Follow an idea
into a calculation.

Begin with the problem

A lesson starts with something familiar and explains why the calculation needs another way of describing it. A calendar, for example, organizes time into days, months and years. Counting days continuously makes finding an elapsed interval a subtraction. Once that purpose is clear, the lesson introduces the astronomical name for the idea.

The prerequisites tell you which earlier lessons and mathematical operations you will use. The explanation supplies the context you need before a new symbol appears in an equation, so you can understand what the numbers represent as well as how to combine them.

Explore a term without leaving the text

Important ideas are explained in the main prose. Some terms also have a dotted underline: click or tap one to open a fuller explanation beside the sentence. You can use the keyboard to open it, and close it or press Escape when you are ready to continue. Your place in the lesson stays the same.

Passages such as “Behind the name” expand where they appear. They offer a historical story, a naming explanation or additional context for readers who want to explore. Sources support those passages, and each computational section also keeps its references in an expandable source list.

Assumptions that affect the calculation stay visible. You will not need to open a definition to discover that an input requires a particular unit or time scale, or that the engine uses an approximation.

Work through numbers before the formula

When a method is unfamiliar, we start with a concrete example and follow what each operation accomplishes. The general equation then captures the pattern you have just used. Once the pattern is familiar, later sections can move more directly from the reasoning to the equation.

Units travel with the calculation. A worked example explains where a sign comes from, how a boundary is handled, and which assumptions apply. Invented teaching values are identified, and a matching arithmetic result is kept distinct from a claim about astronomical accuracy.

Try the idea yourself

The exercise asks you to apply the idea through a numerical answer or a conceptual choice. It gives units, rounding instructions and an acceptance tolerance where needed. Feedback explains the result, and you can retry without a timer or penalty.

Passing the required checks completes a lesson. Progress stays in this browser, and you can revisit the lesson later. An exploratory diagram gives you a way to investigate; the exercise is where you demonstrate understanding.

Start with orientation to try the reading sequence and a small calculation. The Previous and Next links then connect each lesson to the next part of the workflow.