What if the Earth Fell into the Sun?
Have you ever wondered what would happen if our planet suddenly stopped orbiting and began falling straight into the Sun? In this video, we explore this dramatic thought experiment using fundamental principles of physics.
Part 1:
We begin by calculating how long it would take for the Earth to fall into the Sun using energy conservation. Starting from the gravitational potential energy and zero initial kinetic energy, we derive the free–fall time equation and find that, surprisingly, the Earth would have just over two months before it’s consumed.
Part 2:
Next, we analyse how the Earth’s temperature would evolve during this catastrophic fall. By comparing the energy it receives from the Sun with the energy it radiates away—and incorporating effects such as albedo and a simple atmospheric greenhouse model—we trace the rise in surface temperature from Earth’s current climate all the way to thousands of Kelvin as the planet nears the Sun.
Part 3:
We then turn our attention to tidal forces. Using the concept of the Roche limit, we estimate the point at which the Sun’s gravitational pull would tear the Earth apart. Our analysis shows that as the Earth heats up and becomes molten, the fluid approximation becomes valid, and we arrive at a Roche limit of roughly one million kilometers from the Sun.
Part 4:
Finally, we explore how the Sun’s appearance in the sky would dramatically change as the Earth draws closer. We calculate the angular size of the Sun throughout the fall, illustrating just how quickly our familiar celestial disk would grow until it dominates the sky in its final moments.
References:
Aatish Bhatia article: https://www.wired.com/2014/12/empzeal-earthfall/
A Simplified Theoretical Treatment and Simulated Experimental
Calculation of the Roche Limit - https://doi.org/10.1119/1.2336145
Radial Motion of Two Mutually Attracting Particles - https://doi.org/10.1119/1.3246467
From Moon-fall to motions under inverse square laws - https://iopscience.iop.org/article/10.1088/0143-0807/29/5/012
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