GATE AE topic:central-force-motion PYQs & Answers — Page 2

Questions 11–17 of 17. Imported answers require independent review unless marked reviewed.

The ratio of tangential velocities of a planet at the perihelion and the aphelion from the sun is 1.039. Assuming that the planet’s orbit around the sun is planar and elliptic, the value of eccentricity of the orbit is ______ (round off to three decimal places).

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

The product of earth’s mass (

) and the universal gravitational constant (

) is

. The radius of the earth is 6371 km. The minimum increment in the velocity to be imparted to a spacecraft flying in a circular orbit around the earth at an altitude of 400 km to make it exit earth’s gravitational field is ______ km/s (round off to 2 decimal places).

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

The tangential velocity component ‘V’ of a spacecraft, which is in a circular orbit of radius ‘R’ around a spherical Earth (

gravitational parameter of Earth) is given by the following expression.

Your answerChoose one option.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

Equation of the trajectory of a typical space object around any planet, in polar coordinates

(i.e. a general conic section geometry), is given as follows. (h is angular momentum,

is gravitational parameter, e is eccentricity, r is radial distance from the planet center,

, is angle between vectors

and

Your answerChoose one option.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

In an elliptic orbit around any planet, the location at which a spacecraft has the maximum angular velocity is

Your answerChoose one option.

apoapsis.

periapsis.

a point at +45° from periapsis.

a point at −90° from apoapsis.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

A spacecraft forms a circular orbit at an altitude of 150 km above the surface of a spherical Earth. Assuming the gravitational parameter,

and radius of earth, Re = 6,400 km, the velocity required for the injection of the spacecraft, parallel to the local horizon, is ______________ (accurate to two decimal places).

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

The period of revolution of earth about the sun is 365.256 days, approximately. The semi-major axis of the earth’s orbit is close to

m. The semi-major axis of the orbit of Mars is

m. The period of revolution of Mars, about the sun, is __________ Earth days (in three decimal place)

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

GATE AE topic:central-force-motion PYQs

Question 43

Question 42

Question 9

Question 10

Question 11

Question 44

Question 14