A satellite orbits at radius 4.2 × 10⁷ m and speed 3.08 × 10³ m/s. Earth's radius is 6.4 × 10⁶ m. (a) Find altitude. (b) Find period in hours. (c) Identify centripetal force. (d) Explain larger-radius circular speed and period changes. (e) Explain astronaut apparent weightlessness.

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Altitude 3.56 × 10⁷ m; period 8.57 × 10⁴ s = 23.8 h; gravity is inward force; larger orbit is slower with longer period. Altitude is orbital radius minus Earth radius: 4.2 × 10⁷ − 6.4 × 10⁶ = 3.56 × 10⁷ m. Period T = circumference/speed = 2π(4.2 × 10⁷)/(3.08 × 10³) = 8.57 × 10⁴ s = 23.8 h. Earth's gravitational attraction supplies the inward centripetal resultant. Centripetal force is a role of gravity here, not an extra force added to it. At larger radius gravity is weaker, so circular speed is lower. The path is longer and speed lower, producing a longer period, consistent with T² proportional to r³. Spacecraft and astronauts fall together under gravity, leaving little normal contact force from the floor. Apparent weight vanishes although gravitational force does not.

Circular satellite orbit

A satellite orbits at radius 4.2 × 10⁷ m and speed 3.08 × 10³ m/s. Earth's radius is 6.4 × 10⁶ m. (a) Find altitude. (b) Find period in hours. (c) Identify centripetal force. (d) Explain larger-radius circular speed and period changes. (e) Explain astronaut apparent weightlessness.

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