TRAJECTORY ALPHA ACQUISITION CORP. New York, New York 10005 Re: Initial Public Offering Ladies and Gentlemen:

Exhibit 10.3

[     ], 2021

TRAJECTORY ALPHA ACQUISITION CORP.

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New York, New York 10005

Re: Initial Public Offering

Ladies and Gentlemen:

This letter (this “Letter Agreement”) is being delivered to you in accordance with that certain underwriting agreement (the “Underwriting Agreement”) entered into or proposed to be entered into by and between Trajectory Alpha Acquisition Corp., a Delaware corporation (the “Company”), and Guggenheim Securities, LLC, as underwriter (the “Underwriter” ), relating to an underwritten initial public offering (the “Public Offering”), of 17,250,000 of the Company’s units (including up to 2,250,000 units that may be purchased to cover the Underwriter’s option to purchase additional units, if any) (the “Units”), each comprised of one share of Class A common stock of the Company, par value $0.0001 per share (“Class A Common Stock”), and one-third of one redeemable warrant (each whole warrant, a “Warrant”). Each Warrant entitles the holder thereof to purchase one share of Class A Common Stock at a price of $11.50 per share, subject to adjustment, as described in the Prospectus (as defined below). The Units will be sold in the Public Offering pursuant to a registration statement on Form S-1 and a prospectus (the “Prospectus”) filed by the Company with the U.S. Securities and Exchange Commission (the “Commission”) and the Company has applied to have the Units listed on the New York Stock Exchange. Certain capitalized terms used herein are defined in Section 11.

In order to induce the Company and the Underwriter to enter into the Underwriting Agreement and to proceed with the Public Offering and for other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, Trajectory Alpha Sponsor LLC, a Delaware limited liability company (the “Sponsor”), and the other undersigned persons (each such other undersigned persons, an “Insider” and, collectively, the “Insiders”), each hereby agrees, severally but not jointly, with the Company as follows:

1. The Sponsor and each Insider agrees that, if the Company seeks stockholder approval of a proposed Business Combination, then in connection with such proposed Business Combination, it, he or she shall (i) vote any shares of Capital Stock owned by it, him or her in favor of such proposed Business Combination (including any proposals recommended by the Company’s board of directors in connection with such proposed Business Combination) and (ii) not redeem any shares of Capital Stock owned by it, him or her in connection with such stockholder approval. If the Company seeks to consummate a proposed Business Combination by engaging in a tender offer, the Sponsor and each Insider agrees that it, he or she will not sell or tender any shares of Capital Stock owned by it, him or her to the Company in connection therewith.

2. The Sponsor and each Insider hereby agrees that, in the event that the Company fails to consummate a Business Combination within twenty-four (24) months from the closing of the Public Offering (the “Completion Window”), or such later period approved by the Company’s stockholders in accordance with the Company’s amended and restated certificate of incorporation (as further amended, supplemented or otherwise modified from time to time, the “Certificate of

Incorporation”), the Sponsor and each Insider shall take all reasonable steps to cause the Company to (i) cease all operations except for the purpose of winding up, (ii) as promptly as reasonably possible but not more than ten (10) business days thereafter, subject to lawfully available funds therefor, redeem one-hundred percent (100%) of the Class A Common Stock sold as part of the Units in the Public Offering (the “Offering Shares”), at a per share price, payable in cash, equal to the aggregate amount then on deposit in the Trust Account, including interest (which interest shall be net of taxes payable (“Permitted Withdrawals”) and less up to $100,000 of interest to pay dissolution expenses), divided by the number of the then outstanding Offering Shares, which redemption will completely extinguish all of the Public Stockholders’ rights as stockholders (including the right to receive further liquidating distributions, if any), subject to applicable law, and (iii) as promptly as reasonably possible following such redemption, subject to the approval of the Company’s remaining stockholders and the Company’s board of directors, dissolve and liquidate, subject in each case to the Company’s obligations under Delaware law to provide for claims of creditors and any other requirements of applicable law. The Sponsor and each Insider agrees to not propose any amendment to the Certificate of Incorporation (A) to modify the substance or timing of the Company’s obligation to allow redemptions in connection with the Company’s initial Business Combination or to redeem one-hundred percent (100%) of the Offering Shares if the Company does not complete its initial Business Combination within the Completion Window or (B) with respect to any other material provision relating to stockholders’ rights or pre-initial Business Combination activity, unless the Company provides the Public Stockholders with the opportunity to redeem their Offering Shares upon approval of any such amendment at a per share price, payable in cash, equal to the aggregate amount then on deposit in the Trust Account, including interest (which interest shall be net of Permitted Withdrawals), divided by the number of the then outstanding Offering Shares.

