Deimos has an orbital speed of,
\({v}_{d}\) = 2*pi*23460/(30.313*60*60) = 1.351 kms-1
And so requires a centripetal force of,
\({F}_{d}\) = ((1.351)^2)/23460 = 0.0000778 kms-2
Gravity due to Mars at a distance of 23460 km is too low to account for this force. The gravity at this point from the equation 0.00783*(1-e^(-x/3390) is 0.000007732 where Mars gravity has been adjusted from 3.71 to 7.83. The model based on space density also fails. The mass of this moon is too small to attain a significant force to be orbiting at such high speed. The influence of gravity from Mars is greater.
Centripetal force = 0.000007732 + 2e15 / (3.22518e24 + 2e15)*0.000003 = 0.000007732 kms-2
where Deimos surface gravity is 0.000003 kms-2.
Deimos orbiting speed = (0.000007732 * 23460)^(0.5) = 0.425 kms-1
and a period of 2*pi*23460/(0.425*60*60) = 96.34 hrs.
At this distance from Mars, Deimos has a GPE of -26.517 km2s-2. GPE of Mars with the adjusted gravity value is -26.547 km2s-2. Therefore, the escape velocity of Deimos is
(2*(26.547-26.517))^0.5 = 0.245 kms-1 upwards.
Considering orbiting speed also, (0.245^2+0.425^2)^(0.5) = 0.491 kms-1. At an measured speed of 1.351 kms-1 Deimos has the escape velocity to leave Mars' gravity pull. And it seems, it is doing so slowly.
Speed due to \(\triangle GPE\) is \(\sqrt{3{g}_{d}{r}_{d}}\) = (3*0.000003*6.2)^(0.5) = 0.00747 kms-1 which is small.
The conclusion is, either Deimos is a spaceship capable of generating gravity towards Mars 10 times normal and so keep itself in orbit at high speed, or it is on its way leaving the gravitational field of Mars.
