Designing a Miniature Solar System – Part 1

S is for Spacemen

 

o let’s get started making a little solar system of our own.
 

Using our own solar system as an example, gas giants tend to have lots of moons, some of which are approach the size of terrestrial planets. Saturn’s moon Titan, for example, is larger than the planet Mercury, while most other major moons orbiting the solar systems gas giants are approximately the size of Earth’s Moon.

Theories of planetary formation are in the midst an astronomical revolution as new planetary system are found.  So how how they form and how large a moon can grow is uncertain. Given that uncertainty, I’m going to make a lot of assumptions to get started.

First, most large moons form in the vicinity and at the same time as the formation of gas giant they orbiting.

Second, the mass and volume of large moons are proportional to the mass of the gas giants they orbit. Given this, larger gas giants will have larger moons. This is at best a rule of thumb. Saturn and Titan already violate this rule but most of the other major moons of the solar system seem to approximate this.

Now I would like to have a planetary system with at least three habitable moons of approximately the size of Mars or larger.  Given my assumptions, a super Jovian or brown dwarf would be needed to take the place of the Sun as the primary focus of this miniature solar system.  This gas giant will then need to be in an orbit in the habitable zone of the star they collectively orbit.

The reason I want to set it up this way is so travel between habitable worlds can take place in days instead of months or years.

Kepler’s Laws of Planetary motion.

T2 / R3 = (4 * pi2) / (G * MPrimary )

The variables for this are the Mass of the Primary in kilograms (MPrimary), the Radius of the moon’s orbit in meters (R) and the Period of the Moon’s orbit in seconds (T). Given any two of these variables the third can be calculated. (G is the universal gravitational constant 6.67300X10-11 m3 kg-1 s-2 and PI is the ratio of the circumference of a circle to its diameter.)

So if you measure the period of the orbit and its distance from the primary you can calculate the primary’s mass.

Something else to consider is that moons are usually tidally locked to the planet they orbit. In other words a moon’s orbital and rotational periods are equal so that one hemisphere always faces the planet it orbits and the orbital period determines the length of the moon’s day.

For example, an orbital period of a tidally locked moon that is 8 hours long has 4 hours of light and 4 hours of night. While a moon with an orbital period of 12 days will have 6 days of light and 6 days of night. This will definitely affect the weather and climate.

Another issue to consider is the tidal effects the moons will exert on each other. To calculate this, I am going to cheat and just used an approximation of the force of the tides on earth caused by the moon.

The force exerted on the earth by the moon is found by multiplying the mass of the moon by the cube of the distance to the moon.

Force = Mass Moon*Distance to Moon^3

The force of the moon’s tides cause an average height of the mid-ocean tidal bulge tide of about 0.367 meters and ground tides of .04 meters for the Earth.

If we use the force of the tide, mass and distance of the moon as a standard value of 1 we can use the formula to say that.

1 Force of Tide = 1 Mass of Moon * (1 Distance to moon)^3

We can then use this to approximate the tidal effects of different masses and distances to get the force of the tides. For example.

1 Moon Tide                Moon Mass                     Moon Distance^3

—————-            =          —————-  divided   ———————–

Sun Tide ?                    Sun Mass                         Sun Distance^3

or

1 Moon Tide                7.3477 * 1022KG                384399KM^3
—————-                =      ——————— divided ———————
Sun Tide ?                    1.9891 * 1030KG           (1.496 * 10^8KM)^3

 

Rearranging the equation gives:
Sun Tide ?          =  27,071,056 Moon Mass  divided  (389.1789 Moon Distance)^3

Sun Tide ?        = .459 times the size of the moon’s tide

We can use this to approximate the tides that affect our new worlds.

For now, I’m calling the Gas Giant my worlds orbit Ognom.

Ognom Mass KG

2.079E+28

Ognom Radius KM

70000

Ognom Volume KM^3

1.436755E+15

Ognom Density KG/M

1.447E+05

Ognom Standard Gravitational   Parameter

1.388E+18

Meters Cubed * Seconds Squared

And I am placing five major moons in orbit around Ognom

Name Kalmor Palenmor Malmor Balanmor Xalamor
SemiMajor Axis KM

450257

658709

1045635

1370169

2175008

SemiMajor Axis AU

3.01E-03

4.40E-03

6.99E-03

9.16E-03

1.45E-02

Eccentricity

0.00200

0.00100

0.00150

0.00200

0.03000

Inclination

0.03

0.2

2

3

5

Orbital Period Days

0.5898

1.0437

2.0874

3.1311

6.2622

Orbital Velocity (KM/S)

55.51349

45.896772

36.428292

31.82304

25.25797

Radius KM

1821.6

5285

3430

4025

3750

Radius (Earth = 1)

0.285607

0.8286297

0.5377861

0.631076

0.587959

Diameter KM

3643.2

10570

6860

8050

7500

Circumference KM

11445.45

33206.634

21551.326

25289.82

23561.94

Surface Area KM^2

4.17E+07

3.51E+08

1.48E+08

2.04E+08

1.77E+08

Surface Area (Earth = 1)

0.08

0.69

0.29

0.40

0.35

Mass KG

1.32E+23

2.50E+24

6.57E+23

1.17E+24

1.10E+24

Mass (Earth=1)

0.02

0.51

0.11

0.20

0.18

Volume

2.53E+10

6.18E+11

1.69E+11

2.73E+11

2.21E+11

Density Kg/M^3

5202

4050

3887

4273

4971

Surface Gravity Earth 1G

0.27

0.61

0.38

0.49

0.53

Surface Gravity M/S

2.649

5.983

3.727

4.808

5.211

Escape Velocity KM/S

3.11

7.95

5.06

6.22

6.25

DeltaV Liftoff to Orbit M/S

2196.48

5622.83

3575.17

4398.59

4420.24

DeltaV Liftoff to Orbit KM/S

2.20

5.62

3.58

4.40

4.42

Ocean Tides in Meters (1 Earth   Tide =  .367 Meters)
Kalmor Palenmor Malmor Balanmor Xalamor
On Kalmor By

78.4296093

0.8831796

0.425298

0.0607134

On Palenmor By

4.125072

3.2176782

0.919348

0.089353

On Malmor By

0.177039

12.2634191

9.686126

0.2162476

On Balanmor By

0.047996

1.9726196

5.4531149

0.5974989

On Xalamor By

0.007282

0.20377033

0.1293941

0.635047

Ground Tides in Meters (1 Earth   Tide = .04 Meters)
Kalmor Palenmor Malmor Balanmor Xalamor
On Kalmor By

8.5481863

0.0962594

0.046354

0.0066173

On Palenmor By

0.449599

0.3507006

0.100201

0.0097387

On Malmor By

0.019296

1.33661243

1.055709

0.0235692

On Balanmor By

0.005231

0.21499941

0.5943449

0.0651225

On Xalamor By

0.000794

0.0222093

0.0141029

0.069215

Next we’ll work on how long it takes to travel between these worlds.