The Sponsor and each Insider acknowledges that it, he or she has no right, title, interest or claim of any kind in or to any monies or any other asset held in the Trust Account as a result of any liquidation of the Company with respect to the Founder Shares held by it, him or her. The Sponsor and each Insider hereby further waives, with respect to any shares of Capital Stock held by it, him or her, if any, any redemption rights it, he or she may have in connection with (x) a Business Combination, including, without limitation, any such rights available in the context of a stockholder vote to approve such Business Combination or in the context of a tender offer made by the Company to purchase shares of Class A Common Stock and (y) a stockholder vote to approve an amendment to the Certificate of Incorporation (A) to modify the substance or timing of the Company’s obligation to allow redemptions in connection with the Company’s initial Business Combination or to redeem one-hundred percent (100%) of the Offering Shares if the Company has not consummated its initial Business Combination within the Completion Window or (B) with respect to any other material provision relating to stockholders’ rights or pre-initial Business Combination activity (although the Sponsor and each Insider shall be entitled to redemption and liquidation rights with respect to any Offering Shares it, he or she holds if the Company fails to consummate a Business Combination within the Completion Window).

3. Notwithstanding the provisions set forth in Sections 7(a) and (b), during the period commencing on the effective date of the Underwriting Agreement and ending one-hundred-eighty (180) days after such date, the Sponsor and each Insider shall not, without the prior written consent of the Underwriter, (i) offer, sell, contract to sell, pledge or grant any option to purchase or otherwise dispose of (or enter into any transaction that is designed to, or might reasonably be

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expected to, result in the disposition (whether by actual disposition or effective economic disposition due to cash settlement or otherwise)), directly or indirectly, or establish or increase a put equivalent position or liquidate or decrease a call equivalent position within the meaning of Section 16 of the Securities Exchange Act of 1934, as amended, and the rules and regulations of the Commission promulgated thereunder (the “Exchange Act”), with respect to any Units, shares of Class A Common Stock, Warrants or any securities convertible into, or exercisable or exchangeable for, shares of Class A Common Stock, (ii) enter into any swap or other arrangement that transfers to another, in whole or in part, any of the economic consequences of ownership of any Units, shares of Class A Common Stock, Warrants or any securities convertible into, or exercisable or exchangeable for, shares of Class A Common Stock owned by it, him or her, whether any such transaction is to be settled by delivery of such securities, in cash or otherwise, or (iii) or publicly announce an intention to effect any such transaction specified in clause (i) or (ii); provided, however, that the foregoing does not apply to the forfeiture of any Founder Shares pursuant to their terms or any transfer of any Founder Shares to any current or future independent director of the Company (as long as such current or future independent director transferee is subject to this Letter Agreement or executes an agreement substantially identical to the terms of this Letter Agreement, as applicable to directors, officers and advisors at the time of such transfer and as long as, to the extent any reporting obligation pursuant to Section 16 of the Exchange Act is triggered as a result of such transfer, any related filing includes a practical explanation as to the nature of the transfer). The Sponsor and each Insider acknowledge and agree that, prior to the effective date of any release or waiver of the restrictions set forth in this Section 3 or 7, the Company shall announce the impending release or waiver by press release through a major news service at least two (2) business days before the effective date of the release or waiver. Any such release or waiver granted shall only be effective two (2) business days after the publication date of such press release. The provisions of this Section 3 shall not apply if (i) the release or waiver is effected solely to permit a transfer of securities that is not for consideration and (ii) the transferee has agreed in writing to be bound by the same terms described in this Letter Agreement to the extent and for the duration that such terms remain in effect at the time of the transfer.

