The acceleration due to gravity is about 10 m/s2 at the Earth's surface. What is the acceleration due to gravity for a person on the space station orbiting 200 miles above the Earth's surface?

Well, up in space, things can get pretty "elevated." The acceleration due to gravity on the International Space Station (ISS) isn't quite the same as it is on the Earth's surface. You see, the ISS orbits around 200 miles above the surface, and in that lofty realm, the acceleration due to gravity is only about 90% as strong. So, it's sort of like a "light" version of gravity up there, keeping the astronauts from floating too far away.

To find the acceleration due to gravity for a person on the space station orbiting 200 miles above the Earth's surface, we need to use Newton's law of universal gravitation.

The formula for the acceleration due to gravity is:

a = G * (M / r^2)

where:
- a is the acceleration due to gravity
- G is the gravitational constant (approximately 6.674 × 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 space station. We know that the radius of the Earth is approximately 3959 miles (6371 km). So the distance from the center of the Earth to the space station is the sum of the radius of the Earth and the height of the space station above the Earth's surface:

Distance = Radius of Earth + Height of the space station
= 3959 miles + 200 miles
= 4159 miles

Now we need to convert this distance to meters:

Distance in meters = 4159 miles * (1.60934 km / 1 mile) * (1000 m / 1 km)
= 6669 km * 1000 m / km
= 6669000 m

Now we can calculate the acceleration due to gravity using the formula:

a = (6.674 × 10^-11 N(m^2/kg^2)) * (5.972 × 10^24 kg) / (6669000 m)^2

Calculating this, we get:

a ≈ 8.66 m/s^2

Therefore, the acceleration due to gravity for a person on the space station orbiting 200 miles above the Earth's surface is approximately 8.66 m/s^2.

To find the acceleration due to gravity for a person on the space station orbiting 200 miles above the Earth's surface, we need to understand the relationship between gravity and distance.

The acceleration due to gravity depends on the mass of the object and the distance between the objects. It follows a inverse square law, which means that the acceleration decreases as the distance increases.

In this case, the person on the space station is 200 miles (or approximately 321.87 kilometers) above the Earth's surface.

To calculate the acceleration due to gravity for the person on the space station, we need to know the mass of the Earth and the radius of the Earth. The mass of the Earth is approximately 5.97 x 10^24 kg, and the radius of the Earth is approximately 6,371 kilometers.

Using the formula for acceleration due to gravity, which is:

g = G * (m1 / r^2)

where g is the acceleration due to gravity, G is the gravitational constant (approximately 6.67 x 10^-11 N(m/kg)^2), m1 is the mass of the Earth, and r is the distance between the person on the space station and the center of the Earth.

Let's convert the distance to meters: 200 miles = 321,868.8 meters

Now we can substitute the values into the formula:

g = (6.67 x 10^-11 N(m/kg)^2) * (5.97 x 10^24 kg) / (6,371 km + 321.87 km)^2

After calculating, we find that the acceleration due to gravity for a person on the space station orbiting 200 miles above the Earth's surface is approximately 8.94 m/s^2.

Therefore, the acceleration due to gravity is approximately 8.94 m/s^2 for a person on the space station orbiting 200 miles above the Earth's surface.

First of all, at the Earth's surface, g is 9.8 m/s^2, not 10 m/s^2.

As you get higher above the surface of the Earth, g decreases in proportion to the inverse square of the distance from the center. You will need to look up the Earth's radius Re to make the correction.

Multiply the surface g value by
[Re/(Re + 200)]^2
Re must be in miles. It is roughly 4000 miles.