The time in gigayears for the Sun to evaporate via solar wind emission is calculated by dividing the Sun's mass of 2 × 10³⁰ kg by the mass loss rate of 1.4 × 10¹ kg/s and then converting the result from seconds to gigayears.
To estimate the time it will take for the Sun to 'evaporate' via solar wind emission at a constant rate, we first need to know the Sun's current mass and the rate of mass loss. The mass loss rate provided is 1.4 × 10¹ kg/s. The current mass of the Sun is about 2 × 10³⁰ kg.
To calculate the time for the entire Sun to evaporate at the given constant mass loss rate, we use the equation:
Time = Total Mass / Mass Loss Rate
Time = (2 × 10³⁰ kg) / (1.4 × 10¹ kg/s)
After performing the division, we convert the answer from seconds to gigayears:
Time in gigayears (Gyr) = Time in seconds × (1 year/3.15× 10⁷ seconds) × (1 Gyr/10⁹ years)
This calculation will yield the time in gigayears for the mass of the Sun to be completely lost to solar wind emission.
The complete question is- Assume that the solar wind causes the Sun to lose mass at a rate of 1.4 x 109 kg/s. If you assume the wind is emitted a constant rate, estimate the time (in units of Gyr =Gigayears = 10 years) that it will take the entire Sun to evaporate via its solar wind emission. (Of course, the rate won't be constant throughout the lifetime of the Sun--- this is just a rough estimate to understand the timescale associated with this process.) [Hint: you need to look up a number and do several unit conversions; this is a *rate problem. Enter your answer as an integer or decimal, NOT in scientific notation.]