Ykhjuy

Relative to this simple drawing, can someone explain to me,

1. in which direction is the sun and its solar system travelling,


2. which star (irrespective of distance) is closest to that direction,


3. and in which direction the milky way center is.

The direction of solar motion is referred to as the solar apex. It is at around RA=18h28m and Dec=+30d in the constellation of Hercules (you can see a map on the page linked to). Note that this is the direction in which you would see the "star wars" effect of onrushing stars diverging from the apex point.

I cannot explain relative to a 2-dimensional cartoon of the Earth's orbit where that is. However, if you look at the map below (produced by Christian Ready), you can judge where the solar apex is with respect to the ecliptic plane (green line), which is roughly the path (drawn in your diagram) that the Earth takes around the Sun.

The very bright star Vega is reasonably close to this direction.

The Milky way centre is at RA=17h45m, Dec=-29d in the constellation of Sagittarius. In Galactic coordinates (see Best approximation for Sun's trajectory around galactic center? ) the Sun moves at about 10 km/s towards the Galactic centre, about 5 km/s faster than the average circular speed (which is itself about 220 km/s) of local stars in the tangential direction and 7 km/s upwards out of the Galactic plane.

1) and 2) The direction that the Sun is moving is known as the Solar Apex. This Wikipedia article shows a star map, so you can decide which star you want to say is closest. Solar Apex

3) The center of the Milky Way is toward the constellation of Sagittarius.

Relative to your drawing, the sun is moving north-ish:

The solar system is tilted about 60 degrees of the milky way plane, on which it's moving around like everyone else.

To know which star is closest, you'd have to define what "closest" mean. Are we setting a straight line and seeing if it hits any star? If a start is 50 light years away from that straight line and 100 light years away from the sun, is that closer than a start that's 5 light years away from line but 800 light years away from the sun?

The milky way center is to the right of the path the sun is moving on. But I don't know the location when earth is at winter solstice, and you didn't specify northern hemisphere's winter or southern hemisphere's. ;-)