EDIT: It seems that just after posting this, my professor decided this problem is too difficult for us to be responsible for. I can't delete this question, so don't feel obligated to answer it. But who knows? Maybe someone else out there has the same question. 1. The problem statement, all variables and given/known data The Sun loses mass at a rate of 3.64E9 kg/s. During the 5,000-yr period of recorded history, by how much has the length of the year changed due to the loss of mass from the Sun? Suggestions: Assume the Earth's orbit is circular. No external torque acts on the Earth–Sun system, so the angular momentum of the Earth is constant. M2 = current mass of sun = (Wolfram Alpha is source): 1.988E30 kilograms r = average distance between sun and earth (Wolfram Alpha is source): 1.496E11 meters G = 6.67E-11 m3 kg-1 s-2 5000 yr = 1.577E11 s ΔM = 3.64E9 kg/s 2. Relevant equations Kepler's third law: T2 = (4π2r3)/GM 3. The attempt at a solution To solve the equation, I plan on finding the value for T for today (T2) and the value of T for 5000 years ago (T1). I did some Googling and someone found the answer to be ΔT = 1.82E-2 s. I don't know if it is correct or not. Okay, so here's how I started. M2 (current mass of sun) = 1.988E30 kg. I wanted to find M1 (previous mass of sun), so I did M1 = 1.988E30 kg + (3.64E9 kg/s)(1.577E11 s) = 1.988E30 kg. So, according to my equation above, M1 and M2 are almost exactly the same and the difference is negligible. How do I go about this? Thanks.