I have read these questions:
How fast would the Earth need to spin for us to feel weightless?
Why can't we feel the Earth (or being in any non-inertial frame) rotating?
And it made me curious. Is there a certain limit of a planet's spin speed, where it becomes unfit to wear an atmosphere?
Based on the calculation in the question:
The velocity of the Earth at its surface can be calculated by noting it takes $1 \text{ day} = 86400 \text{ s}$ to rotate a full $2\pi$ radians, so
$$v=\frac{2\pi R_\text{Earth}}{T_\text{day}}\sim\frac{2\pi\times6400\times10^3\text{ m}}{86400\text{ s}}\sim470\text{ m s}^{-1}$$
The centripetal acceleration is then
$$a=\frac{v^2}{R_\text{Earth}}\sim\frac{(470\text{ m s}^{-1})^2}{6400\times10^3\text{ m}}\sim0.035\text{ m s}^{-2}\ll9.8\text{ m s}^{-2}$$
So basically, the Earth would need to spin 300 times faster?
Because 0.035m/s^2 *300 ~ 9.8 m/s^2?
This is where gravity would equal the centrifugal force?
Where did I make a mistake?
Question:
- What is the spin limit, where Earth would not be able to keep the atmosphere?
