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#satellite orbit

8 public questions tagged with this topic.

Universal Law of Gravitation

A satellite orbits a planet at 3×107m from its center with a period of 6 hours. What is the planet’s mass? (G\=6.67×10−1

M = 4π2r3GT2. T = 6×3600 = 21600s, T2 = 4.6656×108s2. r3 = (3×107)3 = 2.7×1022m3. M = 4×(3.14)2×2.7×10226.67×10−11×4.6656×108. M = 1.065×10243.112×10−2≈3.42×1025kg. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 3.4 × 10²⁵ kg. This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.

Ref: Halliday & Resnick, Fundamentals of Physics, 11th ed., Chapter 13: Gravitation.

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Universal Law of Gravitation

What is the kinetic energy of a 900kg satellite at 11RE from Earth’s center? (ME\=6×1024kg,RE\=6.4×106m,G\=6.67×10−11N m

K = GMEm2r. r = 11RE = 7.04×107m. K = 6.67×10−11×6×1024×9002×7.04×107. K = 3.602×10171.408×108≈2.56×109J. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 2.6 × 10⁹ J. This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.

Ref: Halliday & Resnick, Fundamentals of Physics, 11th ed., Chapter 13: Gravitation.

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Energy of Satellites and Binding Energy

A satellite orbits Earth at 11RE from the center. What is its orbital speed? (g\=9.8m/s2,RE\=6.4×106m)

v = gRE2r. r = 11RE, v = 9.8×6.4×10611. v = 5.698×106≈2.39×103m/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 2.4 × 10³ m/s. This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.

Ref: Halliday & Resnick, Fundamentals of Physics, 11th ed., Chapter 13: Gravitation.

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Escape Velocity and Bound Systems

What is the total energy of a 100kg satellite orbiting Earth at 3RE from the center? (ME\=6×1024kg,RE\=6.4×106m,G\=6.67×

E = −GMEm2r. r = 3RE = 3×6.4×106 = 1.92×107m. E = −6.67×10−11×6×1024×1002×1.92×107. E = −4.002×10163.84×107≈−1.04×109J. As per NCERT, applying relevant law/formula with correct units and sign convention leads to -1.0 × 10⁹ J. This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.

Ref: Halliday & Resnick, Fundamentals of Physics, 11th ed., Chapter 13: Gravitation.

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Escape Velocity and Bound Systems

A 700kg satellite orbits Earth at 10RE from the center. What is its total energy? (ME\=6×1024kg,RE\=6.4×106m,G\=6.67×10−

E = −GMEm2r. r = 10RE = 6.4×107m. E = −6.67×10−11×6×1024×7002×6.4×107. E = −2.801×10171.28×108≈−2.19×109J. As per NCERT, applying relevant law/formula with correct units and sign convention leads to -2.2 × 10⁹ J. This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.

Ref: Halliday & Resnick, Fundamentals of Physics, 11th ed., Chapter 13: Gravitation.

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Gravitational Potential and Field

A satellite near Earth has a period of 87 minutes. What is its period at h\=6RE? (RE\=6.4×106m)

T2∝(RE+h)3. T02 = kRE3, h = 6RE, r = 7RE. T2 = k(7RE)3 = 343kRE3. T = T0343 = 87×18.52≈1611min. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 1620 min. This satisfies dimensional consistency and physical conditions given, so option D is scientifically correct.

Ref: Halliday & Resnick, Fundamentals of Physics, 11th ed., Chapter 13: Gravitation.

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Gravitational Potential and Field

A satellite orbits Earth at 9RE from the center. What is its orbital speed? (g\=9.8m/s2,RE\=6.4×106m)

v = gRE2r. r = 9RE, v = 9.8×6.4×1069. v = 6.964×106≈2.64×103m/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 2.6 × 10³ m/s. This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.

Ref: Halliday & Resnick, Fundamentals of Physics, 11th ed., Chapter 13: Gravitation.

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