Kepler's Laws Satellites & Escape Velocity — Practice Questions

Free NEET Physics multiple-choice questions on Kepler's Laws Satellites & Escape Velocity. Attempt each question and reveal the answer with a full explanation.

The escape velocity of a body from the Earth's surface is v e . If the mass of the Earth remains constant but its radius shrinks to one-fourth of its original value, the new escape velocity will be: 2v e v e/2 4v e v e/4 For a satellite orbiting very close to the Earth's surface, the ratio of its orbital velocity to the escape velocity is: 1 : 2 2 : 1 1 : 2 2 : 1 A body is projected vertically upwards with a speed v = gR from the Earth's surface. The maximum height attained by it is: R R/2 2R R/4 The binding energy of a satellite of mass m orbiting Earth at a height h = R is: mgR/4 mgR/2 mgR mgR/8 The escape velocity from the Earth's surface is v e . The escape velocity from the surface of another planet having a radius four times that of Earth and the same mass density is: 4v e v e 2v e 1 4 v e The radius of orbit of a geostationary satellite is r . The radius of orbit of another satellite of period 3 hours is: r/4 r/2 r/8 r/16 A satellite of mass m is in a circular orbit of radius r around Earth. If its angular momentum is L , then its kinetic energy is: L 2 / (2mr 2) L 2 / (mr 2) L / (2mr 2) 2L 2 / (mr 2) A body is projected vertically upwards with a speed equal to the orbital speed of a satellite revolving close to the Earth's surface. The maximum height attained by the body is: R R/2 2R R/4 If the kinetic energy of a satellite is doubled, then: The satellite will escape from its orbit The radius of the orbit will be halved The time period will be doubled The potential energy will be doubled The orbital speed of a geostationary satellite is approximately: 3.1 km/s 11.2 km/s 8.0 km/s 1.5 km/s What is the escape velocity of a body from the surface of a planet whose mass is 1/9 of Earth's mass and radius is 1/4 of Earth's radius? (Take v e = 11.2 km/s ) 7.47 km/s 11.2 km/s 22.4 km/s 3.73 km/s If the distance between Earth and Sun were to become half the present distance, the number of days in a year would be approximately: 129 182 365 64 A planet moves in a circular orbit around the Sun. The angle between its velocity vector and the acceleration vector is: 90 0 180 45 A planet moving around the sun in an elliptical orbit is at its maximum distance r 1 and minimum distance r 2 . The eccentricity of the orbit is: (r 1 - r 2) / (r 1 + r 2) (r 1 + r 2) / (r 1 - r 2) r 1 / r 2 r 2 / r 1 The escape velocity from the Earth is v e . The escape velocity from a planet having 100 times the mass of the Earth and 4 times the radius of the Earth is: 5v e 10v e 2v e 25v e A planet orbits a star of mass M in a circular orbit of radius R with a time period T . If the mass of the star is doubled and the radius of the orbit is also doubled, the new time period T' will be: 2T 4T T 2 2T 2 A satellite of mass m is revolving in a circular orbit around the Earth at a height h = R above the surface. Its total mechanical energy is: - mgR 4 - mgR 2 - mgR 8 - 3mgR 4 If the total mechanical energy of a satellite of mass m is E , then its orbital speed v is given by: -2E/m 2E/m -E/m E/2m The binding energy of a satellite of mass m moving in a circular orbit of radius r around a planet of mass M is: GMm 2r GMm r - GMm 2r - GMm r If the acceleration due to gravity on the surface of a planet is g/4 and its radius is R/2 , the escape velocity from its surface is (where v e is escape velocity from Earth): v e / (2 2 ) v e / 2 v e / 4 v e / 2 What is the minimum energy required to launch a satellite of mass m from the surface of Earth of mass M and radius R in a circular orbit at an altitude of 2R ? 5GMm/6R 2GMm/3R GMm/2R GMm/3R A particle of mass m is projected with velocity v = k v e ( k < 1 ) from the surface of Earth. The maximum height above the surface reached by the particle is: Rk 2 1-k 2 R 1-k 2 Rk 2 Rk 1-k The escape velocity on the surface of Earth is 11.2 km/s . If a body is thrown out with twice this velocity, then the speed of the body when it escapes to infinity is: 3 11.2 km/s 2 11.2 km/s 11.2 km/s Zero The ratio of the escape velocity of a planet to the escape velocity of Earth is k . If the radius of the planet is 4 times the radius of Earth and its mass is 16 times the mass of Earth, then the value of k is: 2 4 1 0.5 A geostationary satellite is orbiting the earth at a height of 5R above the surface of the earth, R being the radius of the earth. The time period of another satellite in hours at a height of 2R from the surface of the earth is: 6 2 hours 10 hours 5 hours 6 hours Two satellites S 1 and S 2 are revolving around a planet in coplanar circular orbits in the same sense. Their periods of revolution are 1 hour and 8 hours respectively. The radius of the orbit of S 1 is 10 4 km . When S 2 is closest to S 1 , their speed of relative approach is: 10 4 km/h 2 10 4 km/h 10 3 km/h Zero If the gravitational force between two point masses m 1 and m 2 at a distance r is given by F = k m 1 m 2 r n , then the period of revolution of a satellite in a circular orbit of radius R is proportional to: R (n+1)/2 R n/2 R (n-1)/2 R n The escape velocity of a body from the surface of Earth is 11.2 km/s . A body is projected with a velocity k v e ( k > 1 ). Its velocity at infinite distance from Earth is: v e k 2 - 1 v e (k-1) v e k 2 + 1 k v e If the mass of a planet is 10% of Earth's mass and its radius is 50% of Earth's radius, the escape velocity from its surface would be approximately: 7.1 km/s 11.2 km/s 5.6 km/s 3.2 km/s Two stars of masses m 1 and m 2 form a binary system. If the distance between them is d , the period of revolution T is given by: T = 2 d 3 G(m 1 + m 2) T = 2 d 3 Gm 1 m 2 T = 2 (m 1 + m 2)d 3 G T = 2 d 3 G(m 1 - m 2) The escape velocity of a body on Earth is v e . A planet has radius 1/4 times that of Earth and density double that of Earth. The escape velocity on this planet will be: v e / 2 2 v e v e / 2 2 v e If the period of a satellite is T , its kinetic energy is proportional to: T -2/3 T 2/3 T -4/3 T 2 For a satellite orbiting very close to the Earth's surface, the ratio of its period T to the period of a simple pendulum of length equal to the radius of Earth R on the Earth's surface is: 1 : 2 1 : 1 2 : 1 1 : 2 Two stars of masses m 1 and m 2 distance d apart rotate about their common center of mass. The period of revolution T is: 2 d 3 G(m 1 + m 2) 2 d 3 Gm 1 m 2 2 G(m 1 + m 2) d 3 2 d 3 G(m 1 - m 2) A satellite of mass m revolves around the Earth of radius R at a height x from its surface. If g is the acceleration due to gravity on the surface of the Earth, the orbital speed of the satellite is: gR 2 R+x gR gR 2 R+x gR R+x A planet revolves around the sun in an elliptical orbit. Its maximum speed is v 1 and minimum speed is v 2 . The eccentricity of the orbit is: v 1 - v 2 v 1 + v 2 v 1 + v 2 v 1 - v 2 v 1 2 - v 2 2 v 1 2 + v 2 2 v 1 v 2 If a body is projected with a velocity v = 1.5 v e from the Earth's surface ( v e is escape velocity), its velocity at infinity is: v e / 2 v e / 2 v e 2 v e 1.5 In a binary star system, two stars of masses m 1 and m 2 separated by distance r revolve about their common center of mass. The ratio of their kinetic energies K 1 / K 2 is: m 2 / m 1 m 1 / m 2 (m 2 / m 1) 2 1 In an imaginary system, the gravitational force follows an inverse-cube law ( F 1/r 3 ). In such a system, the time period T of a satellite in a circular orbit of radius R would be proportional to: R 2 R 3/2 R R 3 A body is projected vertically upwards from the surface of Earth with a velocity v = v e/3 where v e is the