This paper deals with present-day gravity changes inresponse to the evolving Greenland ice sheet. We present a detailedcomputation from a three-dimensionalthermomechanical ice-sheet model which is interactivelycoupled with a self-gravitating spherical visco-elastic bedrock model.The coupled model is run over the last two glacial cycles to yield theloading evolution over time. Based on both the ice-sheet's long-term historyand its modern evolution averaged over thelast 200 years, results are presented of the absolute gravity trend that wouldarise from a ground surveyand of the corresponding geoid rate of change a satellite would see from space.The main results yield ground absolute gravity trends of the order of +/-1 microgal/yr over the ice-free areasand total geoid changes in the range between -0.1 and +0.3 mm/yr.These estimates could help to design futuremeasurement campaigns by revealing areas of strongsignal and/or specific patterns, although there are uncertainties associated withthe parameters adopted for the Earth's rheology and aspects of the ice sheetmodel.Given the instrumental accuracy ofa particular surveying method, these theoretical trends could also be useful toassess the required duration of a measurement campaign. According to our results,the present-day gravitational signal is dominated by the responseto past loading changes rather than current mass changes of the Greenland icesheet.We finally discuss the potential of inferring thepresent-day evolution of the Greenlandice sheet from the geoid rate of change measured by the future geodeticGRACE mission. We find that despite the anticipatedhigh quality data from satellites, such a methodis compromised by the uncertainties in the Earth model,the dominance of isostatic recovery on the current bedrock signal,and other inaccuracies inherent to the method itself.