A spy satellite was launched into a circular orbit with a height of 599 km above the surface of the Earth. Determine its orbital speed and period. (The mass of the Earth is 5.97 1024 kg, and the radius of the Earth is 6370 km.)

we know that centripetal acceleration is a=v^2/r.

If we set this equal to g (g= GM/r^2), then we find that v=sqrt[GM/R].

Then we just plug in our variables. *Note: remember what units to use: meters (m), kilograms (kg). This will produce an answer in m/s.

So:
v= sqrt(6.67e-11 x 5.98e24 kg)/(599e3 m + 6.38e6 m)
= 7559.9 m/s

To determine the orbital speed and period of the spy satellite, we can use the following formulas and steps:

1. Orbital Speed:
- The orbital speed (v) of an object in circular orbit can be calculated using the formula: v = √(G * M / r)
where G is the gravitational constant (6.674 × 10^-11 N(m/kg)^2), M is the mass of the Earth, and r is the distance from the center of the Earth to the satellite's orbit.

- Convert the height of the satellite above the Earth's surface into the total distance from the center of the Earth to the satellite's orbit:
r = radius of the Earth + height of the satellite

- Substitute the values into the formula and calculate the orbital speed.

2. Orbital Period:
- The orbital period (T) of an object in circular orbit can be calculated using the formula: T = 2π * √(r^3 / (G * M))
where r is the distance from the center of the Earth to the satellite's orbit.

- Substitute the calculated value of r into the formula and calculate the orbital period.

Let's solve for the orbital speed and period now!

Given:
- Mass of the Earth (M) = 5.97 × 10^24 kg
- Radius of the Earth (R) = 6370 km
- Height of satellite above the Earth's surface = 599 km

Step 1: Orbital Speed
- Calculate the total distance from the center of the Earth to the satellite's orbit:
r = R + height of the satellite
r = 6370 km + 599 km

Step 2: Orbital Speed
- Substitute the values into the formula:
v = √(G * M / r)

Step 3: Orbital Period
- Substitute the calculated value of r into the formula:
T = 2π * √(r^3 / (G * M))

By following these steps and performing the calculations, we can determine both the orbital speed and period of the spy satellite.