In this homework assignment, we will take you through the construction of a whole distance ladder, step by step. But unlike the real world, you will get a green tick or a red cross at each stage to tell you whether you got that step correct. And in the real world (unlike this homework) the input to each step depends on the output of the last, so mistakes and uncertainties cascade. The first step in the distance ladder is parallax. You monitor the position of a star for a year, and observe that its apparent position (relative to a grid of background stars) moves in an ellipse:

In this homework assignment, we will take you through the construction of a whole distance ladder, step by step. But unlike the real world, you will get a green tick or a red cross at each stage to tell you whether you got that step correct. And in the real world (unlike this homework) the input to each step depends on the output of the last, so mistakes and uncertainties cascade. The first step in the distance ladder is parallax. You monitor the position of a star for a year, and observe that its apparent position (relative to a grid of background stars) moves in an ellipse: