Calculating the lifetime of the sun is not so difficult

By MUNGAI KIHANYA

The Sunday Nation

Nairobi,

27 April 2025

From the comfort of our home planet, Earth, astronomers are able to work out seemingly impossible things about outer space. For example; by measuring the intensity of the sun’s radiation from earth, they can extrapolate and determine the total amount of energy it emits every second.

The calculation goes this way: the intensity of solar radiation on the surface of the earth is about 1,000 watts per square metre. But, before reaching here, a significant amount is absorbed by atmosphere. The total energy arriving at the top of the atmosphere is about 1,350W/sqm.

The sun is 150 million kilometres away, that is, 150 billion metres. Now think of a sphere centred at the sun and with a radius of 150 million km (150 billion metres): the sun’s reaches every part over this entire region. The total power emitted by the sun must, therefore, be 1,350W multiplied by the surface area of the gigantic sphere. The answer is a very large number: 38 followed by 25 zeroes watts.

In other words, 380 trillion-trillion watts. Let’s put that number in perspective. In one second, the sun generates more that 10 billion times the energy that the entire world consumes in a whole year!

Having established the 380 trillion-trillion watts of radiation, it is possible to work out how much mass the sun loses every second. That calculation calls for Einstein’s famous equation: energy equals mass times the square of the speed of light. The answer comes to 4.2 million tonnes per second!

Now pause for a moment and think about that: the sun is losing 4.2 million tonnes of matter every second. This immediately makes us wonder how much longer it can keep “burning”. To find out, we need to know its total mass. In tonnes, it is 2 followed by 27 zeroes.

When we divide the current total mass by the rate of loss, we should get the time it will take to get completely depleted – assuming that the rate remains constant. The answer is the number 5 followed by 20 zeroes in seconds. Since one year has 31,536,000 seconds, this works out to about 15 billion years!

However, not all the matter in the sun will be converted to radiation energy and the rate of conversion will gradually reduce as time goes by. Making these corrections in the calculation produces a more accurate life time of about 5 billion years