Answer:
the orbital speed of the communication satellite is approximately 6308.71 meters per second.
Step-by-step explanation:
To find the orbital speed of the communication satellite, we can use the formula for the orbital speed of an object in circular orbit:
Orbital speed (v) = √(G * M / r)
where:
- v is the orbital speed in meters per second,
- G is the gravitational constant (approximately 6.67430 × 10^-11 m^3 kg^-1 s^-2),
- M is the mass of the Earth in kilograms (approximately 5.972 × 10^24 kg),
- r is the distance from the center of the Earth to the satellite's orbit in meters.
Given that the satellite is located at a height of 42,000 km above Earth's surface, we need to convert this distance to meters before plugging it into the formula. The distance from the center of the Earth to the satellite's orbit (r) will be the sum of the Earth's radius and the height of the satellite:
r = (radius of Earth + height of satellite)
The radius of the Earth is approximately 6,371 km (6,371,000 meters).
r = (6,371,000 m + 42,000,000 m) = 42,371,000 meters
Now, we can calculate the orbital speed:
v = √(G * M / r)
v = √(6.67430 × 10^-11 m^3 kg^-1 s^-2 * 5.972 × 10^24 kg / 42,371,000 m)
v ≈ √(3.9860044 × 10^14 m^3 s^-2)
v ≈ 6308.71 m/s
So, the orbital speed of the communication satellite is approximately 6308.71 meters per second.