Calculating a planet's mass & gravitational pull

[dogscoff]

Help!

I'm putting together a spreadsheet to help me create realistic planets for SE4 story writing purposes.

I type in the diameter (km) and surface area covered by ocean (%), and it automatically gives me the planet's circumference (km), total surface area (km^2), land and water surface area(km^2), and compares all these values to Earth for easy reference.

What I'd like in addition is to be able to plug in a Mean Density value (gr./cm^3) for the planet and from that get an estimate of the planet's surface gravity.

Unfortunately I don't know the calculations necessary for this, despite lengthy google searches. Can anyone help?

I assume I'll need the planet's volume, but I should be able to get that from the diameter. I appreciate that any figures I come up with won't be utterly accurate (because I'm working with spheres and planets aren't quite spherical, and because surface gravity is also affected by rotation) but they'll be good enough for my purposes.

[Suicide Junkie]

Just multiply average density by volume.
kg/m^3 x m^3 = kg

Useful for rocky/icy planets, but will be trouble on gas giants due to the extreme changes in density going down to the core.

For surface gravity, F= GMm/r^2
Where gravitational constant G = 6.67300 × 10-11 m3 kg-1 s-2
Big and little masses M & m and the surface radius.
Little m will cancel out when you do F=ma to get the acceleration.
A = GM/R^2
Just remember to use the same units throughout.

PS:
Have fun picking a surface for your gas giant, and don't count any material above the surface in your mass calculation

[ August 20, 2003, 15:24: Message edited by: Suicide Junkie ]

[dogscoff]

Thanks S_J- a few questions:

kg/m^3 x m^3 = kg

So that's kilograms per metre cubed times metres cubed. My "volume" value is in kilometres cubed, so do I just divide by 1000 to get metres cubed?

Where gravitational constant G = 6.67300 × 10-11 m3 kg-1 s-2

Glurp! so if my distant maths lessons are correct, that would be -6.67300 with the decimal place moved 11 spaces to the right. Correct? What does the kg-1 s-2 mean?

A = GM/R^2

so M in this one is the mass of the planet as calculated above.

If I run Earth's vital statistics through the above treadmill I should get a value somewhere near 1, is that right?

[Slick]

1 cubic kilometer = 1,000,000,000 cubic meters (i.e. 1000^3 cubic meters)

Yes, 10^-11 means move the decimal 11 places to the left.

The kg-1 and s-2 refer to exponents in this limited UBB system. Negative means in the denominator, so the units would be: m^3 / [kg x s^2]

Slick.

[dogscoff]

1 cubic kilometer = 1,000,000,000 cubic meters (i.e. 1000^3 cubic meters)

Aha! So if I multiply the result by 1000000000... Yes, i get a value for Earth & Mars masses that (more or less) matches what I find on websites. Excellent, thanks, slick.

Yes, 10^-11 means move the decimal 11 places to the left.

OK, I'll plug that in.

The kg-1 and s-2 refer to exponents in this limited UBB system. Negative means in the denominator, so the units would be: m^3 / [kg x s^2]

Ummm... I didn't understand any of that. Sorry, can you put it into language that can be understood by someone of my high mean density?

=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=

Tomorrow I'm going to have a go at putting all of this functionality into java so I can offer it on my website.
Planned features:
-flexible input values (ie it can automatically calculate circumference from diameter or vice versa.)
-Side by side comparison with a selectable "benchmark" planet (Earth, Mars, Jupiter, Plenty... any others I should have?
-Choose between raw data comparison or proportional comparison (ie Planet X has 125% earth's land surface area)
-Variable input units (miles or kilometres etc)

Anyone likely to use this? I doubt it will see a lot of usage, but thought it might be a handy toy for sci-fi writers. Any particular features I ought to implement? Even if no-one wants it I'll do it anyway as a programming excercise for myself.

[Baron Munchausen]

Originally posted by Suicide Junkie:
Just multiply average density by volume.
kg/m^3 x m^3 = kg

Useful for rocky/icy planets, but will be trouble on gas giants due to the extreme changes in density going down to the core.

For surface gravity, F= GMm/r^2
Where gravitational constant G = 6.67300 × 10-11 m3 kg-1 s-2
Big and little masses M & m and the surface radius.
Little m will cancel out when you do F=ma to get the acceleration.
A = GM/R^2
Just remember to use the same units throughout.

PS:
Have fun picking a surface for your gas giant, and don't count any material above the surface in your mass calculation

Actually, don't forget the stuff overhead when figuring gravity. It has mass, too. The gravity inside a gas giant could be very weird. The atmospheric pressure is probably a more predictable problem.

[Baron Munchausen]

Originally posted by dogscoff:

Tomorrow I'm going to have a go at putting all of this functionality into java so I can offer it on my website.
Planned features:
-flexible input values (ie it can automatically calculate circumference from diameter or vice versa.)
-Side by side comparison with a selectable "benchmark" planet (Earth, Mars, Jupiter, Plenty... any others I should have?
-Choose between raw data comparison or proportional comparison (ie Planet X has 125% earth's land surface area)
-Variable input units (miles or kilometres etc)

Anyone likely to use this? I doubt it will see a lot of usage, but thought it might be a handy toy for sci-fi writers. Any particular features I ought to implement? Even if no-one wants it I'll do it anyway as a programming excercise for myself.[/QB]

Aaron Hall? You ought to share it with him. It might improve SE V.

[Suicide Junkie]

The stuff above you will cancel out with the stuff at the same height on the other sides of the planet.
The stuff above your horizon pulls you away, while the stuff below your horizon at the same altitude pulls you towards (weaker due to distance, but more mass) Given reasonably constant density from one side to the other, it cancels out.

Stormy weather would make for small differences.
Sunlight heating one side would make for bigger differences.
But the density can't vary by that much, since the high pressure air will just blow into the low pressure zone and equalize it.

[Slick]

The kg-1 and s-2 refer to exponents in this limited UBB system. Negative means in the denominator, so the units would be: m^3 / [kg x s^2]

Ummm... I didn't understand any of that. Sorry, can you put it into language that can be understood by someone of my high mean density?

--------------------------------------------

I appologize for being hard to understand. The limitations of this UBB make it hard to use normal mathematical notation.

The units of the gravitational constant G are:

code:

---

                    3

                   m

           ------------------

                       2

               (kg) (s) 

---

Hope this helps.

Slick.

[Fyron]

quote:
--------------------------------------------------------------------------------

Where gravitational constant G = 6.67300 × 10-11 m3 kg-1 s-2

--------------------------------------------------------------------------------

Glurp! so if my distant maths lessons are correct, that would be -6.67300 with the decimal place moved 11 spaces to the right. Correct? What does the kg-1 s-2 mean?

Not quite. It is not negative, just really close to 0. A negative exponent does not change the sign of the base number.