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#planetary motion

14 public questions tagged with this topic.

Universal Law of Gravitation

What ensures that a planet moves faster at perihelion than at aphelion?

Angular momentum conservation (mrv = constant) implies that at perihelion (smaller r), the speed v is greater than at aphelion (larger r), as derived from Kepler’s second law. As per NCERT, applying relevant law/formula with correct units and sign convention leads to Conservation of angular momentum. 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

What causes the elliptical shape of planetary orbits according to Newton’s theory?

The inverse-square law (F∝1/r2) leads to elliptical orbits as a general solution to the two-body problem, matching Kepler’s first law, unlike a linear force which would produce circular orbits. As per NCERT, applying relevant law/formula with correct units and sign convention leads to Inverse-square gravitational force. 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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Orbital Velocity and Time Period

Which of the following statements is correct about Kepler’s third law?

T2∝a3, meaning the period squared is proportional to the semi-major axis cubed, making option 2 correct. As per NCERT, applying relevant law/formula with correct units and sign convention leads to Period squared is proportional to distance cubed. This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.

Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.

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Kepler's Laws and Planetary Motion

What role does the Sun play in planetary motion according to Kepler’s laws?

The Sun is at one focus of the elliptical orbits (first law) and provides the central gravitational force driving the equal-area sweep (second law) and period-distance relation (third law). As per NCERT, applying relevant law/formula with correct units and sign convention leads to It provides the central force. 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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Kepler's Laws and Planetary Motion

Which of Kepler’s laws implies that the gravitational force acting on a planet is a central force?

Kepler’s second law (law of areas) states that the line joining a planet to the Sun sweeps out equal areas in equal times. This is a consequence of the conservation of angular momentum, which holds true for a central force directed along the line joining the two bodies (e.g., the Sun and planet). A central force ensures no torque, preserving angular momentum.

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

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Work, Energy and Orbital Mechanics

What does Kepler’s third law reveal about the motion of planets farther from the Sun?

Kepler’s third law (T2∝a3) shows that planets farther from the Sun (larger semi-major axis a) have longer orbital periods (T), as the period increases with the distance cubed. As per NCERT, applying relevant law/formula with correct units and sign convention leads to They have longer periods. 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

Which of the following statements is correct about Kepler’s first law?

Kepler’s first law (law of orbits) describes planetary orbits as ellipses with the Sun at one focus, not circles, contradicting option 4. As per NCERT, applying relevant law/formula with correct units and sign convention leads to Orbits are elliptical with varying speeds. This satisfies dimensional consistency and physical conditions given, so option C is scientifically correct.

Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.

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Variation of g with Height and Depth

A planet orbits the Sun with a period of 9 years. If Earth’s orbital radius is 1.5×1011m, what is its semi-major axis?

Kepler’s third law: Tp2TE2 = ap3aE3. TE = 1year, Tp = 9years, aE = 1.5×1011m. 9212 = ap3(1.5×1011)3. 81 = ap33.375×1033. ap3 = 81×3.375×1033 = 2.73375×1035. ap = (2.73375×1035)1/3≈6.49×1011m. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 6.5 × 10¹¹ m. This satisfies dimensional consistency and physical conditions given, so option C is scientifically correct.

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

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Variation of g with Height and Depth

Which of the following statements is correct about Kepler’s laws?

Kepler’s laws apply to any central force following an inverse-square law (e.g., gravitation), making option 4 correct as they describe planetary motion around the Sun. They require circular orbits 1 2 3 4 Correct ans: Option (4) They apply only to Earth They depend on planet mass They apply to inverse-square forces 4

Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.

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