Two spherical asteroids, X X\,X and YYY, are separated by a center-to-center distance d d\,d and exert a gravitational force of attraction F1 F_1\,F1 on one another.
The mass of asteroid X X\,X increases to a new value mX′ m_X'\,mX′ such that mX<mX′<3mXm_X < m_X' < 3m_XmX<mX′<3mX. At the same time, the distance between their centers is tripled.
Which statement correctly describes the range of the new gravitational force F2 F_2\,F2 between the two asteroids?
F2>13F1F_2 > \frac{1}{3} F_1F2>31F1
19F1<F2<13F1\frac{1}{9} F_1 < F_2 < \frac{1}{3} F_191F1<F2<31F1
F2=19F1F_2 = \frac{1}{9} F_1F2=91F1
0<F2<19F10 < F_2 < \frac{1}{9} F_10<F2<91F1
