Exhibit 4.1

RIGHTS AGREEMENT SECOND AMENDMENT

This Second Amendment (this “Amendment”), dated as of February 9, 2012 to the Rights Agreement, dated as of June 8, 2011 and amended as of December 9, 2011 (the “Rights Agreement”), is between GeoEye, Inc., a Delaware corporation (the “Company”), and Computershare Shareowner Services, LLC (f/k/a Mellon Investor Services LLC), a New Jersey limited liability company (the “Rights Agent”).

WHEREAS, the Company and the Rights Agent have heretofore executed and entered into the Rights Agreement;

WHEREAS, pursuant to Section 26 of the Rights Agreement, the Company may from time to time supplement or amend the Rights Agreement in accordance with the provisions of Section 26 thereof and the Company desires and directs the Rights Agent to so amend the Rights Agreement; and

WHEREAS, all acts and things necessary to make this Amendment a valid agreement according to its terms have been done and performed, and the execution and delivery of this Amendment by the Company and the Rights Agent have been in all respects authorized by the Company and the Rights Agent.

NOW, THEREFORE, in consideration of the foregoing premises and mutual agreements set forth in the Rights Agreement and this Amendment, the parties hereto agree as follows:

1. Section 1.1 of the Rights Agreement is hereby modified and amended to read in its entirety as follows:

1.1 “Acquiring Person” shall mean any Person who or which, together with all Affiliates and Associates of such Person, shall be the Beneficial Owner of 30% or more of the Common Stock then outstanding, but shall not include (i) an Exempt Person or (ii) any Existing Holder, unless and until such time as such Existing Holder shall become the Beneficial Owner of one or more additional shares of Common Stock (other than pursuant to a dividend or distribution paid or made by the Company on the outstanding Common Stock in Common Stock, or pursuant to a right to convert or a conversion into Common Stock of outstanding Series A Convertible Preferred Stock in respect of accrued but unpaid dividends on the Series A Convertible Preferred Stock, or pursuant to an adjustment to the conversion price for the Series A Convertible Preferred Stock as contemplated by Section (3)(e) of the Series A Certificate of Designations, or pursuant to a split or subdivision of the outstanding Common Stock), unless upon acquiring such Beneficial Ownership, such Existing Holder does not Beneficially Own 30% or more of the Common Stock then outstanding. Notwithstanding the foregoing, no Person shall become an “Acquiring Person” as the result of an acquisition of Common Stock by the Company which, by reducing the number of shares outstanding, increases the proportionate number of shares Beneficially Owned by such Person to 30% or more of the Common Stock then outstanding; provided, however, that if a Person shall become the Beneficial Owner of 30% or more of the Common Stock then outstanding solely by reason of share purchases by the

Company and shall, after such share purchases by the Company, become the Beneficial Owner of one or more additional shares of Common Stock (other than pursuant to a dividend or distribution paid or made by the Company on the outstanding Common Stock in Common Stock, or pursuant to a right to convert or a conversion into Common Stock of outstanding Series A Convertible Preferred Stock in respect of accrued but unpaid dividends on the Series A Convertible Preferred Stock, or pursuant to an adjustment to the conversion price for the Series A Convertible Preferred Stock as contemplated by Section (3)(e) of the Series A Certificate of Designations, or pursuant to a split or subdivision of the outstanding Common Stock), then such Person shall be deemed to be an “Acquiring Person” unless, upon becoming the Beneficial Owner of such additional Common Stock, such Person does not Beneficially Own 30% or more of the Common Stock then outstanding. Notwithstanding the foregoing, if the Board determines in good faith that a Person who would otherwise be an “Acquiring Person,” as defined pursuant to the foregoing provisions of this Section 1.1, has become such inadvertently (including, without limitation, because (A) such Person was unaware that it Beneficially Owned a percentage of Common Stock that would otherwise cause such Person to be an “Acquiring Person” or (B) such Person was aware of the extent of its Beneficial Ownership of Common Stock but had no actual knowledge of the consequences of such Beneficial Ownership under this Agreement) and had no intention of changing or influencing control of the Company, and such Person divests as promptly as practicable a sufficient number of shares of Common Stock so that such Person would no longer be an Acquiring Person, as defined pursuant to the foregoing provisions of this Section 1.1, then such Person shall not be deemed to be or have become an “Acquiring Person” at any time for any purposes of this Agreement. For all purposes of this Agreement, any calculation of the number of shares of Common Stock outstanding at any particular time, including for purposes of determining the particular percentage of such outstanding Common Stock of which any Person is the Beneficial Owner, shall include the number of shares of Common Stock not outstanding at the time of such calculation that such Person is otherwise deemed to Beneficially Own for purposes of this Agreement. The number of shares of Common Stock not outstanding that such Person is otherwise deemed to Beneficially Own for purposes of this Agreement shall be deemed to be outstanding for the purpose of computing the percentage of the outstanding number of shares of Common Stock owned by such Person but shall not be deemed to be outstanding for the purpose of computing the percentage of outstanding Common Stock owned by any other Person.

