the solar energy arriving at the outer edge of earth's atmosphere from the sun has intensity of 1.4 kW/msquared. how much mass does the sun lose per day? what percent of the sun's mass is this?
To calculate the mass loss of the Sun per day, we need to determine the energy emitted by the Sun and then convert it into mass using Einstein's famous equation E=mc^2. Let's break down the process step by step:
Step 1: Calculate the total energy emitted by the Sun per second.
The intensity of solar energy arriving at the outer edge of the Earth's atmosphere is given as 1.4 kW/m^2. Since this is the intensity per square meter, we need to calculate the total energy emitted by the Sun per second across its entire surface. To do this, we multiply the intensity by the surface area of the Sun.
The surface area of a sphere can be calculated using the formula: A = 4πr^2, where r is the radius of the Sun.
Assuming the average radius of the Sun is approximately 696,340 km (or 696,340,000 meters), we can calculate the surface area:
A = 4π(696,340,000)^2
Step 2: Convert the energy emitted by the Sun into mass.
Using Einstein's equation E=mc^2, we can calculate the mass equivalent of the energy emitted by the Sun per second. Rearranging the equation, we get m=E/c^2, where m is the mass, E is the energy, and c is the speed of light (approximately 3 x 10^8 m/s).
Step 3: Calculate the mass loss per day.
To find the mass loss per day, we multiply the mass loss per second (calculated in step 2) by the number of seconds in a day (24 hours x 60 minutes x 60 seconds).
Step 4: Calculate the percentage of the Sun's mass.
To determine what percentage of the Sun's mass is lost per day, we divide the mass loss per day by the total mass of the Sun and multiply by 100.
Please note that the values used in these calculations are approximations and may slightly differ from actual values.
By following the steps above, you can calculate the mass loss of the Sun per day and the percentage of the Sun's mass that represents.