# How high were the tides back when the Moon was much closer to Earth?

In this article it is stated that the Moon was originally much closer to Earth at a distance of 22,500 km rather than the 384,400 km it is today. What was the height of the tides back then in meters? Surely they would've been orders of magnitude higher?

• The tidal force and the height of the tides are proportional to the inverse cube of the Earth-Moon distance. Sep 29, 2020 at 2:01

$$|a_{tidal}| = 2\Delta r G \frac{M}{R^3}$$
where $$\Delta r$$ is the radius of the Earth (6371 km), G is the gravitational constant (6.674 x 10$$^{-11} m^3kg^{-1}s^{-2}$$, M is the mass of the Moon (7.342 x 10$$^{22}$$kg), and R is the distance between the two (here either 22,500km or 384,400km). To check our equation we can calculate the current tidal acceleration: using 384,400km, we arrive at a value of 1.099 μm/s$$^2$$, which is close to the accepted value of 1.10 μm/s$$^2$$ (2). Calculating the tidal force using the distance of 22,500km, we arrive at a value of 0.0055 m/s$$^2$$, or about 5,000 times the current tidal force. That could make for some massive tides, however, were there oceans?