Calculate the force of gravity on a 12 kg mass if it were 6.4 106 m above Earth's surface (that is, if it were 2 Earth radii from Earth's center.)

Think about the inverse square law. At two earth radii from center, the weight force is REDUCED by a factor of 2^2.

Don't forget to convert mass (kg) to force (N)

To calculate the force of gravity on a mass, you can use the formula for gravitational force:

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

Where:
- F is the force of gravity
- G is the gravitational constant (approximately 6.67430 × 10^-11 N m^2/kg^2)
- m1 and m2 are the masses of the two objects (in this case, the mass of the object and the mass of the Earth)
- r is the distance between the centers of the two objects (in this case, the distance between the center of the Earth and the object).

In this case, the mass of the object is 12 kg and the distance from Earth's center is 2 times the radius of the Earth (since it is 2 Earth radii away).

Let's calculate the force of gravity using these values:

Step 1: Calculate the distance between the object and Earth's center:
The radius of the Earth is approximately 6.4 × 10^6 m. Since the object is 2 Earth radii away, the distance from Earth's center is 2 times the radius:
r = 2 * (6.4 × 10^6 m) = 12.8 × 10^6 m

Step 2: Substitute the values into the formula:
F = (6.67430 × 10^-11 N m^2/kg^2 * 12 kg * mass of the Earth) / (12.8 × 10^6 m)^2

The mass of the Earth is approximately 5.972 × 10^24 kg.

F = (6.67430 × 10^-11 N m^2/kg^2 * 12 kg * 5.972 × 10^24 kg) / (12.8 × 10^6 m)^2

Step 3: Simplify and calculate the answer:

F = (8.00816 × 10^14 N m^2/kg^2) / (163.84 × 10^12 m^2)
F = 4.89 × 10^(-1) N

So, the force of gravity on the 12 kg mass, when it is 6.4 × 10^6 m above Earth's surface, is approximately 0.489 N (Newtons).