escape velocity. The maximum height reached by the body from the surface of the Earth is: R/8 R/9 R/3 R/2 Two planets P 1 and P 2 with equal mass have radii R 1 and R 2 , respectively, where R 2= R 1 2 . The escape speeds of P 1 and P 2 are v 1 and v 2 , respectively. Then v 2 v 1 is: 1 2 1 2 2 In a solar system, the time-period of revolution of a planet tracing a circular orbit of radius R is proportional to: R 1/2 R 3/2 R 2 R 3 Which of the following is the evidence to show that there must be a force which keeps Earth going around the Sun? The phenomenon of change of seasons The phenomenon of day and night Apparent motion of Sun around Earth None of these A planet moving in an elliptical orbit is closest to the Sun at distance r 1 and farthest at distance r 2 . If v 1 and v 2 are the linear velocities at these points respectively, then the ratio v 1/v 2 is: r 2/r 1 r 1/r 2 (r 2/r 1) 2 (r 1/r 2) 2 The escape velocity of a projectile from the Earth, which is approximately 11.2 km/s , depends on the angle of projection as: Independent of the angle of projection Directly proportional to Directly proportional to Directly proportional to The escape velocity from the surface of the Earth is v e . The escape velocity from the surface of a planet whose mass and radius are three times those of the Earth is: v e 3v e 9v e v e/3 The ratio of the orbital velocity of a satellite revolving close to the earth's surface to the escape velocity from the earth's surface is: 1 : 2 2 : 1 1 : 2 2 : 1 Which of the following statements is true for a geostationary satellite? It rotates from west to east It rotates from east to west It rotates from north to south It remains stationary in space and does not rotate The time period of a satellite in a circular orbit of radius R is T . The period of another satellite in a circular orbit of radius 9R is: 27T 3T 9T 81T The dimensional formula of the square of the speed of a satellite orbiting very close to the Earth's surface is same as that of: Gravitational potential at the surface Gravitational field at the surface Acceleration due to gravity Universal Gravitational Constant If the acceleration due to gravity on the surface of a planet is g p and its radius is R p , then the escape velocity from the surface of this planet is: 2g p R p g p R p 2 g p R p 1 2 g p R p The orbital velocity of a satellite at a height h = R above the Earth's surface is v 1 . The escape velocity from that same height is v 2 . The ratio v 2/v 1 is: 2 2 1 1 2 Kepler's third law states that T 2 = KR 3 , where K is a constant. The value of K depends on: The mass of the Sun only The mass of the planet only The masses of both the Sun and the planet The Universal Gravitational Constant only The ratio of the kinetic energy to the potential energy of a satellite in a circular orbit is: -1/2 -2 1/2 2 Two satellites of mass m and 2m are orbiting a planet in the same circular orbit of radius R . Their time periods are in the ratio: 1:1 1:2 2:1 1:4 A planet revolves around the Sun in an elliptical orbit. If L is the angular momentum and m is the mass, the areal velocity is: L/(2m) L/m 2L/m L/(4m) The escape velocity for a body projected vertically upwards from the surface of Earth is 11.2 km/s . If the body is projected at an angle of 45 with the vertical, the escape velocity will be: 11.2 km/s 11.2 2 km/s 11.2 / 2 km/s 22.4 km/s Kepler's third law states that the square of the period of revolution ( T ) of a planet around the sun is proportional to the cube of its average distance ( r ) from the sun, i.e., T 2 = K r 3 . The unit of the constant K is: s 2 m -3 s 2 m 3 s -2 m 3 s m -3 The orbital velocity of a satellite revolving at a distance r from the center of Earth is v . If the satellite is moved to a new orbit of radius 4r , its new orbital velocity will be: v/2 v/4 2v 4v The ratio