The Pico-8 code showing off rotations math.

Rotations.lua

--rotations by eis - kino

--globals
--The sprites, the position (x and y) of both star1 and star2
star1 ={sprite=2, x = 58, y = 58}
star2 ={sprite=3, x = 0, y =  0}
degrees = 0

function _update()
  --Here we rotate star2 around star1 by giving rotate star1's position(x, y).
  rotate(star1.x, star1.y, 10, star2)
end

function _draw()
  cls()
  map(0,0,0,0,16,16)
  spr(star1.sprite, star1.x, star1.y)
  spr(star2.sprite, star2.x, star2.y)
end

-- rotation logic

function rotate(x, y, radius, star)
  degrees += 0.05
  --We update star's position by incrementing the degrees and using our formula
  -- x + (radius * cosine(degrees)) = a point on the edge of the circle in the x-axis
  -- y + (radius * sine(degrees)) = a point of the edge of the circle in the y-axis
  star.x = x + (radius * cos(degrees))
  star.y = y + (radius * sin(degrees))  
end


--draw debug inforatmion
function drawdebug()
  print("star2\nx: "..star2.x.." y: "..star2.y)
end