4. In the event of the liquidation of the Trust Account, the Sponsor (which for purposes of clarification shall not extend to any other holder of limited liability company interests or any member or manager of the Sponsor or any other Insider) agrees to indemnify and hold harmless the Company against any and all loss, liability, claim, damage and expense whatsoever (including, without limitation, any and all legal or other expenses reasonably incurred in investigating, preparing or defending against any litigation, whether pending or threatened, or any claim whatsoever) to which the Company may become subject as a result of any claim by (i) any third party (other than the Company’s independent registered public accounting firm) for services rendered or products sold to the Company or (ii) a prospective target business with which the Company has discussed entering into an agreement for a Business Combination (a “Target”); provided, however, that such indemnification of the Company by the Sponsor shall apply only to the extent necessary to ensure that such claims by a third party for services rendered (other than the Company’s independent registered public accounting firm) or products sold to the Company or a Target do not reduce the amount of funds in the Trust Account to below (i) $10.00 per Offering Share or (ii) such lesser amount per Offering Share held in the Trust Account as of the date of the liquidation of the Trust Account due to reductions in the value of the trust assets as of the date of the liquidation of the Trust Account, in each case, net of Permitted Withdrawals, except as to any claims by a third party which executed a waiver of any and all rights to seek access to the Trust

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Account and except as to any claims under the Company’s indemnity of the Underwriter against certain liabilities, including liabilities under the Securities Act of 1933, as amended. In the event that any such executed waiver is deemed to be unenforceable against such third party, the Sponsor shall not be responsible to the extent of any liability for such third party claims. The Sponsor shall have the right to defend against any such claim with counsel of its choice reasonably satisfactory to the Company if, within fifteen (15) days following written receipt of notice of the claim to the Sponsor, the Sponsor notifies the Company in writing that it shall undertake such defense. For the avoidance of doubt, none of the Company’s officers, directors or advisors shall indemnify the Company for claims by third parties, including, without limitation, claims by vendors or any Target.

5. To the extent that the Underwriter does not exercise its over-allotment option up to an additional 2,250,000 Units within forty-five (45) days from the date of the Prospectus (and as further described in the Prospectus), the Sponsor agrees that it shall forfeit, at no cost, an aggregate number of the Founder Shares in the aggregate equal to the product of (a) 562,500 multiplied by a fraction, (i) the numerator of which is 2,250,000 minus the number of Units purchased by the Underwriter upon the exercise of its option to purchase additional Units, and (ii) the denominator of which is 2,250,000. All references in this Letter Agreement to any Founder Shares of the Company being forfeited shall take effect as a contribution of such Founder Shares to the Company’s capital as a matter of Delaware law. The forfeiture will be adjusted to the extent that the over-allotment option is not exercised in full by the Underwriter so that the number of the Founder Shares will equal an aggregate of twenty percent (20.0%) of the Company’s issued and outstanding shares of Capital Stock after the Public Offering. The Sponsor and each Insider further agree that, to the extent that the size of the Public Offering is increased or decreased, the Company will effect a capitalization, stock repurchase or redemption or stock split, reverse stock split or other appropriate mechanism, as applicable, immediately prior to the consummation of the Public Offering in such amount as to maintain the number of the Founder Shares at twenty percent (20.0%) of the Company’s issued and outstanding shares of Capital Stock upon the consummation of the Public Offering. In connection with such increase or decrease in the size of the Public Offering, then (A) the references to 2,250,000 in the numerator and denominator of the formula set forth in the first sentence of this Section 5 shall be changed to a number equal to fifteen percent (15.0%) of the number of shares of Class A Common Stock included in the Units issued in the Public Offering and (B) the reference to 562,500 in the formula set forth in the first sentence of this Section 5 shall be adjusted to such number of the Founder Shares that the Sponsor would have to return to the Company in order for the number of the Founder Shares to equal an aggregate of twenty percent (20.0%) of the Company’s issued and outstanding shares of Capital Stock after the Public Offering.

