A satellite orbits at an average altitude of h = 409 km. What is its orbital speed? Use REarth = 6370 km and

mEarth = 5.98 x 10^24 kg

To find the orbital speed of the satellite, we can use the formula for the orbital speed of an object in circular motion:

V = sqrt(G * mEarth / r)

Where:
V is the orbital speed
G is the gravitational constant (6.67 x 10^-11 N m^2/kg^2)
mEarth is the mass of the Earth (5.98 x 10^24 kg)
r is the distance from the center of the Earth to the satellite's orbit (REarth + h)

Let's calculate the orbital speed step by step:

First, we need to convert the altitude of the satellite from kilometers to meters:
h = 409 km = 409,000 meters

Next, we calculate the distance from the center of the Earth to the satellite's orbit:
r = REarth + h = 6370 km + 409,000 meters = 409,000 + 6,370,000 meters = 6,779,000 meters

Now, we can substitute the values into the formula and solve for V:

V = sqrt(G * mEarth / r)
V = sqrt(6.67 x 10^-11 N m^2/kg^2 * 5.98 x 10^24 kg / 6,779,000 meters)
V = sqrt(40 x 10^13 N m^2 / kg * 5.98 x 10^24 kg / 6,779,000 meters)
V = sqrt(239.2 x 10^13 N m^2 / 6,779,000 meters)
V = sqrt(35.28 x 10^9)
V = 18782.26 m/s

Therefore, the orbital speed of the satellite is approximately 18782.26 m/s.