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Time domain astronomy was highlighted as a key science area for the 2020s in the Astro2020 Decadal Review. Both HST and JWST have the potential to make significant scientific contributions in probing the variable universe at moderate and longer timescales. HST has the advantage of a 30-year legacy of observations spanning the broadest range of celestial sources, and JWST’s ; JWST has the prospect of a 20-year lifetime, with unparalleled sensitivity at near- and mid-infrared wavelengths opens up opportunities in the high redshift universe. Phenomena include both photometric variations and astrometric motions.

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• Solicit input from the community on key science areas that can profit from monitoring observations by HST or JWSTexploit long time-baseline observations, based either on past observations or laying the foundation for future investigations;
• Identify science themes that should be prioritized for exploration by future General Observer programs and/or Archival analyses;
• Provide advice on the optimal timing for substantive follow-up observations and suggest mechanisms for enabling those observations;
• Comment on the appropriate scale of resources likely required to support those programs;
• Develop a specific concept for an observing program that will utilize JWST’s imaging and spectroscopic capabilities to probe transient phenomena at high redshift, with the goal of starting implementation of the program in JWST Cycle 2.

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