A person 12,000 km from the center of earth has a mass of 70 kg and weighs 182 N. What is the acceleration due to gravity at this altitude?

F = ma

182 = 70a
a = 2.6

To find the acceleration due to gravity at this altitude, we can use the formula for gravitational force:

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

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

Let's plug in the given values:

F = 182 N
m1 = 70 kg
r = 12,000,000 meters (12,000 km converted to meters)

Now we can rearrange the formula to solve for the gravitational acceleration:

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

We know that the mass of the Earth (m2) is approximately 5.972 × 10^24 kg.

Substituting the values:

G = ((182 * 12000000^2) / (5.972 × 10^24)) / 70

Now we can calculate the value of G:

G = (263520000000000 / 5.972 × 10^24) / 70
G = 4.9075 × 10^-10 m/s^2

Therefore, the acceleration due to gravity at this altitude is approximately 4.9075 × 10^-10 m/s^2.

To calculate the acceleration due to gravity at a specific altitude from the center of the Earth, we can use the equation:

g = G * (M / r^2)

where:
- g is the acceleration due to gravity
- G is the gravitational constant (approximately 6.67430 x 10^-11 m^3 kg^-1 s^-2)
- M is the mass of the Earth (approximately 5.972 x 10^24 kg)
- r is the distance from the center of the Earth

In this case, the person is 12,000 km from the center of the Earth, which is equal to 12,000,000 meters. The mass of the person is 70 kg, and the weight is given as 182 N.

First, let's calculate the mass of the Earth:

M = 5.972 x 10^24 kg

Next, we can calculate the acceleration due to gravity:

g = G * M / r^2

Substituting the values:

g = (6.67430 x 10^-11) * (5.972 x 10^24) / (12,000,000)^2

Now let's calculate the result: