# Small but Earthlike planet?

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#### neilsox

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If a planet had a core (size of Earth's moon)&nbsp;of platimum group metals = average density 20 and a thin crust with no mantal, radius 2000 kilometers, would the surface gravity be high enough to retain a nitrogen-oxygen atmosphere for a billion years or more?&nbsp;&nbsp; Neil

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#### mithridates

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<p>I don't know the answer but I like these subjects so I'm going to respond to bump the thread and make it easier to find.</p><p>If the mass is the same I don't see why not, but then again I could easily be wrong. </p> <div class="Discussion_UserSignature"> <p>----- </p><p>http://mithridates.blogspot.com</p> </div>

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#### Saiph

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<p>well, lets see:</p><p>Moons radius is ~1,700 Km...and you want a total radius of 2000km, with no mantal, the difference being entirely crustal material (at ~3 g/cm^3 if you wan't earthlike crust).</p><p>You state a core average density of 20 g/cm^3.</p><p>Density = mass/volume so mass=density*volume</p><p>Volume of a sphere is 4/3pi*R^3 giving...&nbsp;</p><p>Well, (170,000,000cm)^3 * 4/3pi * 20 g/cm^3 =&nbsp; 4.1x10^26g or 4.1x10^23 kg</p><p>So far, a factor of 10 less than earth's total mass.</p><p>Throw in the crustal material, which is a bit more complicated, being a hollow sphere.&nbsp; You have to find the volume of the whole thing as if it was a big sphere, then subtract out the inner core that's "empty".</p><p>[(200,000,000cm)^3*4/3pi - (170,000,000cm)^3*4/3pi ] * 3g/cm^3 =3.8x10^22g or 3.8x10^19 kg</p><p>Meaning the crust in this case doesn't add much to our total mass...</p><p>which is 4.10038 x10^23 kg.</p><p>&nbsp;</p><p>So, time for some rough calculations to avoid all those decimal places!</p><p>Mass = 1/10 of earths</p><p>Radius = roughly 1/3 of earths.</p><p>Gravity of earth = 1&nbsp; (yay! making life simple!)</p><p>Ge=me*m/re^2</p><p>Gp=mp*m/Rp^2</p><p>Ge/Gp=(Me*m / Re^2) / (Mp*m / Rp^2)</p><p>Ge/Gp =&nbsp; (Me*m / Re^2) * (Rp^2 / Mp*m)</p><p>"m" cancels</p><p>Substitute those into our equation (with canceled "m")&nbsp;</p><p>Ge/Gp =&nbsp; (10Mp / (3Rp)^2) * (Rp^2 / Mp)</p><p>Cancel out what we can giving us (we can't forget to ^2 the 3)</p><p>&nbsp;Ge/Gp =&nbsp; (10 / 9)</p><p>Bring the Gp over:</p><p>Ge = 10/9 Gp.</p><p>Or 10/9 Ge = Gp...</p><p>&nbsp;</p><p>Pretty close to earth standard gravity. (90%).</p><p>Given the right temperature ranges this planetoid could hold onto a nitrogen/oxygen atmosphere.&nbsp; It would have to be a bit colder than earth though.&nbsp; I don't have the book on hand I'd need to determine atmospheric retention at a given temperature...&nbsp;</p><p>&nbsp;</p> <div class="Discussion_UserSignature"> <p align="center"><font color="#c0c0c0"><br /></font></p><p align="center"><font color="#999999"><em><font size="1">--------</font></em></font><font color="#999999"><em><font size="1">--------</font></em></font><font color="#999999"><em><font size="1">----</font></em></font><font color="#666699">SaiphMOD@gmail.com </font><font color="#999999"><em><font size="1">-------------------</font></em></font></p><p><font color="#999999"><em><font size="1">"This is my Timey Wimey Detector.  Goes "bing" when there's stuff.  It also fries eggs at 30 paces, wether you want it to or not actually.  I've learned to stay away from hens: It's not pretty when they blow" -- </font></em></font><font size="1" color="#999999">The Tenth Doctor, "Blink"</font></p> </div>

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#### Saiph

##### Guest
<p>The cheap and dirty way, or rather without all the math is just to look at the change in M and R.</p><p>&nbsp;</p><p>Gravity is proportional to M, so bigger M = bigger gravity.&nbsp; M = 10x less...so gravity is 10x less.</p><p>Gravity is <em>inversely</em> proportional to R^2...so 3x less R gives 3x stronger gravity...wait!&nbsp; Common mistake there, we have to square that, so it's actually 9x stronger!</p><p>So it's 10x weaker from mass, but 9x stronger from radius giving us...not so coincidentally the ratio I obtained above, of Ge=10/9 Gp.&nbsp; Just about the same.</p><p>Radius saves the day!&nbsp;</p> <div class="Discussion_UserSignature"> <p align="center"><font color="#c0c0c0"><br /></font></p><p align="center"><font color="#999999"><em><font size="1">--------</font></em></font><font color="#999999"><em><font size="1">--------</font></em></font><font color="#999999"><em><font size="1">----</font></em></font><font color="#666699">SaiphMOD@gmail.com </font><font color="#999999"><em><font size="1">-------------------</font></em></font></p><p><font color="#999999"><em><font size="1">"This is my Timey Wimey Detector.  Goes "bing" when there's stuff.  It also fries eggs at 30 paces, wether you want it to or not actually.  I've learned to stay away from hens: It's not pretty when they blow" -- </font></em></font><font size="1" color="#999999">The Tenth Doctor, "Blink"</font></p> </div>

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#### MeteorWayne

##### Guest
Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>.Radius saves the day!&nbsp; <br />Posted by Saiph</DIV><br /><br />I'm sure your arm would agree... <img src="http://sitelife.space.com/ver1.0/content/scripts/tinymce/plugins/emotions/images/smiley-laughing.gif" border="0" alt="Laughing" title="Laughing" /> <div class="Discussion_UserSignature"> <p><font color="#000080"><em><font color="#000000">But the Krell forgot one thing John. Monsters. Monsters from the Id.</font></em> </font></p><p><font color="#000080">I really, really, really, really miss the "first unread post" function</font><font color="#000080"> </font></p> </div>

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