Calculate a space shuttle territory 250 km above Earth's surface. Earth's mass is 6.0 * 10^24kg and its radius is 6.38 * 10^6 m (6380km)

r = 6380+250 = 6630 km = 6.63 * 10^6 m

g there = 9.81 (6.38/6.63)^2 = 9.08 m/s^2

if constant altitude g = centripetal a

v^2/r = 9.08 = v^2/(6.63*10^6)
so
v = 7.76*10^3 m/s
for orbit time
2 pi r = v t = 7.76*10^3 t

t = 5368 seconds
/3600 = 1.5 hours

By the way if you google "low altitude earth orbit" I think you will find lots on this.

To calculate the space shuttle's territory 250 km above Earth's surface, we need to determine the radius of the region from the center of the Earth.

1. Start by finding the total radius of the region:
Earth's radius (r) = 6.38 * 10^6 m
Additional height (h) = 250 km = 250,000 m

Total radius = Earth's radius + additional height
= 6.38 * 10^6 m + 250,000 m
= 6.63 * 10^6 m

2. Now, we know the total radius of the region, which is 6.63 * 10^6 m.

To find the territory, we can calculate the surface area using the formula for the surface area of a sphere:

Surface area = 4 * π * r^2

3. Plug in the value for the radius:
Surface area = 4 * π * (6.63 * 10^6 m)^2

4. Calculate the surface area:
Surface area = 4 * 3.14159 * (6.63 * 10^6 m)^2
≈ 551,101,133,343.17 square meters

Hence, the territory 250 km above Earth's surface is approximately 551,101,133,343.17 square meters.

To calculate the gravitational territory of a space shuttle 250 km above the Earth's surface, we need to consider the gravitational force between the Earth and the shuttle. We can use the concept of gravitational fields to determine this territory.

The formula to calculate the gravitational field strength at a certain distance from a planet's center is:

g = G * (M / r^2)

Where:
- g is the gravitational field strength,
- G is the gravitational constant (approximately 6.674 * 10^-11 N·m^2/kg^2),
- M is the mass of the planet,
- r is the distance from the planet's center.

In this case, we want to find the territory 250 km above the Earth's surface, so we need to calculate the gravitational field strength at that distance.

Step 1: Convert the distance to meters:
250 km = 250,000 m

Step 2: Use the formula to calculate the gravitational field strength at the given distance:
g = (6.674 * 10^-11 N·m^2/kg^2) * ((6.0 * 10^24 kg) / (6.38 * 10^6 m + 250,000 m))^2

Step 3: Simplify the equation:
g = (6.674 * 10^-11 N·m^2/kg^2) * ((6.0 * 10^24 kg) / (6.63 * 10^6 m))^2

Step 4: Calculate the gravitational field strength:
g ≈ 8.858 m/s^2

So, the gravitational field strength at a height of 250 km above the Earth's surface is approximately 8.858 m/s^2. This means that any object in that region will experience a gravitational force of 8.858 m/s^2 towards the Earth.