At the heighest point on earth, the distance to the center of the earth is approximately equal to 1.0014 times the radius of the earth. What would be in N/kg the magnitude of the gravitational field (g) due to the earth at that position? Assume 9.8 N/kg for g at the surface of the earth.

g=GM/R2 also g'=GM/r2 gR2=GM=g'2 9.8R2=g'(1.0014R)2 g'=9.77N/kg

To calculate the gravitational field at the highest point on Earth, we can use the gravitational field formula:

g = (G * M) / r^2

Where:
g is the gravitational field
G is the gravitational constant (approximately 6.67430 × 10^-11 N m^2 / kg^2)
M is the mass of the Earth
r is the distance from the center of the Earth

First, we need to find the distance from the center of the Earth to the highest point. We are given that this distance is approximately 1.0014 times the radius of the Earth.

Let's assume the radius of the Earth (rE) = 6,371 km.

So, the distance to the highest point (d) would be:
d = 1.0014 * rE

Next, we'll use this value of d to calculate the magnitude of the gravitational field (g) at the highest point:

g = (G * M) / d^2

Now, we have all the information we need to solve for g. Let's plug in the known values:

G = 6.67430 × 10^-11 N m^2 / kg^2
M = mass of the Earth (approximately 5.972 × 10^24 kg)
d = 1.0014 * rE

Plugging these values into the equation, we can calculate the gravitational field (g) at the highest point:

g = (6.67430 × 10^-11 N m^2 / kg^2 * 5.972 × 10^24 kg) / (1.0014 * rE)^2

Now, substituting the value of rE (6,371 km) and performing the calculation, we can find the magnitude of the gravitational field:

g = (6.67430 × 10^-11 N m^2 / kg^2 * 5.972 × 10^24 kg) / (1.0014 * 6,371,000 m)^2

Evaluating this expression will give us the final answer for the magnitude of the gravitational field (g) at the highest point on Earth.