Question

The sun produces energy by nuclear fusion reactions, in which matter is converted into energy. By measuring the amount of energy we receive from the sun, we know that it is producing energy at a rate of 3.8 x 10²⁶ W.

How many kilograms of matter does the sun lose each second?

Answer 1

Using Einstein's equation E = mc², the sun's mass loss per second due to energy production is calculated to be approximately 4.2 million kilograms, which is significant when compared to the mass of large asteroids.

Step-by-step explanation:

The sun is a fusion power plant, converting mass directly into energy. According to Einstein's famous equation E = mc², the energy E produced can be calculated if the mass m is known, with c being the speed of light. The sun produces energy at a rate of about 3.8 × 10² watts.

To find out how much mass the sun converts into energy per second, we can rearrange Einstein's equation to solve for m: m = E/c². Given that c, the speed of light, is approximately 3 × 10 meters per second, and the energy output of the sun is 3.8 × 10² watts (joules per second), we can calculate the mass loss.

m = (3.8 × 10²) / (3 × 10)² ≈ 4.2 × 10¹ kg/s

This means the sun loses about 4.2 million kilograms of mass per second. Compared to the sun's total mass, this amount is small; however, it is on such a scale that, when compared to an asteroid 50 km in diameter with a density of 2,000 kg/m³, the sun's mass loss per second is significant. The energy of the sun and its capacity to convert matter into energy is vital for understanding many aspects of astrophysics and the life cycles of stars.