The earths mass is m=5.98*10^24 kg and physics students masss is 70 kg. Knowing that the gravitational force between the student and the earth is 392 N of force, what is the distance between the student and the Earths center?

To find the distance between the student and the Earth's center, we can use Newton's Law of Universal Gravitation, which states that the gravitational force between two objects is given by:

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

where F is the force between the two objects, G is the gravitational constant (approximately 6.67 × 10^-11 N(m/kg)^2), m1 and m2 are the masses of the two objects, and r is the distance between their centers.

In this case, we know the mass of the Earth (m1 = 5.98 × 10^24 kg), the mass of the student (m2 = 70 kg), and the force between them (F = 392 N). We are trying to find the distance between the student and the Earth's center (r).

Rearranging the formula, we have:

r = sqrt((G * m1 * m2) / F)

Plugging in the given values:

G = 6.67 × 10^-11 N(m/kg)^2
m1 = 5.98 × 10^24 kg
m2 = 70 kg
F = 392 N

r = sqrt((6.67 × 10^-11 N(m/kg)^2 * 5.98 × 10^24 kg * 70 kg) / 392 N)

Now we can calculate the distance using a calculator:

r ≈ 6.38 × 10^6 meters

Therefore, the distance between the student and the Earth's center is approximately 6.38 × 10^6 meters.