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**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.**

## Homework Statement

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.

M

_{2}= 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 m

^{3}kg

^{-1}s

^{-2}

5000 yr = 1.577E11 s

ΔM = 3.64E9 kg/s

## Homework Equations

Kepler's third law: T

^{2}= (4π

^{2}r

^{3})/GM

## The Attempt at a Solution

To solve the equation, I plan on finding the value for T for today (T

_{2}) and the value of T for 5000 years ago (T

_{1}). 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. M

_{2}(current mass of sun) = 1.988E30 kg. I wanted to find M

_{1}(previous mass of sun), so I did M

_{1}= 1.988E30 kg + (3.64E9 kg/s)(1.577E11 s) = 1.988E30 kg.

So, according to my equation above, M

_{1}and M

_{2}are almost exactly the same and the difference is negligible. How do I go about this?

Thanks.

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