6. The Sponsor and each Insider hereby agree and acknowledge that (i) the Underwriter and the Company would be irreparably injured in the event of a breach by the Sponsor or such Insider of its, his or her obligations under Sections 1, 2, 3, 4, 5, 7(a), 7(b) and 9, as applicable, of this Letter Agreement, (ii) monetary damages may not be an adequate remedy for such breach and (iii) the non-breaching party shall be entitled to seek injunctive relief, in addition to any other remedy that such party may have in law or in equity, in the event of such breach.

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7.      (a) Subject to the exceptions set forth in this Letter Agreement, the Sponsor and each Insider agree that it, he or she shall not Transfer (as defined below) any Founder Shares (or shares of Class A Common Stock issuable upon conversion thereof) until the earlier of (A) one (1) year after the completion of the Company’s initial Business Combination and (B) subsequent to the Business Combination, (x) if the last reported sale price of the Class A Common Stock equals or exceeds $12.00 per share (as adjusted for stock splits, stock dividends, reorganizations, recapitalizations and the like) for any twenty (20) trading days within any thirty (30)-trading day period commencing at least one-hundred-fifty (150) days after the Company’s initial Business Combination or (y) the date on which the Company completes a liquidation, merger, stock exchange, reorganization or other similar transaction that results in all of the Public Stockholders having the right to exchange their shares of Class A Common Stock for cash, securities or other property (the “Founder Shares Lock-Up Period”).

(b) Subject to the exceptions set forth this Letter Agreement, the Sponsor and each Insider agree that it, he or she shall not Transfer any Private Placement Warrants or Working Capital Warrants (as defined below) (or shares of Class A Common Stock issued or issuable upon the conversion or exercise of the Private Placement Warrants or Working Capital Warrants, as the case may be), until thirty (30) days after the completion of the Company’s initial Business Combination (the “Private Placement Warrants Lock-Up Period” and, together with the Founder Shares Lock-Up Period, the “Lock-Up Periods”).

(c) Notwithstanding the provisions set forth in Sections 3, 7(a) and (b), Transfers of the Founder Shares, Private Placement Warrants, Working Capital Warrants and shares of Class A Common Stock issued or issuable upon the exercise or conversion of the Private Placement Warrants, the Working Capital Warrants or the Founder Shares and that are held by the Sponsor or any Insider or any of their respective permitted transferees (that have complied with this Section 7(c)), are permitted (a) to the Company’s officers, directors or advisors, any Affiliates or family members of any of the Company’s officers, directors or advisors, any direct or indirect members, partners or stockholders of the Sponsor or any employee or partner of any such member, partner or stockholder, or any Affiliates of the Sponsor, (b) in the case of an individual, transfers by gift to a member of the individual’s immediate family, to a trust, the beneficiaries of which are one or more of the individual’s immediate family or an Affiliate of such person, or to a charitable organization, (c) in the case of an individual, transfers by virtue of laws of descent and distribution upon death of such individual, (d) in the case of an individual, transfers pursuant to a qualified domestic relations order, (e) transfers by virtue of law or the Sponsor’s operating agreement upon dissolution of a person other than an individual, (f) transfers by private transfers or sales and transfers made in connection with the consummation of the Company’s initial Business Combination at prices no greater than the price at which the securities were originally purchased, (g) to an entity that is an Affiliate of such holder, (h) transfers in the event of the Company’s liquidation prior to the completion of the Company’s initial Business Combination, (i) to the Company for no value for cancellation in connection with the consummation of the Company’s initial Business Combination, (j) in the event of the Company’s completion of a liquidation, merger, stock exchange, reorganization or other similar transaction which results in all of the Company’s stockholders having the right to exchange their shares of Common Stock for cash, securities or other property subsequent to the completion of the Company’s initial Business Combination, and (k) to a nominee or custodian of a person or entity to whom a disposition or transfer would be permissible under clauses (a) through (h) above; provided, however, that, in the case of clauses (a)

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through (f) and (j), these transferees must enter into a written agreement with the Company agreeing to be bound by the transfer restrictions in this Letter Agreement. “Affiliate” means, with respect to any holder any other person who, directly or indirectly (including through one or more intermediaries), controls, is controlled by, or is under common control with, such person. For purposes of this definition, “control,” when used with respect to any specified person, shall mean the power, direct or indirect, to direct or cause the direction of the management and policies of such person, whether through ownership of voting securities or partnership or other ownership interests, by contract or otherwise, and the terms “controlling” and “controlled” shall have correlative meanings.

