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Cake day: November 8th, 2023

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  • The thing you’re looking for is (almost) called the “velocity vector.” You can get the values for any date and time here with these settings

    Ephemeris Type: Vector Table

    Target Body: Earth

    Coordinate Center: Solar System Barycenter (SSB) [500@0]3

    Time Specification: Start=2023-11-21 TDB , Stop=2023-12-21, Step=1 (days) (or whatever you want)

    Table Settings: defaults

    That will give you a table that includes VX, VY, and VZ. Those will be the velocity of the earth at that moment, relative to the J2000.0 reference frame. I don’t know if there’s any straightforward way to convert that into a point in the sky.

    Easier, at sunrise, stand facing the sun. Point your right arm straight up (left arm if you’re in the southern hemisphere). Lower your arm to the side by an angle equal to your latitude. You’re now pointing more-or-less in the direction the earth is moving. That’s only completely accurate on the equinoxes. To improve accuratcy at other times, in the winter move your hand a bit away from the sun and in the summer towards the sun.