How many times does the speed of a satellite in orbit change if, with a 2-fold decrease

How many times does the speed of a satellite in orbit change if, with a 2-fold decrease in the radius of a circular orbit, its orbital period decreases by 4 times?

To find the change in the speed of the specified satellite in orbit, we use the ratio: k = Vк / Vн = (2 * Π * Rк / Тк) / (2 * Π * Rн / Тн) = Тн * Rк / (Тк * Rн).

Variable relations: Тн (initial period of circulation) = 4Тк (final period); Rн (initial radius of the orbit) = 2Rк (final radius).

Let’s make a calculation: k = Tn * Rk / (Tk * Rn) = 4Tk * Rk / (Tk * 2Rk) = 4/2 = 2 p.

Answer: The speed of movement of the indicated satellite will increase 2 times.