8. The Sponsor and each Insider represent and warrant with respect to such Insider that it, he or she has never been suspended or expelled from membership in any securities or commodities exchange or association or had a securities or commodities license or registration denied, suspended or revoked. Each Insider represents and warrants with respect to such Insider that such Insider’s biographical information furnished to the Company, if any (including any such information included in the Prospectus), is true and accurate in all respects and does not omit any material information with respect to such Insider’s background. The Sponsor and each Insider’s questionnaires furnished to the Company, if any, are true and accurate in all respects. The Sponsor and each Insider represent and warrant with respect to such Insider that it, he or she (a) is not subject to, or a respondent in, any legal action for, any injunction, cease-and-desist order or order or stipulation to desist or refrain from any act or practice relating to the offering of securities in any jurisdiction, (b) has never been convicted of, or pleaded guilty to, any crime (i) involving fraud, (ii) relating to any financial transaction or handling of funds of another person, or (iii) pertaining to any dealings in any securities and (c) is not currently a defendant in any such criminal proceeding.

9. Except as disclosed in, or as expressly contemplated by, the Prospectus, neither the Sponsor nor any Insider nor any affiliate of the Sponsor or any Insider, nor any director, officer or advisor of the Company, shall receive from the Company any finder’s fee, reimbursement, consulting fee, monies in respect of any repayment of a loan or other compensation prior to, or in connection with any services rendered in order to effectuate, the consummation of the Company’s initial Business Combination (regardless of the type of transaction that it is), other than the following, none of which will be made from the proceeds held in the Trust Account prior to the completion of the Company’s initial Business Combination: (i) repayment of a loan and advances of up to $300,000 made to the Company by the Sponsor to cover expenses related to the organization of the Company and the Public Offering; (ii) reimbursement for any reasonable out-of-pocket expenses related to identifying, investigating and consummating an initial Business Combination; and (iii) repayment of loans, if any, and on such terms as to be determined by the Company from time to time, made by the Sponsor, an affiliate of the Sponsor or certain of the Company’s officers and directors to finance transaction costs in connection with the Company’s initial Business Combination; provided, however, that, if the Company does not consummate an initial Business Combination, a portion of the working capital held outside the Trust Account may be used by the Company to repay such loaned amounts so long as no proceeds from the Trust Account are used for such repayment. Up to $2,000,000 of such loans may be convertible into warrants (the “Working Capital Warrants”) of the post Business Combination entity at a price of $1.50 per warrant at the option of the lender. Such warrants would be identical to the Private Placement Warrants, including as to the exercise price, exercisability and exercise period.

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10. The Sponsor and each Insider has full right and power, without violating any agreement by which it is bound (including, without limitation, any non-competition or non-solicitation agreement with any employer or former employer), to enter into this Letter Agreement and, as applicable, to serve as an officer, a director on the board of directors and/or an advisor on the board of advisors of the Company and hereby consents to being named in the Prospectus as an officer, a director and/or an advisor of the Company.

11. As used herein, (i) “Business Combination” shall mean a merger, capital stock exchange, asset acquisition, stock purchase, reorganization or similar business combination, involving the Company and one or more businesses or companies; (ii) “Capital Stock” shall mean, collectively, the Class A Common Stock and the Founder Shares; (iii) “Founder Shares” shall mean the 4,312,500 shares of Class B common stock, par value $0.0001 per share, issued and outstanding immediately prior to the consummation of the Public Offering; (iv) “Private Placement Warrants” shall mean the Warrants to purchase up to an aggregate of 3,666,667 shares of Class A Common Stock of the Company (or 3,966,667 shares of Class A Common Stock if the over-allotment option is exercised in full) that the Sponsor has agreed to purchase for an aggregate purchase price of $5,500,000 (or $5,950,000 if the over-allotment option is exercised in full), or $1.50 per Warrant, in a private placement that shall occur simultaneously with the consummation of the Public Offering; (v) “Public Stockholders” shall mean the holders of securities issued in the Public Offering; (vi) “Trust Account” shall mean the trust fund into which a portion of the net proceeds of the Public Offering and the sale of the Private Placement Warrants shall be deposited; and (vii) “Transfer” shall mean the (a) sale or assignment of, offer to sell, contract or agreement to sell, hypothecate or pledge, grant of any option to purchase or otherwise dispose of or agreement to dispose of, directly or indirectly, or establishment or increase of a put equivalent position or liquidation with respect to or decrease of a call equivalent position within the meaning of the Exchange Act with respect to, any security, (b) entry into any swap or other arrangement that transfers to another, in whole or in part, any of the economic consequences of ownership of any security, whether any such transaction is to be settled by delivery of such securities, in cash or otherwise, or (c) public announcement of any intention to effect any transaction specified in clause (a) or (b) above.

