Back to Sections

Type:ALLMCQNATMSQ

Central Force Motion and Orbits(8)Central Force Motion and Orbital Mechanics(8)

Central Force Motion and Orbits

8 Questions

GATE→2026→Space Dynamics→Central Force Motion and Orbits

Q9

MCQ[2 Marks]

An earth satellite has the instantaneous position vector 𝑟⃗ and velocity vector 𝑣⃗ as given below. Here 𝑝̂ and 𝑞̂ denote the unit vectors along the 𝑥 and 𝑦 axes of the perifocal frame, respectively. Assume that the value of gravitational parameter is 398600 km3/s2. Which one of the following trajectories does the satellite follow? 𝑟⃗ = (8000𝑝̂ + 9000𝑞̂) km and 𝑣⃗ = (−6𝑝̂ + 6𝑞̂) km/s

(A)

Circle

(B)

Hyperbola

(C)

Parabola

(D)

Straight line

Explanation

GATE→2026→Space Dynamics→Central Force Motion and Orbits

Q10

NAT[2 Marks]

An earth satellite moves in an elliptical orbit with a perigee altitude of 300 km and an apogee altitude of 3000 km. Assume that the radius of the earth is 6378 km. The eccentricity of the orbit is __________ (rounded off to three decimal places).

Explanation

GATE→2025→Space Dynamics→Central Force Motion and Orbits

Q11

NAT[2 Marks]

F and G denote two points on a spacecraft’s orbit around a planet, as indicated in the figure. O is the center of the planet, P is the periapsis, and the angles are as indicated in the figure. If OF = 8000 km, OG = 10000 km, 𝜃𝐹= 0 deg, and 𝜃𝐺= 60 deg, the eccentricity of the spacecraft’s orbit is ____ (rounded off to two decimal places).

Explanation

GATE→2024→Space Dynamics→Central Force Motion and Orbits

Q12

NAT[2 Marks]

Consider an artificial satellite moving around the Moon in an elliptic orbit. The altitude of the satellite from the Moon’s surface at the perigee is 25 km and that at the apogee is 134 km. Assume the Moon to be spherical with a radius of 1737 km. The trajectory is considered with reference to a coordinate system fixed to the center of mass of the Moon. The ratio of the speed of the satellite at the perigee to that at the apogee is ___________ (rounded off to 2 decimal places).

Explanation

GATE→2023→Space Dynamics→Central Force Motion and Orbits

Q13

MCQ[1 Mark]

Which one of the following figures represents the qualitative variation of absolute dV deceleration with altitude h (measured from the mean sea level) for a space dt vehicle undergoing a ballistic entry into the Earth’s atmosphere?

(A)

[Visual option A — diagram not captured in source JSON]

(B)

[Visual option B — diagram not captured in source JSON]

(C)

[Visual option C — diagram not captured in source JSON]

(D)

[Visual option D — diagram not captured in source JSON]

Explanation

GATE→2023→Space Dynamics→Central Force Motion and Orbits

Q14

NAT[2 Marks]

The universal gravitational constant is 6.67 10−11 Nm2/kg2. For a planet of mass 6.4169 1023 kg and radius 3390 km, the escape velocity is _____ km/s. (round off to one decimal place).

Explanation

GATE→2023→Space Dynamics→Central Force Motion and Orbits

Q15

NAT[2 Marks]

A satellite is in a circular orbit around Earth with a time period of 90 minutes. The radius of Earth is 6370 km, mass of Earth is 5.98 1024 kg and the universal gravitational constant is 6.67 10−11 Nm2/kg2. The altitude of the satellite above mean sea level is ____ km. (round off to the nearest integer) Aerospace Engineering (AE)

Explanation

GATE→2022→Space Dynamics→Central Force Motion and Orbits

Q16

MSQ[2 Marks]

Consider a high Earth-orbiting satellite of angular momentum per unit mass $\vec{h}$ and eccentricity $e$. Which of the following statements is/are true?