of the speed of a satellite at perihelion to aphelion in an elliptical orbit is 4:1 . The ratio of the maximum distance to minimum distance from the sun is: 4:1 1:4 16:1 2:1 A satellite of mass m is in a circular orbit of radius r around Earth. Its angular momentum with respect to the center of Earth is L . The kinetic energy of the satellite is: L 2 / (2mr 2) L 2 / (mr 2) L / (2mr 2) 2L 2 / (mr 2) A planet moves around the sun in an elliptical orbit. When it is at its perihelion (closest point) at distance r p it has velocity v p . When it is at its aphelion (farthest point) at distance r a , its velocity v a is: v p r p / r a v p r a / r p v p r p / r a v p (r p / r a) 2 If the radius of Earth's orbit is made 1/4 th, then the duration of an year will become: 1/8 year 1/4 year 1/2 year 1/16 year Two satellites of masses M and 9M are orbiting a planet in a circular orbit of radius r . The ratio of their periods of revolution is: 1:1 1:3 1:9 3:1 The ratio of the radii of two planets is k 1 and the ratio of the acceleration due to gravity on their surfaces is k 2 . The ratio of the escape velocities from their surfaces is: k 1 k 2 k 1 k 2 k 1 / k 2 k 2 / k 1 A satellite is orbiting the Earth in a circular orbit of radius R . Its period of revolution is T . If the radius of the orbit is increased to 9R , the new period of revolution will be: 27T 3T 9T 81T A planet of mass M has a satellite of mass m orbiting it at distance r . If the planet's mass is doubled and the satellite's mass is halved, while keeping the distance r same, the orbital speed of the satellite becomes: 2 times 2 times 1/ 2 times Unchanged Two planets A and B have the same material density. If the radius of A is twice that of B , then the ratio of the escape velocity v A / v B is: 2 2 1/2 4 A satellite is moving in a circular orbit around the Earth. If its height above the Earth's surface is very small compared to the radius of Earth R , its orbital velocity is approximately: gR 2gR gR g/R Two satellites revolve around the sun in circular orbits with radii R 1 and R 2 . If their orbital speeds are v 1 and v 2 , then v 1/v 2 is equal to: R 2 / R 1 R 1 / R 2 R 2 / R 1 (R 2 / R 1) 2 A satellite is launched into a circular orbit close to Earth's surface. What is the ratio of its orbital velocity to the escape velocity? 1 / 2 2 2 1/2 The escape velocity from Earth is 11.2 km/s . If a body is projected at an angle of 30 with the horizontal, the escape velocity will be: 11.2 km/s 11.2 30 km/s 11.2 30 km/s 11.2 / 2 km/s What is the escape velocity from a planet whose mass is 8 times the mass of the Earth and whose radius is 2 times the radius of the Earth? ( v e = 11.2 km/s ) 22.4 km/s 11.2 km/s 44.8 km/s 5.6 km/s Which of the following physical quantities for a planet revolving around the sun in an elliptical orbit remains constant? Angular momentum Linear velocity Kinetic energy Potential energy The orbital velocity of a satellite revolving around a planet of mass M in an orbit of radius R is v . If the satellite is moved to an orbit of radius 9R , its new orbital velocity will be: v/3 v/9 3v v/27 A satellite is orbiting the earth in a circular orbit with a velocity v . If its velocity is increased by 41.4 % , then the satellite will: Escape from the earth's gravitational field Move into an elliptical orbit Fall on the surface of earth Continue in its circular orbit with higher speed A satellite of mass m is orbiting the Earth at a height h = R above the surface. Its orbital speed is: gR 2 gR 2gR gR 2 The escape velocity from the Earth is 11.2 km/s . The escape velocity from a planet having twice the radius and the same mean density as the Earth is: 22.4 km/s 11.2 km/s 5.6 km/s 15.8 km/s A satellite is revolving very close to the Earth's surface. Its orbital velocity is v . The velocity required for it to escape