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  • Calculate Orbital Speed: Geosynchronous Satellite Problem
    This problem has a bit of a trick in it. It seems like we're dealing with a satellite orbiting the sun, but the key information is "it takes 24 hours to revolve around the sun". This is the same time it takes Earth to revolve around the sun.

    Therefore, the satellite is actually in geosynchronous orbit around Earth. Here's how to calculate its speed:

    1. Understand the Relationship:

    * Geosynchronous orbit: A satellite in geosynchronous orbit stays above the same point on Earth's surface as the Earth rotates.

    2. Calculate the Circumference:

    * The radius of the orbit is 42,050 km.

    * The circumference of the circular orbit is 2πr = 2π(42,050 km) ≈ 264,600 km

    3. Calculate the Speed:

    * The satellite completes one orbit in 24 hours (86,400 seconds).

    * Speed = Distance / Time = 264,600 km / 86,400 seconds ≈ 3.06 km/s

    Therefore, the speed of the artificial satellite in geosynchronous orbit is approximately 3.06 km/s.

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