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Answer :
Final answer:
The period of a satellite's orbit can be calculated using Kepler's third law, the speed with the formula involving the orbital radius and period, and the centripetal acceleration through the satellite's speed squared over the orbital radius.
Explanation:
When calculating the period of a satellite's orbit, we can use Kepler's third law, which relates the orbital period to the radius of the orbit. This law states that the square of the period (T) of an orbit is directly proportional to the cube of the semi-major axis (r) of the orbit, with this relationship being governed by the equation T² = (4π²r³) / (GM), where G is the gravitational constant, and M is the mass of the more massive body, in this case, Earth.
To find the speed of the satellite in orbit, we use the formula v = 2πr / T, where r is the orbit radius and T is the period of the orbit. The satellite's speed is constant because its orbit is circular.
For the acceleration, which is asked for in the question but cut off, we know that in a circular orbit, the acceleration is centripetal and is given by a = v² / r, where v is the orbital speed and r is the orbital radius. This acceleration is directed towards the center of the orbit.
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