12. This Letter Agreement constitutes the entire agreement and understanding of the parties hereto in respect of the subject matter hereof and supersedes all prior understandings, agreements or representations by or among the parties hereto, written or oral, to the extent they relate in any way to the subject matter hereof or the transactions contemplated hereby. This Letter Agreement may not be changed, amended, modified or waived (other than to correct a typographical error) as to any particular provision, except by a written instrument executed by (1) each Insider that is the subject of any such change, amendment modification or waiver and (2) the Sponsor.

13. Except as otherwise provided in this Letter Agreement, no party hereto may assign either this Letter Agreement or any of its rights, interests or obligations hereunder without the prior written consent of the other parties. Any purported assignment in violation of this Section 13 shall be void and ineffectual and shall not operate to transfer or assign any interest or title to the purported assignee. This Letter Agreement shall be binding on the Sponsor and each Insider and their respective successors, heirs and assigns and permitted transferees.

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14. Nothing in this Letter Agreement shall be construed to confer upon, or give to, any person or entity other than the parties hereto any right, remedy or claim under or by reason of this Letter Agreement or of any covenant, condition, stipulation, promise or agreement hereof. All covenants, conditions, stipulations, promises and agreements contained in this Letter Agreement shall be for the sole and exclusive benefit of the parties hereto and their successors, heirs, personal representatives and assigns and permitted transferees.

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

16. This Letter Agreement shall be deemed severable, and the invalidity or unenforceability of any term or provision hereof shall not affect the validity or enforceability of this Letter Agreement or of any other term or provision hereof. Furthermore, in lieu of any such invalid or unenforceable term or provision, the parties hereto intend that there shall be added as a part of this Letter Agreement a provision as similar in terms to such invalid or unenforceable provision as may be possible and be valid and enforceable.

17. This Letter Agreement shall be governed by and construed and enforced in accordance with the laws of the State of New York, without giving effect to conflicts of law principles that would result in the application of the substantive laws of another jurisdiction. The parties hereto (i) all agree that any action, proceeding, claim or dispute arising out of, or relating in any way to, this Letter Agreement shall be brought and enforced in the courts of New York City, in the State of New York, and irrevocably submit to such jurisdiction and venue, which jurisdiction and venue shall be exclusive and (ii) waive any objection to such exclusive jurisdiction and venue or that such courts represent an inconvenient forum.

18. Any notice, consent or request to be given in connection with any of the terms or provisions of this Letter Agreement shall be in writing and shall be sent by express mail or similar private courier service, by certified mail (return receipt requested), by hand delivery or facsimile or other electronic transmission.

19. Each party hereto shall not be liable for any breaches or misrepresentations contained in this Letter Agreement by any other party to this Letter Agreement (including, for the avoidance of doubt, any Insider with respect to any other Insider), and no party shall be liable or responsible for the obligations of another party, including, without limitation, indemnification obligations and notice obligations.

20. This Letter Agreement shall terminate on the earlier of (i) the expiration of the Lock-Up Periods and (ii) the liquidation of the Company; provided, however, that this Letter Agreement shall terminate earlier in the event that the Public Offering is not consummated and closed by [___________], 2021; provided, further, that Section 4 shall survive such liquidation.

[Signature Pages Follow]

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[Signature Page to Letter Agreement—Trajectory Alpha Acquisition Corp.]