Calculating the Increase in Earth's Mass Due to Solar Energy | e=mc2 Explained

[blackflub]

i need a lil help with this problem

The Earth receives 3 x 10^22 joules of energy from the sun per day. If theis energy is expressed as mass, what is the proportional increase in the Earth's mass in one year? (the ass of the Earth is presently 6x10^24 kg.)
i know to use e=mc2 but I'm not sure how and the answer is 2x10^-17

 

[HallsofIvy]

e= mc² so m= e/c². (Since e is in joules, m will be in kg.) that's the "increase in mass" (per DAY!). Calculate the increase in one year and then find what proportion that is to the actual mass of the earth.

 

[M98Ranger]

kg

To calculate the increase in Earth's mass due to solar energy, we can use the famous equation e=mc^2. This equation relates energy (e) to mass (m) and the speed of light (c). In this case, we are given the energy received from the sun per day, which is 3 x 10^22 joules. We can use this value to calculate the increase in mass over one year.

First, we need to convert the energy received per day to energy received per year. There are 365 days in a year, so we can multiply 3 x 10^22 joules by 365 to get the total energy received in one year, which is 1.095 x 10^25 joules.

Next, we can rearrange the equation e=mc^2 to solve for mass (m). This gives us m = e/c^2. Plugging in the value for energy (1.095 x 10^25 joules) and the speed of light (3 x 10^8 m/s), we get:

m = (1.095 x 10^25 joules) / (3 x 10^8 m/s)^2
m = 1.095 x 10^25 joules / 9 x 10^16 m^2/s^2
m = 1.216667 x 10^8 kg

This is the increase in mass over one year due to the solar energy received by the Earth. However, we need to find the proportional increase in mass, which is the increase in mass divided by the original mass of the Earth. So, we can divide this value by the mass of the Earth (6 x 10^24 kg):

Proportional increase in mass = (1.216667 x 10^8 kg) / (6 x 10^24 kg)
Proportional increase in mass = 2.027778 x 10^-17

Therefore, the proportional increase in Earth's mass due to solar energy in one year is 2.027778 x 10^-17 kg. This is a very small increase, as the mass of the Earth is already extremely large.