A spy satellite is in circular orbit around Earth. It makes one revolution in 6.02 hours.
How high above Earth's surface is the satellite
Use keplers law, comparing the moon period and distance from Earth to the Satellite.
There are other ways of doing this.
I am workin on this one too, let me know if you get it.
To determine the height above Earth's surface at which the spy satellite is orbiting, we can use Kepler's Third Law, which relates the period (time taken for one revolution) and the orbital radius (distance from the center of Earth to the satellite) of a satellite.
First, let's find the average orbital radius of the satellite. Since it is in a circular orbit around Earth, the satellite's orbital radius is equal to the distance from the center of Earth to the satellite.
Next, we need to calculate the satellite's period in seconds. The given period is 6.02 hours, so we convert it to seconds by multiplying it by 3600 seconds per hour.
6.02 hours x 3600 seconds/hour = 21,672 seconds
After converting the period to seconds, we can use Kepler's Third Law, which states that the orbital radius cubed is proportional to the period squared.
Let's use the following equation to find the orbital radius:
R^3 = k * T^2
Where R is the orbital radius, T is the period, and k is a proportionality constant.
Now, we compare it with the Moon's average distance from Earth and its period to find the proportionality constant (k).
The Moon's average distance from Earth is approximately 384,400 kilometers, and its period is about 27.3 days. To convert the period to seconds, we multiply it by 24 hours/day and 3600 seconds/hour.
27.3 days x 24 hours/day x 3600 seconds/hour = 2,360,320 seconds
Now, let's substitute the values into the equation:
(384,400 km)^3 = k * (2,360,320 seconds)^2
Cubing the Moon's average distance from Earth (384,400 km) gives us:
56,937,086,784,000,000,000 km^3 = k * (2,360,320 seconds)^2
Now we solve for k:
k = 56,937,086,784,000,000,000 km^3 / ((2,360,320 s)^2)
k ≈ 8.99 x 10^10 km^3/s^2
Finally, we can determine the height above Earth's surface at which the satellite is orbiting by substituting the orbital period (21,672 seconds) into the equation and solving for R:
R^3 = (8.99 x 10^10 km^3/s^2) * (21,672 seconds)^2
R ≈ 42,253 km
Therefore, the spy satellite is orbiting at an altitude of approximately 42,253 kilometers above Earth's surface.