Daily Loss of Solar Mass

Introduction

I occasionally work with customers on using solar power to drive some of their remote optical interfaces. These remote interfaces are used to monitor things like pipelines. In one case, it was used to provide Internet service to a bunkhouse for cowboys where AC power was not available. When I work on these systems, I always find myself amazed at the amount of power that the Sun puts out. Every watt that the Sun puts out comes from fusion, which means that the Sun is constantly losing mass. I started to wonder today about the amount of mass that the Sun must be losing every second. We should be able to compute that. Let's dig in ...

Analysis

As always, we need to gather a little data.

  • Distance from the Sun to the Earth, R= 149·106 km (Source)
  • Solar power density measured at the edge of the Earth's atmosphere σ = 1366 W/m2(Source)

I threw this into Mathcad to get the following result.

Figure 1: Solar Mass Loss Calculation.

Figure 1: Solar Mass Loss Calculation.

So a quick calculation shows that the Sun must be losing 4 million metric tons of mass per second. As a check, I found a similar result through a Google search.

Conclusion

The amount of power that the Sun generates is amazing. The amount of mass it loses per second is also amazing. However, when you look at its total mass (2·1030 kg), the Sun will be here for billions of years to come.

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2 Responses to Daily Loss of Solar Mass

  1. Jakov Kucan says:

    Interesting fact -- hard to get one's head around numbers of this magnitude. Gald too se you reach for Mathcad as a tool of choice to do a quck calculaiton like this (with units too).

    • mathscinotes says:

      I have access to all the various computer algebra systems, but I tend to use Mathcad the most. It generally is the quickest way for me to get to a production ready document, both at work and at home (i.e. blogging).

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