(A)

Trajectory equation is r = |h| / (GM(1 + e cos θ))

(B)

Trajectory equation is r = |h|^2 / (GM(1 + e cos θ))

(C)

h is conserved

(D)

Sum of potential and kinetic energy is conserved

Explanation

Central Force Motion and Orbital Mechanics

8 Questions

GATE→2026→Space Dynamics→Central Force Motion and Orbital Mechanics

Q9

MCQ[2 Marks]

An earth satellite has the instantaneous position vector 𝑟⃗ and velocity vector 𝑣⃗ as given below. Here 𝑝̂ and 𝑞̂ denote the unit vectors along the 𝑥 and 𝑦 axes of the perifocal frame, respectively. Assume that the value of gravitational parameter is 398600 km3/s2. Which one of the following trajectories does the satellite follow? 𝑟⃗ = (8000𝑝̂ + 9000𝑞̂) km and 𝑣⃗ = (−6𝑝̂ + 6𝑞̂) km/s

(A)

Circle

(B)

Hyperbola

(C)

Parabola

(D)

Straight line

Explanation

GATE→2026→Space Dynamics→Central Force Motion and Orbital Mechanics

Q10

NAT[2 Marks]

An earth satellite moves in an elliptical orbit with a perigee altitude of 300 km and an apogee altitude of 3000 km. Assume that the radius of the earth is 6378 km. The eccentricity of the orbit is __________ (rounded off to three decimal places).

Explanation

GATE→2025→Space Dynamics→Central Force Motion and Orbital Mechanics

Q11

NAT[2 Marks]

F and G denote two points on a spacecraft’s orbit around a planet, as indicated in the figure. O is the center of the planet, P is the periapsis, and the angles are as indicated in the figure. If OF = 8000 km, OG = 10000 km, 𝜃𝐹= 0 deg, and 𝜃𝐺= 60 deg, the eccentricity of the spacecraft’s orbit is ____ (rounded off to two decimal places).

Explanation

GATE→2024→Space Dynamics→Central Force Motion and Orbital Mechanics

Q12

NAT[2 Marks]

Consider an artificial satellite moving around the Moon in an elliptic orbit. The altitude of the satellite from the Moon’s surface at the perigee is 25 km and that at the apogee is 134 km. Assume the Moon to be spherical with a radius of 1737 km. The trajectory is considered with reference to a coordinate system fixed to the center of mass of the Moon. The ratio of the speed of the satellite at the perigee to that at the apogee is ___________ (rounded off to 2 decimal places).

Explanation

GATE→2023→Space Dynamics→Central Force Motion and Orbital Mechanics

Q13

MCQ[1 Mark]

Which one of the following figures represents the qualitative variation of absolute dV deceleration with altitude h (measured from the mean sea level) for a space dt vehicle undergoing a ballistic entry into the Earth’s atmosphere?

(A)

[Visual option A — diagram not captured in source JSON]

(B)

[Visual option B — diagram not captured in source JSON]

(C)

[Visual option C — diagram not captured in source JSON]

(D)

[Visual option D — diagram not captured in source JSON]

Explanation

GATE→2023→Space Dynamics→Central Force Motion and Orbital Mechanics

Q14

NAT[2 Marks]

The universal gravitational constant is 6.67 10−11 Nm2/kg2. For a planet of mass 6.4169 1023 kg and radius 3390 km, the escape velocity is _____ km/s. (round off to one decimal place).

Explanation

GATE→2023→Space Dynamics→Central Force Motion and Orbital Mechanics

Q15

NAT[2 Marks]

A satellite is in a circular orbit around Earth with a time period of 90 minutes. The radius of Earth is 6370 km, mass of Earth is 5.98 1024 kg and the universal gravitational constant is 6.67 10−11 Nm2/kg2. The altitude of the satellite above mean sea level is ____ km. (round off to the nearest integer) Aerospace Engineering (AE)

Explanation

GATE→2022→Space Dynamics→Central Force Motion and Orbital Mechanics

Q16

MSQ[2 Marks]

Consider a high Earth-orbiting satellite of angular momentum per unit mass $\vec{h}$ and eccentricity $e$. Which of the following statements is/are true?

(A)

Trajectory equation is r = |h| / (GM(1 + e cos θ))

(B)

Trajectory equation is r = |h|^2 / (GM(1 + e cos θ))

(C)

h is conserved

(D)

Sum of potential and kinetic energy is conserved

Explanation