Across the universe on a butter mountain

‘You could therefore, if you arranged the packs as steps, climb this “butter mountain” and reach all of the planets in the solar system, then go on to Andromeda.’ Photograph: Alamy Stock Photo

Tony Robinson asks to what depth 40 trillion trillion trillion packs of butter would cover a country the size of Wales (Letters, 29 June). In scientific notation this is 40x10³⁶ packs. Wales is about 2x10¹⁰ square metres. A pack of butter measured 95x63x41mm, so 2x10¹⁰÷6x10^–3 or 3.4x10¹² packs would cover the surface. The height of 40x10³⁶ packs stacked on top of each other comes to 40x10³⁶÷3.4x10¹² x 0.041 metres, or 4.8x10²³ metres. The sun is only 1.5x10¹¹ metres away, but Saturn is a little farther at 1.4x10¹² metres from the sun, while Pluto is at 5.9x10¹² metres. Andromeda is a mere 2.4x10²² metres away. You could therefore, if you arranged the packs as steps, climb this “butter mountain” and reach all of the planets in the solar system, then go on to Andromeda, but you’d have to do it at night or the stairway to the solar system would swing past the sun and melt.
Dr John Ellis
Tavistock, Devon