You should be able to get time just by labeling the orbits in your diagram of the solar system. Of course, you'll have to remember that the sidereal year is one day longer. Just label the Earth's orbit "year" and the Earth's spin "sidereal" and then write 1(year)=366.25 days. Hopefully the aliens are tolerant of approximations. They may first think these are distances, but their next guess when they see the math doesn't work would probably be time.
Then draw a line on your diagram between the Earth and the sun. Thats 1AU. The speed of light is about 173 AU/day (it's a little less with sidereal days, a little more with solar days).
The problem then is that all the constants you're used to are based the solar day. Eventually the aliens will get confused. One solar day = 1.00273791 sidereal days. But no one will remember that. It might be easier to remember 1 sidereal day is 23 hours 56 minutes and 4 seconds.
Or I guess if you have a constellation chart your could draw in the ecliptic plane and label that. But dang are our units screwed up.
1AU =149 598 000 kilometers but if you're a provincial American like me you know miles. 1AU=92 955 887.6 miles...
I don't think a lot of scientists have this stuff memorized (1 obviously looked up just about all these numbers, except for hrs/sidereal day).
I would be really nice if we had all our units based off the speed of light or something. That would make this so much easier.
Allow me to propose a thought experiment. Suppose you, and you alone, were to make first contact with an alien species. Since your survival and the survival of the entire human race may depend on the extraterrestrials recognizing you as a member of a rational species, how would you convey your knowledge of mathematics, logic, and the scientific method to them using only your personal knowledge and whatever tools you might reasonably have on your person on an average day?
When I thought of this question, the two methods that immediately came to mind were the Pythagorean Theorem and prime number sequences. For instance, I could draw a rough right triangle and label one side with three dots, the other with four, and the hypotenuse with five. However, I realized that these are fairly primitive maths. After all, the ancient Greeks knew of them, and yet had no concept of the scientific method. Would these likely be sufficient, and if not what would be? Could you make a rough sketch of the first few atoms on the periodic table or other such universal phenomena so that it would be generally recognizable? Could you convey a proof of rationality in a manner that even aliens who cannot hear human vocalizations, or see in a completely different part of the EM spectrum? Is it even in principle possible to express rationality without a common linguistic grounding?
In other words, what is the most rational thought you could convey without the benefit of common language, culture, psychology, or biology, and how would you do it?
Bonus point: Could you convey Bayes' theorem to said ET?