is: 2 v 2v v/ 2 v 2 If the radius of Earth is R and its period of rotation is T , a geostationary satellite is at a distance r from the center of Earth. Another satellite is at distance r/4 . Its period is: T/8 T/4 T/2 T/16 The ratio of the linear momentum of a satellite in a circular orbit to its mass is equal to: Orbital velocity Angular velocity Centripetal acceleration Gravitational potential A satellite orbits Earth at a height h . If the gravitational force suddenly becomes zero, the satellite will: Move tangentially to the original orbit with same speed Fall down to Earth Move radially outwards Continue to move in the same circular orbit The time period of a geostationary satellite is 24 hours. At what height above the Earth's surface does it orbit? (Take R = 6400 km ) 36000 km 6400 km 42000 km 24000 km The ratio of escape velocity at Earth ( v e ) to the escape velocity at a planet ( v p ) whose radius and mean density are twice as that of Earth is: 1 : 2 2 1 : 4 1 : 2 1 : 2 A planet moving around sun sweeps area A 1 in 2 days, A 2 in 3 days and A 3 in 6 days. Then the relation between A 1 , A 2 and A 3 is: 3A 1 = 2A 2 = A 3 2A 1 = 3A 2 = 6A 3 A 1/2 = A 2/3 = A 3/6 A 1 2 = A 2 3 = A 3 6 If the gravitational force between two objects were proportional to 1/R (instead of 1/R 2 ), then the orbital speed v of a particle in a circular orbit of radius R would be proportional to: R 0 R R 2 1/R A remote-sensing satellite of Earth revolves in a circular orbit at a height of 0.25 10 6 m above the surface of Earth. If Earth's radius is 6.38 10 6 m and g = 9.8 m/s 2 , then the orbital speed of the satellite is: 7.76 km/s 6.67 km/s 8.24 km/s 9.11 km/s The period of revolution of planet A around the sun is 8 times that of planet B. The distance of planet A from the sun is how many times greater than that of planet B? 4 2 8 16 The escape velocity for a rocket from Earth is 11.2 km/s . Its value on a planet where acceleration due to gravity is double that on the Earth and diameter of the planet is twice that of the Earth will be: 22.4 km/s 11.2 km/s 5.6 km/s 33.6 km/s A satellite S is moving in an elliptical orbit around the earth. The mass of the satellite is very small compared to the mass of the earth. Then: The angular momentum of S about the center of the earth is conserved The linear momentum of S is conserved The acceleration of S is always directed towards the center of the earth The total mechanical energy of S varies periodically The period of revolution of a satellite in an orbit of radius R is T . What will be its period of revolution in an orbit of radius 4R ? 8T 4T 2T 16T A satellite is launched into a circular orbit of radius R around the Earth. A second satellite is launched into an orbit of radius 1.01 R . The period of the second satellite is larger than the first one by approximately: 1.5% 0.5% 1.0% 3.0% The ratio of the escape velocities from two planets of same mass but having radii R 1 and R 2 is: R 2/R 1 R 1/R 2 R 2/R 1 (R 2/R 1) 2 A satellite of mass m is orbiting the Earth in a circular orbit with velocity v . The energy required to be given to this satellite so that it escapes from the Earth's gravitational pull is: 1 2 mv 2 mv 2 3 2 mv 2 2mv 2 The orbital velocity of an artificial satellite in a circular orbit just above the Earth's surface is v . For a satellite orbiting at an altitude of half of the Earth's radius, the orbital velocity is: 2 3 v 3 2 v 3 2 v 2 3 v Two satellites A and B go round a planet P in circular orbits having radii 4R and R respectively. If the speed of satellite A is 3v , then the speed of satellite B will be: 6v 12v 3v/2 3v/4 A geostationary satellite orbits around the Earth in a circular orbit of radius 36,000 km (approx from center). Then the time period of a spy satellite orbiting a few hundred km above the Earth's surface ( R 6400 km ) is approximately: 1.5 hr 2 hr 12 hr 24 hr What is the direction of the areal velocity of a planet revolving around the sun? Perpendicular to the plane of the orbit Along the radius vector Parallel to the linear velocity Towards the sun If the distance between the sun and earth is r , then the angular momentum of the earth around the sun is proportional to: r r r 2 r 3/2 A satellite is orbiting just above the surface of the earth with period T . If d is the density of the earth and G is the universal gravitational constant, the quantity 3 / (Gd) represents: T 2 T T 1/T 2 The escape velocity on Earth is v e . A body is projected with velocity 2v e . What is the speed of the body at far away distance from the Earth? 3 v e 5 v e v e 2v e A satellite of mass m is moving in a circular orbit of radius R around the Earth. If the kinetic energy of the satellite is K , its angular momentum is: 2mKR 2 mKR 2 2mKR 2mKR A particle of mass m is kept at rest at a height 3R from the surface of Earth, where R is the radius of Earth and M is mass of Earth. The minimum speed with which it should be projected so that it does not return back is: GM 2R GM R 2GM R GM 4R The time period of a satellite orbiting very close to the surface of a planet is T . If the mass of the planet is M and its radius is R , then T is: Independent of the mass of the satellite Proportional to the mass of the satellite Inversely proportional to the mass of the satellite Proportional to the square of the mass of the satellite A satellite is launched into a circular orbit close to the Earth's surface. What additional velocity must be imparted to the satellite so that it overcomes the gravitational pull of the Earth? ( 2 -1) gR 2gR ( 2 +1) gR gR The mean distance of Mars from the Sun is 1.52 times that of the Earth from the Sun. What is the approximate period of Mars' revolution in Earth years? 1.87 years 1.52 years 2.31 years 0.88 years A satellite orbits Earth at a height h . If the total energy of the satellite is E , then its kinetic energy is: -E E 2E -2E The work done in shifting a satellite of mass m from an orbit of radius 2R to an orbit of radius 3R is: GMm 12R GMm 6R GMm R GMm 2R The escape velocity from the surface of Earth is v e . If a body is projected with a velocity three times v e , what will be its speed in interstellar space? v e 8 3v e v e 10 2v e A satellite is moving around the Earth in a circular orbit. If the gravitational force between them were to suddenly vanish, the satellite would: Move tangentially to its original orbit with the same speed Fall down to the Earth Continue to move in its circular orbit Move radially outwards A satellite is orbiting just above the surface of a planet with a time period T . If the mean density of the planet is , what is the value of the product T 2 ? 3 G 4 3G G 3 3G A satellite of mass m is moving in a circular orbit of radius R around the Earth. If it loses 25 % of its total energy due to atmospheric resistance, its new orbital radius will be: 0.75 R 0.80 R 1.25 R 1.33 R The ratio of the acceleration due to gravity at the surface of a planet to that on Earth is 2:3 , and the ratio of their radii is 4:9 . The ratio of their escape velocities is: 2 2 : 3 3 8 : 27 4 : 9 2 : 3 For a planet, the graph of T 2 against r 3 (where T is the orbital period and r is the semi-major axis) is a straight line passing through the origin. The slope of this line depends on: The mass of the Sun The mass of the planet The radius of the planet The density of the planet The escape velocity of a particle from the surface of a thin uniform spherical shell of mass M and radius R is: 2GM R GM R GM 2R Zero A body is projected vertically upwards from the surface of Earth with a velocity equal to half the escape velocity. The maximum height attained by the body is: R/3 R/2 R/4 R A satellite is launched into a circular orbit close to the surface of Earth. What is the ratio of its kinetic energy to the energy required to escape from that orbit? 