Without having SQL and database in front of me, can't verify this, but I "think" this should do it as long as all the columns from table A are distinct to the System Id...
SELECT
A.[solarSystemName]
,A.[solarSystemID]
,A.[constellationID]
,A.[x]
,A.[y]
,A.[z]
,A.[security]
,SUM(CASE WHEN B.[Planets] > 0 THEN 1 ELSE 0 END) as [Num_Planets]
,SUM(CASE WHEN B.[Moons] > 0 THEN 1 ELSE 0 END) as [Num_Moons]
,SUM(CASE WHEN B.[belts] > 0 THEN 1 ELSE 0 END) as [Num_Belts]
,0 as [Zero_1]
,0 as [Zero_2]
FROM [dbo].[mapSolarSystems] A
JOIN [dbo].[OtherTableName] B
ON A.[solarSystemID] = B.[solarSystemID]
GROUP BY
A.[solarSystemName]
,A.[solarSystemID]
,A.[constellationID]
,A.[x]
,A.[y]
,A.[z]
GO