jats:titleAbstract</jats:title> jats:pThis Letter develops a method to constrain the cosmological constant Λ from binary galaxies, focusing on the Milky Way and Andromeda galaxies. We provide an analytical solution to the two-body problem with Λ and show that the ratio between the Keplerian period and jats:inline-formula jats:tex-math

</jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> mml:msub mml:mrow mml:miT</mml:mi> </mml:mrow> mml:mrow <mml:mi mathvariant="normal">Λ</mml:mi> </mml:mrow> </mml:msub> mml:mo=</mml:mo> mml:mn2</mml:mn> mml:miπ</mml:mi> mml:mrow <mml:mo stretchy="true">/</mml:mo> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> mml:mic</mml:mi> mml:msqrt mml:mrow <mml:mi mathvariant="normal">Λ</mml:mi> </mml:mrow> </mml:msqrt> <mml:mo stretchy="false">)</mml:mo> mml:mo≈</mml:mo> mml:mn63.2</mml:mn> <mml:mspace width="0.25em" /> mml:miGyr</mml:mi> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjlace90bieqn1.gif" xlink:type="simple" /> </jats:inline-formula> controls the importance of effects from the cosmological constant. The Andromeda–Milky Way orbit has a period of ∼17 Gyr, and so dark energy has to be taken into account. Using the current best mass estimates of the Milky Way and Andromeda galaxies, we find the cosmological constant value has an upper bound that is 5.44 times the value obtained by Planck. With future astrometric measurements, the bound on the cosmological constant can be reduced to jats:inline-formula jats:tex-math

</jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mfenced close=")" open="("> mml:mrow mml:mn1.67</mml:mn> mml:mo±</mml:mo> mml:mn0.79</mml:mn> </mml:mrow> </mml:mfenced> mml:msub mml:mrow <mml:mi mathvariant="normal">Λ</mml:mi> </mml:mrow> mml:mrow mml:miPL</mml:mi> </mml:mrow> </mml:msub> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjlace90bieqn2.gif" xlink:type="simple" /> </jats:inline-formula>. Our results offer the prospects of constraints on Λ over very different scales than previously. The Local Group provides also a completely novel platform to test alternative theories of gravity. We illustrate this by deriving bounds on scalar-tensor theories of gravity over megaparsec scales.</jats:p>