This gives a simple derivation of the formulae to determine
due to the Sun’s mass loss caused by solar wind from its surface and fusion at its core.
For simplicity it is assumed that the Earth’s orbit around the Sun is circular, in which case the rules of orbital mechanics means it must move with a constant velocity.
Fundamental Principal – The Conservation of Angular Momentum
As the Sun loses mass its gravitational pull on the Earth weakens, as a result the Earth spirals out to a higher orbit, its orbital speed slows and its orbital period lengthens. To calculate the magnitude of these changes we use the fact that the changes to the Earth’s orbit must obey the law of conservation of angular momentum.
This states:
“the total angular momentum of a system (e.g. the Earth orbiting the Sun) remains constant if no external torque (i.e. a twisting force) acts upon it”
Derivation of the Formula for the Rate of change of Orbital Radius
The Earth’s orbital angular momentum L is given by:
Derivation of the Formula for the Rate of Change of Orbital Velocity
Derivation of the Formula for the Rate of Change of Orbital Period
For a circular orbit the orbital period is given by:
Calculation of the Rates of Change
To calculate the actual rate of change we will assume the following.
Using the previous formulae, we obtain:
And Finally...
I hope this article been interesting and valuable. A pdf version can also be downloaded
Solar Mass Loss and Earths Orbital Parameters pdf
Explaining Science
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