## TWO/1 Year And Tidal Lock

STEP ONE: Consult 2.1.1 to calculate the year of the planet.

STEP TWO: Check 2.1.2 to determine if the planet is tidally locked to the primary.

Table 2.1.1 Year (orbital period around primary)

Local Year (in earth years) = (D3 / M)0.5

 ... where: D is the orbital distance (in AU) M is the mass of the star (in sol masses)

Technically M should be for combined planet and primary but the planet's mass in normally trivial ... combine the masses when the planet is a superjovian, brown dwarf, or companion star.

Table 2.1.2 Tidal Lock

Calculate the tidal force the primary exerts on the planet:

T = (M x 26,640,000) / (D x 400)3

 ... where: D is the orbital distance (in AU) M is the mass of the star (in sol masses)

Technically M should be for combined planet and primary but the planet's mass in normally trivial ... combine the masses when the planet is a superjovian, brown dwarf, or companion star.

From that calculate:

L = [ (1d10 x 0.03) + 0.83 ] x T x A / 6.6

 ... where: T is the tidal force calculated above A is the system age (in Gy)

If L is greater than 1 then the world is tidally locked to the primary.

EFFECTS OF YEAR LENGTH:

If an Earth-like world has seasons (due to axial tilt or eccentricity), the longer the year is the more notable the differences tend to be between the seasons. This is far more affected by axial tilt and eccentricity, however.

TIDALLY LOCKED WORLDS:

A world which is tidally locked to the primary experience huge differences in temperature over the planetary surface. On a gas giant or superjovian, this might produce immense wind patterns. A terrestrial planet will have one "hot pole" and a "cold pole", and it is possible that the world might be habitable in certain regions - typically the hot pole or the twilight region. APPENDIX/4 describes tidally locked terrestrial planets in more detail.

ALTERNATIVES TO TIDAL LOCK:

When the tidal force is around 6-8, it is possible that a world isn't locked but in a regular rotation. Most commonly, the world has a fairly eccentric orbit (0.1-0.2) and has a day of two-thirds or half the year (thus, the slightly deformed planet "lines up" at closest separation). Mercury is an example of a world in this situation. Note that for regular rotation of this kind to occur the world must have a rather distinctive eccentricity. Faster regular orbits of this kind occur with higher eccentricities. It is likely that a world with high eccentricity would eventually settle in the closest "stable" eccentricity range.

 Eccentricity Day:YearRatio 0.00 1:1 0.21 3:2 0.39 2:1 0.57 5:2 0.72 1:1 0.87 7:2

Another alternative may be a somewhat chaotic rotation, due to tidal influence from other bodies (such as a close binary or a superjovian orbiting nearby). Small chunks may be so irregular that they are easily put into chaotic motion.

TIDALLY LOCKED WORLDS AND SATELLITES:

Tidally locked worlds (due to high tidal force from the primary, and not merely a very slow rotation or a very old system) typically don't have moons. (The tidal force would lock them too, and the stress would either tear them apart or rip them away, into orbits where they may later impact with the world.) However, a special case with a large enough moon that can lock the planet and moon together may prevent tidal lock to the star, at least for a while, if the lunar tidal force is greater than the solar tidal force. Ring systems may survive for a while around tidally locked worlds, and so might very small chunk-moons. However, worlds which aren't locked due to very high tidal forces but merely by an abnormally slow rotation might have satellites and rings.