Anons, just a little digging on the Judges who make up the D.C. Circuit Ct. of Appeals and a section of the Federal Rules regarding Writs of Mandamus:
U.S. Court of Appeals D.C. Circuit - Judges
Sri Srinivasan, Chief Judge (5/2013, Chief Judge 2/2020)
Karen LeCraft Henderson (7/1990)
Judith W. Rogers (3/1994)
David S. Tatel ( _ /1994)
Merrick B. Garland (4/1997, Chief Judge 2/2013 - 2/2020)
Thomas B. Griffith (6/2005)
Patricia A. Millett (12/2013)
Cornelia T.L. Pillard (12/2013)
Robert L. Wilkins (1/2014)
Gregory G. Katsas (12/2017)
Neomi Rao (3/2019)
Harry T. Edwards (1980, senior status 2005)
Laurence H. Silberman (10/1985, senior status 11/2000)
Stephen F. Williams (6/1986, senior status 9/2001)
Douglas H. Ginsburg (11/1986, senior status 11/2011)
David B. Sentelle (10/1987, senior status 2/2013)
A. Raymond Randolph (7/1990, senior status 11/2008)
https://www.cadc.uscourts.gov/internet/home.nsf/Content/VL+-+Judges+-+ARR
Federal Rules of Appellate Procedure
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Rule 21. Writs of Mandamus and Prohibition, and Other Extraordinary Writs
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(b) Denial; Order Directing Answer; Briefs; Precedence.
(1) The court may deny the petition without an answer. Otherwise, it must order the respondent, if any, to answer within a fixed time.
(2) The clerk must serve the order to respond on all persons directed to respond.
(3) Two or more respondents may answer jointly.
(4) The court of appeals may invite or order the trial-court judge to address the petition or may invite an amicus curiae to do so. The trial-court judge may request permission to address the petition but may not do so unless invited or ordered to do so by the court of appeals.
(5) If briefing or oral argument is required, the clerk must advise the parties, and when appropriate, the trial-court judge or amicus curiae.
(6) The proceeding must be given preference over ordinary civil cases.
(7) The circuit clerk must send a copy of the final disposition to the trial-court judge.
https://www.law.cornell.edu/rules/frap/rule_21