The dot’s speed (5.4 km/s) is too slow to keep it in a circular orbit (the centrifugal force is not as great as the gravity).

Centrifugal force: mv²/r

Gravity: GMm/r²

So the ratio of the two is v²r/GM.

Putting in numbers, v = 5400 m/s, M = 17.5x2.0x10³⁰kg and r = 360AU = 360x1.5x10¹¹m. The ratio is thus 0.67.

If gravity were larger than the centrifugal force, the dot might not be in an orbit at all: it might fly off into space. If they were equal, it would be in a circular orbit. As it is, it must fall closer to Twinky. As its velocity is currently perpendicular to Twinky, it must be at the furthest-out point (the ap-astron) at present. The orbit simulator shows that it will move in an elliptical orbit, taking several thousand years, and at its closest point it will be slightly less than 200 AU from Twinky.

What is the equilibrium temperature of the dot at the moment? If it is D metres from Twinky, r metres in diameter, and absorbs 80% of the light that falls on it, it will receive power given by

P = (80% x p r² L_sun)/(4p D²)

It will radiate a power (from the Stefan Boltzman equation) of

P = 80% x 4p r^{2 s} T⁴

Equating the two, and solving for T, we find that the temperature at present is around 220K (-53^o Celsius). When the dot is at its closest approach to Twinky, however, the temperature will be a balmy 300K (27^o Celsius).

So at present, it is bitter winter on the Dot, but at peri-astron it could be quite pleasant and Earth-like.

The power the Dot will reflect is 20% of the power it receives from Twinky, ie.

P = (20% x p r² L_sun)/(4p D²)

We can measure this power as well as the power emitted by Twinky in the same (B) wavelength band. We can thus solve for r, which turns out to be around 24,000km.

So: the dot is in orbit around Twinky. The orbit is quite eccentric. At present, it is as far from Twinky as it ever gets. In the absence of a greenhouse effect or such-like, it will currently be very cold on Twinky. 200 or so years from now, however, the dot will be much closer to Twinky, and the temperature could be quite pleasant.

The dot appears to be quite large: around 20,000km. This suggests that it is some small type of gas giant, or an extremely large rocky planet.