# Water from Ceres to Deimos

## approximate calculations

 Mars 1.52 AU 24.0 km/s 5.0 km/s Ceres 2.77 AU 17.9 km/s 0.5 km/s Deimos 1.35 km/s

Assume ice can be delivered to a catcher by impact. (WHAM!) We are only concerned with launching the water to Deimos intercept.

G = V²R ≅ 17.9² × 2.77 AU-km²/s² ≅ 24.0² × 1.523 AU-km²/s² ≅ 880 AU-km²/s²

Ceres Hohmann aphelion = sqrt( 880 * 2 × 1.52 / (( 2.77 + 1.52 ) × 2.77 ) ) = 15 km/s

Ceres Launch ≅ sqrt( ( 17.9 - 15 )² + 0.5² ) ≅ 2.95 km/s

Ceres Hohmann perhelion = sqrt( 880 * 2 × 2.77 / (( 2.77 + 1.52 ) × 1.52 ) ) = 27.3 km/s

Ceres to Deimos arrival velocity = sqrt( ( 27.3 - 24.0 )² + 2 × 1.35² ) ± 1.35 km/s ≅ 3.81 ± 1.35 km/s ( 2.46 to 5.16 km/s )

Mars Launch ≅ sqrt( 5² - 1.35² ) ≅ 4.8 km/s ... 1.6 times larger than Ceres launch

Mars to Deimos apoapsis velocity ≅ 0.68 km/s

Deimos arrival velocity = 0.67 km/s ... 0.27 times smaller than the lowest Ceres arrival

Ice launched from Ceres needs only a 0.5 km/s direct boost; the rest of the delta V can be provided with electric thrust engines. Those can also slow the delivery velocity at Deimos, if necessary. That's a lot of repeated delta V's, though, and the electric thrust could be used with a Mars/Deimos synchronous cycler system.

So ... it's complicated.