Building a Miniture Solar System – Part 3

D is for Droid


esigning a Miniature Solar System Part 3


A Real Worlds Example – Gliese 677 C

A team of astronomers announced in June of 2013 the possible existence of three planets in the habitable zone of a star Gliese 677C.

By taking new observations of the star along with using a more fine-tuned analysis of previously collected data they were able to determine that GJ 677C had at least five planets with some indications of a two other planets orbiting the star. The more interesting result is that three of the confirmed planets are within the habitable zone for this star.

The articles can be found here

A dynamically-packed planetary system around GJ 667C with three super-Earths in its habitable zone

A nearby star with three potentially habitable worlds

Gliese 667 is a triple star system in the constellation Scorprius. In the typically naming conventions used for stars by astronomers, the individual stars of the system are named A, B and C. The A and B stars are both K type dwarfs that are about 70% the size of the Sun. The A and B stars orbit each with in a fairly eccentric orbit where they get as close as 5 AU then separate out to a distance of 20 AU.

For my purpose of trying to design a miniature solar system the third star “C” is more interesting.

Gliese 667 C is an M type red dwarf that has one third the mass of the Sun. It orbits the other two stars of the system at a current distance of 230 AU.

Below is the basic data for the star

GJ 667C

Mass KG                          6.16451E+29
Mass % of Sun               0.31
Radius % of Sun            0.4

Distance Parsecs          6.8
Distance Light Years  22.178
Right Ascension           17 H 18 M 57 S
Declination                    31 Deg 44 M 39 S
Apparent Magnitude 10.25
Absolute Magnitude  11.03
Spectral Class                M1.5V
Age (estimated)           2 to 10 Billion years. (In other words it is somewhere on the main sequence)
Habitable Zone            .11 to .25 AU from the star

As with the names of the stars themselves, astronomers searched deep within their creative souls and named them B, C, D, E, F, H and G. The letters were assigned in the order of discovery, not by their distance from the start. A list of the planets in order from the sun is B, H, C, F, E,D, and G. (Note: Planet H and G still needs to be verified.)

Below is the basic data about the planets orbiting GJ667C. Some of the data is conjectural and a best guess. I left out the data for the B and G planets to save space.

Name H C F E D
SemiMajor Axis KM 13,359,280 18,700,000 23,337,600 31,864,800 41,289,600
SemiMajor Axis AU 8.93E-02 1.25E-01 1.56E-01 2.13E-01 2.76E-01
Eccentricity 0.06000 0.02000 0.03000 0.02000 0.03000
Inclination (Unknown) 0 0 0 0 0
Orbital Period Days 17.5061 28.9920 40.4203 64.4885 95.1210
Orbital Velocity (KM/S) 55.49568 46.90616 41.98775 35.93313 31.56678
Radius KM (Estimated) 11750 10000 8000 9000 11200
Radius (Earth = 1) 1.84227 1.56789 1.254312 1.411101 1.756036
Diameter KM (Estimated) 23500 20000 16000 18000 22400
Circumference KM 73827.43 62831.85 50265.48 56548.67 70371.68
Surface Area KM^2 1.73E+09 1.26E+09 8.04E+08 1.02E+09 1.58E+09
Surface Area (Earth = 1) 3.39 2.46 1.57 1.99 3.08
Mass KG (Estimated) 3.55E+25 2.30E+25 1.16E+25 1.60E+25 3.11E+25
Mass (Earth=1) 5.94 3.86 1.94 2.68 5.21
Volume 6.80E+12 4.19E+12 2.14E+12 3.05E+12 5.88E+12
Density Kg/M^3 (Estimated) 5219 5501 5400 5240 5285
Surface Gravity Earth 1G 1.75 1.57 1.23 1.35 1.69
Surface Gravity M/S 17.143 15.380 12.078 13.183 16.549
Escape Velocity KM/S 20.07 17.54 13.90 15.40 19.25
DeltaV Liftoff to Orbit M/S 14191.29 12400.56 9828.87 10891.65 13613.12
DeltaV Liftoff to Orbit KM/S 14.19 12.40 9.83 10.89 13.61
Liftoff Acceleration M/S (Input) 15.00 20.00 15.00 10.00 15.00

All of these worlds have semi-majors axis less than the 57,909,100 KM of Mercury. If they orbited the sun they would all be within the orbit of Mercury. Gliese 667 C has 1.5% of the Sun’s luminosity and is so faint that an Earth like temperature can exist at less than half the orbital distance of Mercury.

Depending on the atmospheric makeup of theses worlds, their albedo, the insolation and any greenhouse effects, conditions on the planets could be habitable for human interstellar voyagers.

However the observations of these worlds do not give any indication of what their atmospheres, if any, are made of.

Given the example of our own solar system, most terrestrial planets above the size of mars do have an atmosphere. The atmosphere could be oxygen nitrogen, carbon dioxide, methane or something else. Earth for example had a methane based atmosphere for several hundred million years before oxygen nitrogen became dominate.

Also all of these worlds are larger in mass then Earth. Their surface gravity would range from 1.23 to 1.75 times that of Earth. I you stood on these worlds admiring the scenery you would weigh about a quarter to three/fourths more than you do on Earth.  They are not worlds for weight watchers.

