Calculating the Height of the Satellite above Earth's Surface

Given data:
- Radius of Earth (r) = 6400 km
- Time taken for one orbit (T) = 90 min
- Acceleration due to gravity (g) = 9.8 m/s²

Step 1: Converting the given data to appropriate units
Before proceeding with the calculations, we need to ensure that all the data is in the same units.
- Convert the radius of Earth from kilometers to meters:
- 1 km = 1000 m
- Therefore, r = 6400 km = 6400 × 1000 m = 6,400,000 m

Step 2: Finding the radius of the satellite's orbit
Since the satellite makes a circle around the Earth, the radius of its orbit will be the sum of the radius of the Earth and the height of the satellite above the Earth's surface.
Let h be the height of the satellite above the Earth's surface.
- Radius of satellite's orbit (R) = r + h

Step 3: Calculating the time period of the satellite's orbit
The time period of the satellite's orbit is the time taken for one complete revolution.
- Given: Time taken for one orbit (T) = 90 min
- Convert 90 min to seconds:
- 1 min = 60 s
- Therefore, T = 90 min × 60 s/min = 5400 s

Step 4: Applying the formula for the time period of a satellite's orbit
The time period of a satellite's orbit can be calculated using the formula:
- T = 2π√(R³/g)
- Rearranging the formula, we get:
- R = [(gT²)/(4π²)]^(1/3)

Step 5: Calculating the height of the satellite above Earth's surface
Substitute the values of g and T in the formula obtained in Step 4 to calculate the radius of the satellite's orbit (R).
- R = [(9.8 m/s²) × (5400 s)² / (4π²)]^(1/3)
- R ≈ 7,034,882.8 m

Now, subtract the radius of the Earth (r) from the radius of the satellite's orbit (R) to find the height of the satellite above the Earth's surface (h).
- h = R - r
- h ≈ 7,034,882.8 m - 6,400,000 m
- h ≈ 634,882.8 m

Answer:
The height of the satellite above the Earth's surface is approximately 634,882.8 meters.

2600km