Answer:4.72 * 10^6 meters
Explanation: the distance between the astronaut and Mercury's center, we can use the formula for gravitational force:
F = (G * m1 * m2) / r^2
Where:
- F is the gravitational force
- G is the gravitational constant (approximately 6.67430 x 10^-11 N m^2/kg^2)
- m1 and m2 are the masses of the two objects
- r is the distance between the centers of the two objects
In this case, we know the following information:
- Mass of Mercury (m1) = 3.2 * 10^23 kg
- Mass of the astronaut (m2) = 125 kg
- Gravitational force (F) = 902.83 N
We want to find the distance (r) between the astronaut and Mercury's center.
Rearranging the formula, we can solve for r:
r = sqrt((G * m1 * m2) / F)
Substituting the values into the formula, we get:
r = sqrt((6.67430 x 10^-11 N m^2/kg^2 * 3.2 * 10^23 kg * 125 kg) / 902.83 N)
Simplifying the calculation:
r ≈ 4.72 * 10^6 meters