You A satellite in a circular orbit of radius R around planet X has an orbital period T. If Planet X had one-fourth as much mass, the orbital period of this satellite in an orbit of the same radius would be: A) 2T B) T square root(2) C) T/4 D) T/2 E) 4

The orbital period of a satellite in a circular orbit depends on the mass of the central body (planet X) and the radius of the orbit (R) according to Kepler's laws of planetary motion.

If the mass of planet X is reduced to one-fourth (M/4), while the orbital radius (R) remains constant, the orbital period (T) will increase.

The relationship between the orbital period (T) and the mass of the central body (M) is proportional to the square root of M (T ∝ √M).

Therefore, if the mass is reduced to one-fourth, the orbital period will increase by a factor of the square root of 4 (which is 2).

So the new orbital period (T') would be:

T' = T * √(M/4) / √M

T' = T * √(1/4)

T' = T / 2

Therefore, the answer is D) T/2.

You A satellite in a circular orbit of radius R around planet X has an orbital period T. If Planet X had one-fourth as much mass, the orbital period of this satellite in an orbit of the same radius would be: A) 2T B) T square root(2) C) T/4 D) T/2 E) 4​

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You A satellite in a circular orbit of radius R around planet X has an orbital period T. If Planet X had one-fourth as much mass, the orbital period of this satellite in an orbit of the same radius would be: A) 2T B) T square root(2) C) T/4 D) T/2 E) 4