Many people mistakenly believe that the astronauts that orbit the Earth are "above gravity". Calculate g for space-shuttle territory, 206 kilometers above the Earth's surface. Earth's mass is 6e24 kg, and its radius is 6.38e6 m (6380 km). Your answer is what percentage of 9.8 m/s^2?

Again g = GM/r^2 where r is (6380+206)e3

Plane A has radius of 6000km and a mass of 6E24kg. The plane B has a radius 1500km and a mass of 1.5E22kg. Which of the planetsame is more likely to have a large metal core?

To calculate the value of "g" (acceleration due to gravity) at a specific height above the Earth's surface, we can use the formula for gravitational acceleration:

g = G * M / r^2

Where:
- G is the gravitational constant (approximately 6.67 x 10^-11 N m^2/kg^2)
- M is the mass of the Earth
- r is the distance between the center of the Earth and the point of interest (in this case, 206 km above the surface)

First, we need to convert the given height of 206 km to meters:
height = 206 km = 206,000 m

Next, we substitute the given values into the equation:
g = (6.67 x 10^-11 N m^2/kg^2) * (6 x 10^24 kg) / (6.38 x 10^6 m + 2.06 x 10^5 m)^2

Simplifying the expression:
g = (6.67 x 10^-11 N m^2/kg^2) * (6 x 10^24 kg) / (6.38 x 10^6 m + 2.06 x 10^5 m)^2
= (6.67 x 10^-11 N m^2/kg^2) * (6 x 10^24 kg) / (6.38 x 10^6 m)^2

Now we calculate g using a calculator:

g = (6.67 x 10^-11) * (6 x 10^24) / (6.38 x 10^6)^2

The value of "g" in space-shuttle territory at a height of 206 km above the Earth's surface is approximately 8.722 m/s^2.

To find the percentage of 8.722 m/s^2 in relation to 9.8 m/s^2, we can use the following equation:

percentage = (8.722 / 9.8) * 100

Calculating the percentage value:

percentage = (8.722 / 9.8) * 100

The percentage value of 8.722 m/s^2 in relation to 9.8 m/s^2 is approximately 89.12%.

Therefore, the answer is approximately 89.12% of 9.8 m/s^2.