a geosynchronous satellite orbits at a distance from earth's center of about 6.6 earth radii and takes 24 h to go around once. what distance in meters does the satellite travel in one day? what is its orbital velocity in m /s?

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http://www.jiskha.com/display.cgi?id=1290712922

To find the distance that a geosynchronous satellite travels in one day, we need to calculate the circumference of its orbit. The circumference of a circle can be found using the formula C = 2πr, where C is the circumference and r is the radius of the circle.

In this case, the radius of the satellite's orbit is given as 6.6 Earth radii. We can calculate the distance in meters by multiplying the radius by the Earth's radius, which is approximately 6,371,000 meters.

Distance traveled in one day = Circumference of orbit = 2π × radius

Let's calculate it now:

Radius of satellite's orbit = 6.6 Earth radii × 6,371,000 meters
= 42,066,600 meters

Circumference of orbit = 2π × 42,066,600 meters
≈ 264,895,343.53 meters

Therefore, the geosynchronous satellite travels approximately 264,895,343.53 meters in one day.

To find the orbital velocity of the satellite, we can divide the distance traveled in one day by the time taken for one revolution.

Orbital velocity = Distance traveled ÷ Time taken
= 264,895,343.53 meters ÷ 24 hours

However, we need to convert the time from hours to seconds since the unit of velocity is meters per second. There are 60 minutes in an hour, and 60 seconds in a minute.

Time taken in seconds = 24 hours × 60 minutes × 60 seconds
= 86,400 seconds

Now we can calculate the orbital velocity:

Orbital velocity = 264,895,343.53 meters ÷ 86,400 seconds
≈ 3068.8 m/s

Therefore, the geosynchronous satellite has an orbital velocity of approximately 3068.8 meters per second.