It is thought that because of their proximity to their sun that these worlds would be tidally locked with one hemisphere constantly exposed to the sun and the other looking out into the darkness. However astronomers also thought the same for Mercury before 1960’s when the radar measurements showed it was not tidally locked but was in a 3/2 orbital resonance with the sun. Mercury has a 3/2 ratio for its orbital/rotational period. For each three orbits it makes around the sun it rotates around it axis two times. This is due to the eccentricity of its orbit. Another force that might break tidal locking is the interacting tidal forces between the planets can effect each other’s rotational period. So we currently don’t know what their length of each of these planets days are. Their days can be the same as its orbital periods or they can be significantly shorter, or longer. If they are tidally locked, we might have to revive the old idea of a habitable area at the twilight zone of tidally locked planets.

Climatically speaking, if these worlds are tidally locked this would the constant head from the sun shining on the daylight hemisphere would cause strong winds to develop from the atmospheric heating. These winds would flow out around the world until they cross over into the night time hemisphere where it would be much colder. The resulting climate and weather patterns would be very different than what we are used to on Earth.

But back to the how to get around quicker in a science fiction solar system.

I punched in the number and get the following Hohmann transfer information for this solar system.

To H
From Travel Time Days Phase Angle Synodic Days Total ΔV in KM/S
C 11.50 -56.58 44.18 -8.52
F 14.08 -109.73 30.88 -13.25
E 19.27 -216.37 24.03 -18.69
D 25.60 -346.53 21.45 -22.21
To C
From Travel Time Days Phase Angle Synodic Days Total ΔV in KM/S
H 11.50 37.14 44.18 8.53
F 17.27 -34.49 102.54 -4.90
E 22.78 -102.96 52.67 -10.78
D 29.44 -185.66 41.70 -14.76
To F
From Travel Time Days Phase Angle Synodic Days Total ΔV in KM/S
H 14.08 54.52 30.88 13.25
C 17.27 26.15 102.54 4.90
E 25.99 -51.52 108.30 -6.02
D 32.93 -113.27 70.29 -10.21
To E
From Travel Time Days Phase Angle Synodic Days Total ΔV in KM/S
H 19.28 72.40 24.03 18.70
C 22.79 52.78 52.67 10.78
F 25.99 34.89 108.30 6.02
D 39.66 -41.37 200.25 -4.35
To D
From Travel Time Days Phase Angle Synodic Days Total ΔV in KM/S
H 25.60 83.09 21.45 22.22
C 29.45 68.55 41.70 14.77
E 39.66 29.92 200.25 4.35
F 32.93 55.38 70.29 10.21

Travel times can be as short as 11.5 to 39.66 days. Synodic periods range from 21 to over 200 days between launch windows. The total ΔV ranges from 4.35 to 22.22 KM/S. That is a significant improvement over the Earth to Mars travel time of 9 months that can occur once every 25 months in our own solar system but still takes long term planning with travel times from a month to 3/4th of a year. Also the ΔV requirement can be higher than what is needed to go from Earth to Mars although the actual distance travelled if far less. The heavier surface gravity also makes it more difficult to lift off the planet’s surface.

Any questions or comments would be appreciated. Also as I easily make error with math, feel free to let me know of any math errors you might find.


4 thoughts on “Building a Miniture Solar System – Part 3

  1. What do you mean by delta V for Hohmann transfer?

    If you mean departing from one planetary surface to land on another planetary surface, all your figures are too small.

    If you mean departing one planetary orbit to park in an orbit about another planet, your delta Vs are too large.

    Your delta V figures seem to be the sum of the departure and arrival Vinf.

    • I am using the sum of the departure and arrival Vinf to see what is required to move from one planets orbit to another. I was more intrested in the actual travel times and synodic period of these planets. I am not including the Δv required to lift off from a planet’s surface because what I am interested in seeing how quickly or easily it is to move around in a solar system that is much smaller then our own.

      I’m using the following to calcuate the Δv
      total deltaV

      Δv1 = Change in velocity when we depart.
      Δv2 = Change in velocity when we arrive.
      Δvtotal = Total change in velocity
      r1 = Radius of the Interior (Or Inferior) Planet’s Orbit
      r2 = Radius of the Exterior (Or Superior) Planet’s Orbit
      µ = Standard Gravitation Parameter

      If this is not correct or the calculations are wrong, please explain.

      • I agree with your travel times as well as synodic periods. I also agree with your figures if they’re the sum of departure and arrival Vinf. But the sum of these Vinfs aren’t your delta V.

        I write about Vinf and hyperbolic orbits here:

        Departing the planet for Hohmann injection requires a hyperbolic orbit wrt planet. Hyperbolic velocity is sqrt(Vesc^2 + Vinf^2). I like to visualize hyperbolic velocity as the hypotenuse of a right triangle with Vesc and Vinf as legs.

        If you’re going from one planet orbit to another, you’d subtract the planet orbit’s velocity from hyperbolic velocity to get Hohmann injection burn as well as burn to depart Hohmann for a parking orbit at destination planet.

        Your delta Vs are too high for this system as well as Mongo’s moons.

      • Sorry for the long delay in replying. I wanted to double check my work.

        I am just getting the departure and arrival orbital velocities. I am not attempting to patch conic sections or hyperbolic velocity. I’m just looking for the change of velocity needed to get from orbit A to orbit B as a general way to compare manuvering around different size solar systems.

        I was just using the following.

        Orbital Manuvering

        Than you for checking and for the feedback.

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