GATE AE Central force motion PYQs & Answers

Questions 1–10 of 17. Imported answers require independent review unless marked reviewed.

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,

deg, and

deg, the eccentricity of the spacecraft’s orbit is

(rounded off to two decimal places).

Diagram for Aerospace Engineering question 53

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Which of the following statements is/are correct about a satellite moving in a geostationary orbit?

Your answerSelect all correct options. You can choose more than one.

The orbit lies in the equatorial plane

The orbit is circular about the center of the Earth

The time period of motion is 90 minutes

The satellite is visible from all parts of the Earth

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At a point in the trajectory of an unpowered space vehicle moving about the Earth, the altitude above the mean sea level is 600 km, and the speed with reference to a coordinate system fixed to the center of mass of the Earth is 9 km/s. Assume that the Earth is a sphere with a radius 6400 km and

, where G is the universal gravitational constant and

is mass of the Earth. The trajectory is:

Your answerChoose one option.

Circular

Elliptic

Parabolic

Hyperbolic

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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).

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The universal gravitational constant is

/kg

. For a planet of mass

kg and radius 3390 km, the escape velocity is _____ km/s. (round off to one decimal place).

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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

kg and the universal gravitational constant is

/kg

. The altitude of the satellite above mean sea level is ___ km. (round off to the nearest integer)

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Consider a high Earth-orbiting satellite of angular momentum per unit mass h⃗ and eccentricity e.

The mass of the Earth is M and G is the universal gravitational constant.

The distance between the satellite’s center of mass and the Earth’s center of mass is r, the true anomaly is θ, and the phase angle is zero.

Which of the following statements is/are true?

Your answerSelect all correct options. You can choose more than one.

The trajectory equation is r = r(θ) = |h⃗|/[GM(1 + e cos θ)]

The trajectory equation is r = r(θ) = |h⃗|²/[GM(1 + e cos θ)]

h⃗ is conserved

The sum of potential energy and kinetic energy of the satellite is conserved

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The velocity required to launch a space shuttle from the surface of the earth to achieve a circular orbit of 250 km altitude is ______ (round off to two decimal places).

For earth,

km³/s² and surface radius

km.

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For hyperbolic trajectory of a satellite of mass

having velocity

at a distance

from the center of earth (

: gravitational constant,

: mass of earth), which one of the following relations is true?

Your answerChoose one option.

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Burnout velocity of a space vehicle in circular orbit at an angle 5 degrees above the local horizon around earth is 13.5 km/s. Tangential velocity of the space vehicle in the orbit is ______ km/s (round off to two decimal places).

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GATE AE Central force motion PYQs

How to practice Central force motion

Question 53

Question 26

Question 39

Question 60

Question 62

Question 63

Question 46

Question 25

Question 11

Question 20