Calculating Sun Mass Loss Over Time Using E=mc^2

[bobo1455]

I am working on a question: Doing this, the Sun produces it luminosity, the 3.8 × 10^26 Joules
of energy it emits each second. Use this information to determine the percentage decrease of
the Sun’s mass over its total lifetime of 10 billion years.

It's a multiple choice question and each answer is a ratio, as in the mass I calculate divided by the Sun's mass (from what I believe it to be)

Here's what I attempted:

My first thought was to use the equation E=mc^2 and I used E = 3.8 x 10^26 Joules and c = speed of light constant and then I solved for mass and got: 4.22807 x 10^9 kg

So I assume the answer I got is the mass that is lost per second by the Sun. So then I converted 10 billions years to seconds and multiplied the mass I got previously by this number (3.15569 x 10^17) and the result was 1.3342478e+27 kg

Then I took this result (1.3342478e+27 kg) and divided by Sun's mass and got 0.0006 which is not an answer choice at all.

If anyone can help me, I'd appreciate it.

 

[jackarms]

It looks like your calculations are correct but the reasoning is off a bit. I think you need to do the comparison with what the sun's mass was at the beginning of its lifetime. So the percent decrease is from this initial mass, compared to the final mass after 10 billion years.

 

[Doc Al]

They want it expressed as a percent, not as a fraction.

 

[bobo1455]

How would I express it as a percent? I thought that's what I did, take the smaller one and divide it by the total, this gives you a percent right

 

[Doc Al]

How would I express it as a percent? I thought that's what I did, take the smaller one and divide it by the total, this gives you a percent right

That gives you a fraction. To get a percent, you must multiply by 100. (For example: 1/2 = 50 percent.)

 

[bobo1455]

If I multiply 0.0006 by 100, I get 0.006%, which is close to one of the answers (0.007%) but it's still off by 0.001%, so not sure if it is correct or not. Going to try to solve using initial mass of sun as a different number

 

[Doc Al]

If I multiply 0.0006 by 100, I get 0.006%, which is close to one of the answers (0.007%) but it's still off by 0.001%, so not sure if it is correct or not. Going to try to solve using initial mass of sun as a different number

Check your arithmetic and don't round off until the end.

 

[bobo1455]

I can't find the mass of the Sun at the beginning of its lifetime? What is the number?

 

[Doc Al]

I can't find the mass of the Sun at the beginning of its lifetime? What is the number?

Just Google the mass of the sun. That's all you need.

 

[gneill]

Just Google the mass of the sun. That's all you need.

Or work it out using the same methodology, knowing that the Sun's age is currently estimated to be ~4.57 billion years.

 

[lendav_rott]

You could backtrack provided you know the current age of the sun and its "date of birth" in terms of X billion years ago and determine its lost mass over the years.

 

[bobo1455]

the mass I googled is 1.99 x 10^30 and I already have used this to calculate the answer to be 0.007%, so I think I got it.

 

[Doc Al]

the mass I googled is 1.99 x 10^30 and I already have used this to calculate the answer to be 0.007%, so I think I got it.

Good!