Final answer:
After converting kilometers to meters and performing the calculation, the value of g is approximately 3.706 m/s².
Step-by-step explanation:
To calculate the value of g as given in the question, we need to ensure all units are consistent. Since g is provided in units of Nm²/Kg², and the distance is given in kilometers, we need to convert kilometers to meters. One kilometer is equal to 1,000 meters.
Using the provided formula: g = (6.67x10^-11 Nm²/Kg²) (6.4x10^23 Kg) / (3396 km)^2, we convert kilometers to meters by multiplying 3396 km by 1,000 which gives us 3396000 meters. Now we have g in consistent units:
g = (6.67x10^-11 Nm²/Kg²) (6.4x10^23 Kg) / (3396000 m)^2,
Now, performing the calculation:
g = (6.67x10^-11 Nm²/Kg²) (6.4x10^23 Kg) / (3.396x10^6 m)^2,
g = (6.67x10^-11 x 6.4x10^23) / (3.396x10^6)^2,
g = (4.2688x10^13) / (1.1528816x10^13),
g ≈ 3.706x10^0 m/s² or g ≈ 3.706 m/s² (to four significant figures).
Therefore, the value of g after performing the calculation is approximately 3.706 m/s².