Depends on the time of day.

Actually it doesn't. The difference between perihelion and aphelion is around 6 million km, and it takes approximately 6 months to cover.

That means Earth is moving away or towards the sun at 1 million km per month. That's 33,000 km per day. So 1300 km/h or so? Basically unless you're really fast, climbing the stairs is overwhelmed by other effects.

Haven't taken the Earth's rotation into account but it should be less of an effect.

I could be wrong, but I think the GP was commenting specifically about time of day? At idealized midnight the vector between you and the sun goes through the center of the Earth, indicating that increasing altitude takes you away from the Sun, instead of towards it. At idealized Noon, the opposite is true.

But the speed at which the earth is approaching the sun makes a biggers difference than your flight of stairs?

Yeah, I guess that's one way of looking at it; I guess on my first read of the comments I saw it as a related rates problem where "the act of climbing the stairs adds a velocity away from the Sun", but yeah, the second comment makes the case that at certain times of year the sum of the Earth's velocity and your stairs could still be positive in the "towards sun" direction.

(Sigh) this is why I'm poorly suited for Twitter...

There's an interesting problem for an astrophysics final, find the date and time where the your radial velocity is 0 and tell me if it is near zero long enough to make the dominate motion running down the stairs.

July 4 is aphelion day this year, so celebrate by doing an entirely useless physics problem.

even closer.