A satellite orbits Earth in a circular path of radius 7,000 km with a period of 100 minutes. Calculate its linear speed in km/s.

A satellite orbits Earth in a circular path of radius 7,000 km with a period of 100 minutes. Calculate its linear speed in km/s.

["Title: Satellite Orbiting Earth in a Circular Path – Calculating Linear Speed", "When understanding satellite motion, one fascinating question arises: what is the linear speed of a satellite orbiting Earth in a circular path with a given radius and orbital period? Consider a satellite circling Earth at a constant radius of 7,000 kilometers, completing one full orbit in 100 minutes. In this article, we’ll explore how to calculate its linear speed in kilometers per second (km/s), and why precise orbital dynamics matter in satellite engineering and space exploration.", "---", "### The Physics Behind Circular Satellite Motion", "A satellite moving in a circular orbit around Earth is governed by gravitational force providing the centripetal acceleration. This balance determines the satellite’s orbital speed. The key parameters are:", "- Radius of orbit:\n ( r = 7,000 ) km\n- Orbital period (time for one revolution):\n ( T = 100 ) minutes", "First, convert the period from minutes to seconds:\n[\nT = 100 \ imes 60 = 6,000 \ ext{ seconds}\n]", "---", "### Calculating Linear Speed", "The linear speed ( v ) of a satellite in circular orbit is given by the formula:\n[\nv = \frac{\ ext{circumference}}{\ ext{period}} = \frac{2\pi r}{T}\n]", "Insert the known values:\n[\nv = \frac{2\pi \ imes 7,000}{6,000}\n]", "Calculate step-by-step:\n[\n2\pi \ imes 7,000 \approx 2 \ imes 3.1416 \ imes 7,000 = 43,982 \ ext{ km}\n]\n[\nv \approx \frac{43,982}{6,000} \approx 7.33 \ ext{ km/s}\n]", "---", "### Result: The satellite’s linear speed is approximately 7.33 km/s", "This means the satellite travels roughly 7.33 kilometers every second along its orbit — a typical and efficient speed for low Earth orbit satellites.", "---", "### Why This Matters", "Understanding orbital speed helps engineers:", "- Design stable satellite trajectories\n- Calculate fuel requirements and mission durations\n- Predict orbital decay and re-entry windows", "The precise relationship between radius, period, and speed confirms fundamental principles of orbital mechanics derived from Newton’s law of gravitation and centripetal force.", "---", "### Final Answer", "The satellite orbits Earth at a linear speed of approximately 7.33 km/s.", "---", "For further reading, explore how real satellites adjust speed via orbital maneuvers, or dive into Kepler’s laws and their application in modern satellite networks like GPS and communication constellations."]

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