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force_x = 0 -- Start with zero force
force_y = 0
for i = 1, numplanets, 1 do -- Iterate through each planet and calculate the force with which it attracts the spaceman
  dist = math.sqrt((p_pos_x[i] - sm_pos_x)^2 + (p_pos_y[i] - sm_pos_y)^2) -- This line calculates the distance between the spaceman and the planet (Pythagoras' theorem)

...Some other stuff...

  if dist ~= 0 then -- This is to avoid potential divide by zero errors, because at one point the code was buggy and it was possible to fall under the planet's surface so the distance could be zero
    force = (G * p_mass[i] * sm_mass) / dist^2 -- Calculate gravitational force using Newton's Law. G is just a constant I tweaked until it seemed good
    dir_x = (p_pos_x[i] - sm_pos_x) / dist -- Calculate the direction the force is pulling
    dir_y = (p_pos_y[i] - sm_pos_y) / dist
    force_x = force_x + force * dir_x - 0.0002 * sm_v_x -- Calculate the gravitational force due to this planet as separate x and y components and add it to the running total
    force_y = force_y + force * dir_y - 0.0002 * sm_v_y
  end
end

...Some other stuff...

sm_acc_x = sm_mass * force_x -- Newton's 2nd law, though I just realised I wrote it wrong. It should be sm_acc_x = force_x / sm_mass, not that it matters that much since the spaceman's mass doesn't change and the units of mass and force are arbitrary
sm_acc_y = sm_mass * force_y
sm_v_x = sm_v_x + sm_acc_x -- Update velocity
sm_v_y = sm_v_y + sm_acc_y
sm_pos_x = sm_pos_x + sm_v_x * dt -- Update position
sm_pos_y = sm_pos_y + sm_v_y * dt