2. Section 3.1 of the Rights Agreement is hereby modified and amended to read in its entirety as follows:

3.1. Rights Evidenced by Stock Certificates. Until the earlier of (i) the close of business on the tenth (10^th) Business Day after the Stock Acquisition Date or (ii) the close of business on the tenth (10^th) Business Day after the date of the commencement of, or first public announcement of the intent of any Person (other than an Exempt Person) to commence, a tender or exchange offer the consummation of which would result in any Person (other than an Exempt Person) becoming the Beneficial Owner of Common Stock aggregating 30% or more of the then outstanding Common Stock (the earlier of (i) and (ii) being herein referred to as the “Distribution Date”), (x) the Rights (unless earlier expired, redeemed or terminated) will be evidenced (subject to the provisions of Section 3.2) by the certificates for Common Stock registered in the names of the holders thereof or, in the case of uncertificated Common Stock registered in book entry form (“Book Entry Shares”), by notation in book entry (which

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certificates for Common Stock and Book Entry Shares shall also be deemed to be Right Certificates) and not by separate certificates, and (y) the Rights (and the right to receive certificates therefor) will be transferable only in connection with the transfer of the underlying Common Stock. The preceding sentence notwithstanding, prior to the occurrence of a Distribution Date specified as a result of an event described in clause (ii) (or such later Distribution Date as the Board may select pursuant to this sentence), the Board may postpone, one or more times, the Distribution Date which would occur as a result of an event described in clause (ii) beyond the date set forth in such clause (ii). Nothing herein shall permit such a postponement of a Distribution Date after a Person becomes an Acquiring Person, except as a result of the operation of the third sentence of Section 1.1. As soon as practicable after the Distribution Date, the Company will prepare and execute, the Rights Agent will countersign and the Company (or, if requested, the Rights Agent) will send, by first-class, postage-prepaid mail, to each record holder of Common Stock as of the close of business on the Distribution Date (other than any Acquiring Person or any Associate or Affiliate of an Acquiring Person), at the address of such holder shown on the records of the Company, one or more certificates for Rights, in substantially the form of Exhibit B hereto (a “Right Certificate”), evidencing one Right (subject to adjustment as provided herein) for each share of Common Stock so held. As of the Distribution Date, the Rights will be evidenced solely by such Right Certificates. The Company shall promptly notify the Rights Agent in writing upon the occurrence of the Distribution Date and, if such notification is given orally, the Company shall confirm same in writing on or prior to the Business Day next following. Until such notice is received by the Rights Agent, the Rights Agent may presume conclusively for all purposes that the Distribution Date has not occurred.

3. Except as expressly amended hereby, the Rights Agreement remains in full force and effect in accordance with its terms.

4. This Amendment to the Rights Agreement shall be governed by and construed in accordance with the laws of the State of Delaware.

5. This Amendment to the Rights Agreement may be executed in any number of counterparts and each of such counterparts shall for all purposes be deemed an original, and all such counterparts shall together constitute but one and the same instrument.

6. Except as expressly set forth herein, this Amendment to the Rights Agreement shall not by implication or otherwise alter, modify, amend or in any way affect any of the terms, conditions, obligations, covenants or agreements contained in the Rights Agreement, all of which are ratified and affirmed in all respects and shall continue in full force and effect.

7. If any term, provision, covenant or restriction of this Amendment is held by a court of competent jurisdiction or other authority to be invalid, void or unenforceable, the remainder of the terms, provisions, covenants and restrictions of this Amendment shall remain in full force and effect and shall in no way be affected, impaired or invalidated

8. Capitalized terms used herein but not defined shall have the meanings given to them in the Rights Agreement.

[Signature page follows.]

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IN WITNESS WHEREOF, the parties hereto have caused this Amendment to the Rights Agreement to be duly executed as of the day and year first above written.

[Signature Page to Rights Agreement Second Amendment]