Geosynchronous　Earth　Orbit　(GEO)　satellites,　which　can　relay　image　data　for　Low　Earth　Orbit　(LEO)　satellites,　play　an　important　role　in　remote　sensing.　With　the　development　of　satellite　technologies,　the　significantly　improved　computation　capabilities　of　GEO　satellites　have　enabled　space　service　computing,　through　which　GEO　satellites　can　provide　data　processing　services　before　forwarding　to　reduce　the　quantity　of　transmitted　data.　In　the　presence　of　multiple　LEO　satellites,　how　to　make　effective　use　of　limited　communication　and　computation　resources　in　GEO　satellites　has　become　crucial.　At　present,　the　research　on　satellite　resource　management　typically　focuses　on　either　communication　or　computation　resources.　Existing　resource　management　algorithms　are　usually　of　slow　convergence　speed,　which　limits　their　applicability　in　real-time　remote　sensing　scenarios.　Therefore,　we　propose　an　aggregated　resource　management　method　for　remote　sensing　applications.　We　first　propose　models　for　transmission　tasks　and　processing　tasks　of　remote　sensing　images.　Then　we　formulate　the　aggregated　resource　management　for　satellite　edge　computing　as　a　hybrid　Stackelberg　game　and　simplify　the　problem　to　speed　up　its　convergence　speed.　Then　we　propose　a　distributed　resource　management　algorithm　to　determine　the　optimal　strategies.　Simulation　results　show　that　the　proposed　method　can　quickly　obtain　the　optimal　resource　allocation　strategy　and　outperforms　typical　dynamic　iterative　algorithms　in　terms　of　service　quantity　and　throughput.