If the Earth had a moon that orbited at a distance of 10 Earth radii, how long would its orbital period be?
10 Earth radii away, the gravitational force of the Earth (per unit mass)

$$
\frac{g}{10^{2}}
$$

must be equal to the centrifugal force of the respective moon:

$$
\frac{g}{10^{2}}=\frac{4 \pi^{2} \cdot 10 \cdot r}{T^{2}}
$$

from which

$$
T=160070 \mathrm{sec}=1 \text { day } 20 \text { hours } 27 \mathrm{m} 50 \mathrm{s}
$$

(Rézó Földes, Budapest.)

The problem was also solved by: L. Bánó, J. Blum, I. Csada, K. Epstein, V. Gráf, A. Haar, Gy. Jánosy, J. Koritsanszky, F. Kräuter, P. Merse, T. Pözel, O. Szilas, J. Székely, K. Sztrokay.