1:1 1:2 2:1 1:4 A body of mass m is projected vertically upwards from the surface of Earth with a velocity equal to 1/4 th of the escape velocity. What is the maximum height attained by the body from the surface of Earth? R/15 R/16 R/4 R/8 Two stars of masses m 1 and m 2 are part of a binary system. If they rotate in circular orbits of radii r 1 and r 2 respectively about their center of mass, their periods of revolution T 1 and T 2 satisfy: T 1 = T 2 T 1 > T 2 if m 1 > m 2 T 1 < T 2 if m 1 > m 2 T 1 / T 2 = r 1 / r 2 A satellite of mass m is revolving in a circular orbit of radius r around a planet of mass M . The angular momentum of the satellite about the center of the planet is: GMm 2r GMr/m 2 GMmr m GM/r What is the work done in rotating a satellite of mass m from a circular orbit of radius r to a circular orbit of radius 2r around the Earth (mass M )? GMm/4r GMm/2r GMm/r 3GMm/4r What is the ratio of the potential energy to the total energy of a satellite in a circular orbit? 2 1/2 -2 -1 The binding energy of a satellite of mass m in a circular orbit of radius r around a planet of mass M is: GMm 2r GMm r - GMm 2r 2GMm r A satellite is revolving in a circular orbit at a height ' h ' from the earth's surface (radius of earth R ; h R ). The minimum increase in its orbital velocity required, so that the satellite could escape from the earth's gravitational field, is close to: (Neglect the effect of atmosphere) ( 2 -1) gR gR gR/2 ( 2 -1) 2gR The work done to increase the radius of the orbit of a satellite of mass m from r to 2r around a planet of mass M is: GMm 4r GMm 2r GMm 8r 3GMm 4r According to Kepler's second law, the areal velocity of a planet revolving around the Sun is constant and equal to (where L is angular momentum and m is mass): L / (2m) L / m 2L / m L 2 / (2m) The escape velocity of a body from the surface of Earth is v e . The escape velocity of the same body from a height equal to 7R from the Earth's surface is: v e / 8 v e / 4 v e / 2 v e / 7 A satellite is moving in an elliptical orbit around the sun. If its maximum and minimum distances from the sun are r 1 and r 2 respectively, then the eccentricity of the orbit is: r 1 - r 2 r 1 + r 2 r 1 + r 2 r 1 - r 2 r 1 r 2 r 1 2 - r 2 2 r 1 2 + r 2 2 If the gravitational constant G were to decrease with time, then for a planet revolving around the sun: The orbital radius will increase The orbital radius will decrease The period of revolution will decrease The orbital speed will increase A satellite is launched into a circular orbit of radius R . If the radius of the orbit is increased by 2 % , the time period of the satellite will increase by approximately: 3 % 2 % 1 % 4 % What is the escape velocity of a body on a planet whose density is same as Earth but radius is double the radius of Earth? 22.4 km/s 11.2 km/s 15.8 km/s 5.6 km/s The period of revolution of an artificial satellite orbiting very close to the Earth's surface is T . If d is the density of Earth, then T is proportional to: 1/ d d d 1/d The escape velocity from the surface of Earth is v e . The escape velocity from a height h = R above the surface is: v e / 2 v e / 2 v e 2 v e / 4 A planet has mass M/10 and radius R/2 where M and R are the Earth's mass and radius. If the escape velocity on Earth is 11.2 km/s, the escape velocity on the planet is: 5.0 km/s 11.2 km/s 2.5 km/s 7.9 km/s If the distance between the Earth and the Sun is increased by 2 % , the duration of the year will increase by approximately: 3 % 2 % 4 % 1 % Two planets of radii R 1 and R 2 have the same density. The ratio of the escape velocities from their surfaces is: R 1 / R 2 (R 1 / R 2) 2 R 1 / R 2 (R 1 / R 2) 3/2