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To see how weak the effect of dark energy is compared to gravity, it is useful to compute the effect of dark energy on the solar orbit of earth and Pluto.

The acceleration on a planet orbiting the sun is -G*M/R², where G is the gravitational constant, M is the solar mass, and R is the sun-planet distance. The effect of dark energy (DE) is to give a repulsive force; the DE acceleration between the sun and a planet is given by +k*R, where k = 3.7*10^-36/s². Note that with growing distance between two objects, the effect of gravity decreases, while the effect of dark energy increases; for example, doubling the separation between two objects increases the DE-to-gravity acceleration ratio by a factor of eight.

Now let's plug in the numbers. For earth, the acceleration from dark energy is 9.3*10^-23 times that from the sun's gravity. The corresponding change in the earth's orbit, compared to an orbit without dark energy (and with the same orbital velocity), is a tiny 140 nanometers, or about the size of a virus! For Pluto, the distance from the sun is 40 times greater than the earth-sun distance; the corresponding change in Pluto's orbit due to dark energy is 1 micron.