# What fraction of the Sun’s total mass is lost during fusion?

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1. Oct 13, 2014

### !Jon Snow!

1. The problem statement, all variables and given/known data
During fusion of hydrogen to helium, 4 billion kg of matter are converted
to energy each second. What fraction of the Sun’s total mass is lost each
year to this process?

2. Relevant equations
None.

3. The attempt at a solution
First:
Convert how many seconds are there in a year
1 year = 365 days
1 day = 24 hours
1 hour = 60 minutes
1 minute = 60 seconds

365x24x60x60
= 31,536,000 seconds or 3.154x10^7

4 billion
= 4x10^9

Finally, I multiple the number of seconds in a year with 4 billion matter converted.
3.154x10^7 * 4x10^9

∴ 1.2616 × 10^17 kg per year

Last edited: Oct 13, 2014
2. Oct 13, 2014

### Orodruin

Staff Emeritus
You need to work a bit on keeping your units throughout your computations, "billion matter" is not a well defined unit. A good mnemonic to remember the number of seconds in a year is that it is "approximately $\pi\cdot 10^7$ seconds", which you have found correctly. Your last number I assume is the mass lost per year in kg. The question asks you to find the fraction of the solar mass that is lost each year, not the mass that is lost every year.

Edit: Also note that your input data has only one significant digit. Quoting five significant digits in your answer gives an impression of more accuracy than you can possibly claim.

Last edited: Oct 13, 2014