_2 has pointed out, the mass of the earth is $6$$⋅$$10^{24}$ kg, instead of $6$$⋅$$10^{27}$.

Second, $km^{3}$ and $m^{3}$ are different things. $km^{3}$ is off $m^{3}$ by a factor of 1 billion ($1km^{3}$=$10^9m^{3}$).

Correct your calculations using these factors. If calculations are correct, you should obtain $1.08321 × 10^{21}$$m^3$ as your correct answer.


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