a 1kg satellite has an orbital period of 4 hours. what's the altitude?

To determine the altitude of a 1kg satellite with a given orbital period, you need to use the following formula:

h = ((G * M * T^2) / (4 * π^2))^(1/3) - R

Where:
- h is the altitude of the satellite from the Earth's surface
- G is the gravitational constant (approximately 6.67430 × 10^(-11) m^3 kg^(-1) s^(-2))
- M is the mass of the Earth (approximately 5.972 × 10^24 kg)
- T is the orbital period in seconds
- π is a mathematical constant (approximately 3.14159)
- R is the radius of the Earth (approximately 6,371 km)

In this case, we know the following information:
- M = 5.972 × 10^24 kg
- T = 4 hours = 4 * 60 * 60 seconds = 14,400 seconds
- R = 6,371 km = 6,371,000 meters

Now, let's plug in these values into the formula and calculate the altitude.

h = ((6.67430 × 10^(-11) * 5.972 × 10^24 * 14,400^2) / (4 * 3.14159^2))^(1/3) - 6,371,000

After evaluating this expression, you will have the altitude of the satellite from the Earth's surface in meters.