Determine the ratio of Earth's gravitational force exerted on an 80-kg person when at Earth's surface and when 1000km above Earth's surface. The radius of Earth is 6370 km.

I have tried (6370)^2/(7370)^2 = 0.747 and it is wrong??

That is the correct answer for a ratio.

What equation did you use?

It is the also 1/0.747 or 1.376

To determine the ratio of Earth's gravitational force exerted on a person when at the Earth's surface and when 1000 km above Earth's surface, we can use the inverse square law of gravitation.

The formula for gravitational force is given by:

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

Where:
F is the gravitational force between two objects,
G is the gravitational constant (approximately 6.674 × 10^-11 N m^2 / kg^2),
m1 and m2 are the masses of the objects, and
r is the distance between the centers of the two objects.

In this case, one of the objects is Earth, and the other object is the person. We want to find the ratio of the gravitational forces exerted on the person when at the Earth's surface and when 1000 km above the Earth's surface.

Let's denote the gravitational force at the Earth's surface as F1 and the gravitational force 1000 km above Earth's surface as F2.

For the gravitational force at Earth's surface, the mass of Earth can be considered much larger than the person's mass, so we can neglect the person's mass in the calculations. The distance from the person to the center of Earth is the Earth's radius, r1 = 6370 km. Therefore, we have:

F1 = (G * m * Me) / r1^2

Where:
Me is the mass of Earth (approximately 5.972 × 10^24 kg).

For the gravitational force 1000 km above Earth's surface, the distance from the person to the center of Earth is (r1 + 1000) km. Therefore, we have:

F2 = (G * m * Me) / (r1 + 1000)^2

Now, we can calculate the ratio of the two forces:

Ratio = F2 / F1
= [(G * m * Me) / (r1 + 1000)^2] / [(G * m * Me) / (r1)^2]
= (r1^2) / (r1 + 1000)^2

Substituting the values given in the question:

r1 = 6370 km
r1 + 1000 = 7370 km

Therefore, the correct calculation for the ratio is:

Ratio = (6370^2) / (7370^2) ≈ 0.749

Therefore, the correct ratio of Earth's gravitational force exerted on an 80-kg person when at Earth's surface and when 1000 km above Earth's surface is approximately 0.749.