Gravitation : Planets and Satellites
ICSE · Class 11 · Physics
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A satellite is moving close to Earth with orbital speed 8.0 km/s. Using the relation between orbital velocity and escape velocity, find the escape velocity of Earth.
A body is projected from Earth with speed 2 times the escape velocity. Find the speed of the body in interstellar space.
A projectile is launched from Earth with speed equal to one-fourth of Earth’s escape velocity. Find the maximum height attained in terms of Earth’s radius.
An artificial satellite revolves very close to Earth. If its period is 84 minutes, find the approximate orbital radius using the relation T = 2π√(r^3/GMe). Take the standard close-orbit result from the chapter and identify the correct radius.
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A geostationary satellite has orbital radius 42200 km and period 24 h. Find its orbital speed.
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3.1 km/s
Use v = 2πr/T. With r = 42200 km and T = 24 h, v ≈ 2 × 3.14 × 42200 / 24 ≈ 11042 km/h = 3.1 km/s.
At Earth’s surface, g = 9.8 m/s^2 and R_e = 6.37 × 10^6 m. Find the escape velocity using v_e = √(2gR_e).
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11.2 km/s
v_e = √(2gR_e) = √(2 × 9.8 × 6.37 × 10^6) ≈ √1.248 × 10^8 ≈ 1.12 × 10^4 m/s = 11.2 km/s.
A satellite of mass m moves in a circular orbit of radius r around Earth. If its orbital speed is v_o, find the total energy in terms of G, Me, m and r.
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-1/2 GMe m / r
For a circular orbit, K = GMe m /(2r) and U = -GMe m / r. So E = U + K = -GMe m/r + GMe m/(2r) = -1/2 GMe m/r.
A satellite orbits Earth in a circle of radius 2R_e. Find its orbital speed in terms of the orbital speed close to Earth’s surface, v_0.
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v_0/√2
Orbital speed varies as 1/√r. If r becomes 2R_e, speed becomes √(R_e/2R_e) = 1/√2 times the close-orbit speed v_0.
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