#### Answer

At a distance of $3.0\times 10^{11}~m$, the gravitational force between the astronauts is as strong as the gravitational force of the earth on one of the astronauts.

#### Work Step by Step

Let $M_a$ be the mass of each astronaut. Let $M_e$ be the earth's mass. Let $R$ be the astronauts' distance from the center of the earth.
To find the required distance $R$, we can equate the gravitational force $F_a$ between the astronauts to the gravitational force $F_e$ of the earth on one of the astronauts.
$F_a = F_e$
$\frac{G~M_a~M_a}{(1.0~m)^2} = \frac{G~M_e~M_a}{R^2}$
$R^2 = \frac{(1.0~m)^2~M_e}{M_a}$
$R = \sqrt{\frac{(1.0~m)^2~M_e}{M_a}}$
$R = \sqrt{\frac{(1.0~m)^2~(5.98\times 10^{24}~kg)}{65~kg}}$
$R = 3.0\times 10^{11}~m$
At a distance of $3.0\times 10^{11}~m$, the gravitational force between the astronauts is as strong as the gravitational force of the earth on one of the astronauts.