Mobile object analysis is a well-studied area of transportation and geographic information science (GIScience). Mobile objects may include people, animals, or vehicles. Time geography remains a key theoretical framework for understanding mobile objects' movement possibilities. Recent efforts have sought to develop probabilistic methods of time geography by exploring questions of data uncertainty, spatial representation, and other limitations of classical approaches. Along these lines, work has blended time geography and kernel density estimation in order to delineate the probable locations of mobile objects in both continuous and discrete network space. This suite of techniques is known as time geographic density estimation (TGDE). The present paper explores a new direction for TGDE, namely the creation of a density-based accessibility measure for assessing mobile objects' potential for interacting with opportunity locations. As accessibility measures have also garnered widespread attention in the literature, the goal here is to understand the magnitude and nature of the opportunities a mobile object had access to, given known location points and a time budget for its movement. New accessibility measures are formulated and demonstrated with synthetic trip diary data. The implications of the new measures are discussed in the context of people-based vs. placed-based accessibility analyses.