Calculate the magnitude of the gravitational force between the Earth and an m = 6.00 kg mass on the surface of the Earth. The distance to the center of the Earth from the surface is 6.37×103 km and the mass of the Earth is 5.98×1024 kg.

F = GMm/r^2

= (6.67*10^-11)(5.98*10^24)(6.00)/(6.37*10^6)^2 = 58.9 N

But then, we knew that, since 6.00*9.8 = 58.9

To calculate the magnitude of the gravitational force between the Earth and the mass on its surface, you can use the equation for gravitational force:

F = (G * m1 * m2) / r^2

where F is the gravitational force, G is the gravitational constant (6.67430 × 10^-11 N m^2/kg^2), m1 is the mass of the Earth, m2 is the mass of the object, and r is the distance from the center of the Earth to the object's location (in this case, the surface of the Earth).

Given:
m1 = 5.98 × 10^24 kg
m2 = 6.00 kg
r = 6.37 × 10^3 km = 6.37 × 10^6 m

Substituting these values into the equation, we get:

F = (6.67430 × 10^-11 N m^2/kg^2 * 5.98 × 10^24 kg * 6.00 kg) / (6.37 × 10^6 m)^2

Now, let's calculate it step by step.

First, find the square of the distance (r^2):
r^2 = (6.37 × 10^6 m)^2 = 4.07 × 10^13 m^2

Next, multiply G, m1, and m2:
G * m1 * m2 = 6.67430 × 10^-11 N m^2/kg^2 * 5.98 × 10^24 kg * 6.00 kg = 2.38844412 × 10^14 N m^2

Now, divide the previous result by r^2 to find the gravitational force:
F = (2.38844412 × 10^14 N m^2) / (4.07 × 10^13 m^2)

Simplifying this division gives us:
F ≈ 5.86 N

Therefore, the magnitude of the gravitational force between the Earth and the mass on its surface is approximately 5.86 Newtons.