<PAGE>   1
                                                                    EXHIBIT 3.11

                       LIMITED LIABILITY COMPANY AGREEMENT

                                       OF

                              IRIDIUM (POTOMAC) LLC


       This LIMITED LIABILITY COMPANY AGREEMENT OF IRIDIUM (POTOMAC) LLC dated
as of February 17, 1999 (this "Agreement") is made by IRIDIUM OPERATING LLC, a
Delaware limited liability company, and the sole member (the "Member") of
Iridium (Potomac) LLC (the "Company").

       WHEREAS, the Member has formed the Company as a limited liability company
pursuant to and in accordance with the Delaware Limited Liability Company Act (6
Del. C. Section 18-101, et seq.), as amended from time to time (the "Act"), and
hereby establishes the following:

       1.     Name. The name of the Company is IRIDIUM (POTOMAC) LLC. The
              business of the Company may be conducted under any other name
              deemed necessary or desirable by the Member in order to comply
              with local law.

       2.     Purpose. The purpose for which the Company is organized is any
              lawful purpose permitted pursuant to the Act.

       3.     Registered Office. The address of the registered office of the
              Company in the State of Delaware is c/o The Corporation Trust
              Company, 1209 Orange Street, City of Wilmington, County of New
              Castle, Delaware.

       4.     Registered Agent. The name and address of the registered agent of
              the Company for service of process on the Company in the State of
              Delaware is the Corporation Trust Company, 1209 Orange Street,
              City of Wilmington, County of New Castle, Delaware.

       5.     Member. The name and the business, residence or mailing address of
              the Member is as follows:

                  Name                                 Address

              IRIDIUM OPERATING LLC                1575 Eye Street, N.W.
                                                   Washington, D.C. 20005


                                       1
<PAGE>   2



       6.     Powers; Authorized Officers; Authorized Signatories. The power and
              authority to manage and conduct the business and affairs of the
              Company shall be vested in the sole Member, acting through its
              Authorized Officers. The Authorized Officers are, and each of them
              hereby is, designated as an authorized person within the meaning
              of the Act, to execute, deliver and file any certificates (and any
              amendments or restatements thereof) necessary for the Company to
              do business in a jurisdiction in which the Company may wish to
              conduct business. Subject to paragraph 7, any Authorized Officer
              shall have the power and authority to do any and all acts
              necessary or convenient to or for the furtherance of the purpose
              described herein, including all powers, statutory or otherwise,
              possessed by the Member under the laws of the State of Delaware.
              Subject to paragraph 7, any decisions regarding any matter
              involving or affecting the Company shall be made by any Authorized
              Officer, acting singly or jointly.

       7.     Restriction on Powers. Notwithstanding any other provision of this
              Agreement and any provision of law, the Company shall not, without
              the written consent of the Chairman or the Vice Chairman and Chief
              Executive Officer of the Member, (a) dissolve or liquidate, in
              whole or in part, or institute proceedings to be adjudicated
              bankrupt or insolvent, (b) consent to the institution of
              bankruptcy or insolvency proceedings against it or to
              reorganization or relief under any applicable federal or state law
              relating to bankruptcy or insolvency, (c) file a petition seeking
              reorganization or relief under any applicable federal or state law
              relating to bankruptcy or insolvency, (d) consent to the
              appointment of a receiver, liquidator, assignee, trustee,
              sequestrator (or other similar official) of the Company or a part
              of its property, (e) make a general assignment for the benefit of
              creditors, (f) admit in writing its inability to pay its debts
              generally as they become due, (g) take any corporate action in
              furtherance of the actions set forth in clauses (a) through (f) of
              this paragraph 7, or (h) admit additional members.

       8.     Authorized Officers. For Purposes of this Agreement the term
              Authorized Officers shall mean the Chairman, Vice Chairman and
              Chief Executive Officer, any Vice President, the Secretary or any
              Assistant Secretary of the Member.

       9.     Liability of Member. The Member shall not have any liability for
              the obligations or liabilities of the Company except to the extent
              provided in the Act.

       10.    Amendment. This Agreement may not be changed or amended or
              observance of any provisions by the Company waived without the
              consent of any of the Chairman or the Vice Chairman and Chief
              Executive Officer of the Member.


                                       2
<PAGE>   3

       11.    Governing Law. This Agreement shall be governed by, and construed
              under, the laws of the State of Delaware, all rights and remedies
              being governed by said laws.

       12.    Dissolution. The Company shall dissolve, and its affairs shall be
              wound up, upon the first to occur of the following: (a) December
              31, 2095, (b) the written consent of the Member, (c) the
              bankruptcy or dissolution of the Member or (d) the entry of a
              decree of judicial dissolution under Section 18-802 of the Act.

       IN WITNESS WHEREOF, the undersigned, intending to be legally bound 
       hereby, has duly executed this Limited Liability Company Agreement as 
       of the 17th day of February, 1999.

                                                 IRIDIUM OPERATING LLC



                                                 By:
                                                    --------------------
                                                 Name:
                                                 Title:


                                       3