The sun radiates energy at the rate of 3.92x 10^26 W. (a) What is the change in the sun's mass in one second? (b)How much mass does the sun lose in the lifetime of your average earthling (say, 75 years)?

(a) Use Einstein's equation

E = m c^2

The mass loss rate is
1/c^2 * (Energy loss rate)

(b) Mass loss = (Mass loss rate)* T
where T = 75 years, expressed in seconds

75 y = 2.37*10^9 s
Use the mass loss rate that you calculate for (a)

To determine the change in the sun's mass in one second, we can use Einstein's famous equation, E = mc^2, which relates energy, mass, and the speed of light.

Given:
Energy radiated by the Sun per second = 3.92 x 10^26 W

(a) Change in the sun's mass in one second:
Using the equation E = mc^2, we can solve for mass (m):
E = mc^2
m = E / c^2

where:
E = energy radiated by the Sun per second
c = speed of light in a vacuum (approximately 3 x 10^8 m/s)

Plugging in the values:
m = (3.92 x 10^26 W) / (3 x 10^8 m/s)^2

Calculating:
m ≈ 4.36 x 10^9 kg

Therefore, the change in the sun's mass in one second is approximately 4.36 x 10^9 kg.

(b) To calculate the amount of mass the Sun loses in the lifetime of an average earthling of 75 years, we need to determine the number of seconds in 75 years.

Number of seconds in 1 year:
1 year = 365 days * 24 hours * 60 minutes * 60 seconds ≈ 31,536,000 seconds

Number of seconds in 75 years:
75 years = 75 * 31,536,000 seconds ≈ 2,365,200,000 seconds

To find the mass lost, we multiply the change in mass per second by the number of seconds in 75 years:
Mass loss = (4.36 x 10^9 kg/s) * (2,365,200,000 s)

Calculating:
Mass loss ≈ 1.03 x 10^19 kg

Therefore, the Sun would lose approximately 1.03 x 10^19 kg of mass in the lifetime of an average earthling of 75 years.

To determine the change in the sun's mass in one second, we can use Einstein's mass-energy equivalence formula, E=mc^2, where E is the energy radiated by the sun, m is the change in mass, and c is the speed of light.

(a) To solve for the change in mass, we need to rearrange the equation to solve for m:

m = E / c^2.

Given that the sun radiates energy at the rate of 3.92 x 10^26 W and the speed of light is approximately 3 x 10^8 m/s, we can substitute the values into the equation:

m = (3.92 x 10^26 W) / (3 x 10^8 m/s)^2.

Calculating this equation will give us the change in mass in one second.

(b) To determine the mass lost by the sun in the lifetime of an average earthling (75 years), we need to calculate the change in mass per second and then multiply it by the number of seconds in 75 years.

First, let's find the number of seconds in 75 years. There are 365 days in a year and 24 hours in a day, so:

Number of seconds in 75 years = 75 years x 365 days/year x 24 hours/day x 3600 seconds/hour.

Once we have the number of seconds, we can multiply it by the change in mass per second to find the mass lost by the sun.

Please note that the calculation above assumes a constant rate of energy radiation by the sun. In reality, the sun's energy output can vary over time.