de sun radites energy in all direction . de average raditians receved on earth surface on earth frm sun per sec is 1.4kilowatt/metre2 de average earth earth sun distance is 1.5*10¹¹

metre de mass lost by de sun per day [ i day = 86400] is

1. 4.4 *10 raise to 9

2.7.6*10 raise to 14

3. 3.8 *10 raise to 12

4. 3.8*10 raise 14

To determine the mass lost by the Sun per day, we can use the information provided about solar energy and the relationship between energy and mass. The average solar radiation received on Earth is approximately 1.4 kilowatts per square meter, and the average distance from the Earth to the Sun is about 1.5 x 10^11 meters. Let's break this down step by step.

Understanding Solar Energy Output

The Sun emits energy in all directions, and the total power output of the Sun is known as its luminosity. The energy that reaches the Earth is just a small fraction of this total output. The energy received per square meter at the distance of the Earth is 1.4 kW/m².

Calculating Total Energy Received by Earth

To find the total energy received by the Earth, we need to calculate the surface area of a sphere with a radius equal to the average distance from the Earth to the Sun. The formula for the surface area of a sphere is:

• Surface Area = 4πr²

Substituting the radius (r = 1.5 x 10^11 m):

• Surface Area = 4π(1.5 x 10^11)²
• Surface Area ≈ 4π(2.25 x 10^22) ≈ 2.83 x 10^23 m²

Now, we can calculate the total power received by Earth:

• Total Power = Solar Radiation × Surface Area
• Total Power = 1.4 kW/m² × 2.83 x 10^23 m²
• Total Power ≈ 3.96 x 10^23 watts

Relating Energy to Mass

According to Einstein's famous equation, E = mc², we can relate energy (E) to mass (m) and the speed of light (c). The speed of light is approximately 3 x 10^8 m/s. Rearranging the equation gives us:

• m = E/c²

Now, we need to find out how much energy the Sun loses per day. Since we have the total power output, we can calculate the energy lost in one day:

• Energy per day = Total Power × Time
• Energy per day = 3.96 x 10^23 watts × 86400 seconds
• Energy per day ≈ 3.42 x 10^28 joules

Calculating Mass Loss

Now we can find the mass lost by the Sun using the energy calculated:

• m = E/c²
• m = (3.42 x 10^28 joules) / (3 x 10^8 m/s)²
• m ≈ (3.42 x 10^28) / (9 x 10^16) ≈ 3.8 x 10^11 kg

Final Calculation and Answer

Thus, the mass lost by the Sun per day is approximately 3.8 x 10^11 kg. Looking at the options provided:

• 1. 4.4 x 10^9
• 2. 7.6 x 10^14
• 3. 3.8 x 10^12
• 4. 3.8 x 10^14

The closest answer to our calculation is option 3: 3.8 x 10^12 kg.