Keplers laws of planetary motion, gravitational potential energy and gravitational potential - One Line Questions
1.
What is the gravitational potential at the center of a uniform solid sphere of mass M and radius R? —
-3GM/(2R)
2.
The gravitational potential at the center of a uniform spherical shell of mass M and radius R is: —
-GM/R
3.
The gravitational potential energy of a satellite of mass 'm' in a circular orbit of radius 'r' around the Earth of mass 'M' is: —
-GMm/r
4.
Kepler's Third Law relates the orbital period (T) and the semi-major axis (a) of an elliptical orbit for planets around the same star. For two planets 1 and 2, the ratio of their periods squared is equal to: —
(T1/T2)^2 = (a1/a2)^3
5.
The gravitational potential energy of a satellite in orbit around the Earth is: —
Always negative
6.
For a planet orbiting the Sun, the quantity that remains constant according to Kepler's Second Law is: —
Angular momentum
7.
Kepler's First Law is a specific case of which mathematical conic section? —
Ellipse
8.
Kepler's Second Law implies that a planet's orbital speed is: —
Not constant, varying such that the line joining the planet to the Sun sweeps out equal areas in equal intervals of time
9.
According to Kepler's Third Law, for planets orbiting the Sun, the ratio T^2/a^3 is: —
The same for all planets
10.
According to Kepler's First Law, the eccentricity 'e' of a circular orbit is: —
e = 0
11.
Which planet has the shortest orbital period around the Sun? —
Mercury
12.
Kepler's Second Law is a consequence of the conservation of: —
Angular momentum
13.
The 'areal velocity' of a planet, as described by Kepler's Second Law, is: —
Constant
14.
What is the relationship between gravitational potential energy (U) and gravitational force (F) for a system of two masses? —
F = -dU/dr
15.
For a planet in an elliptical orbit, the speed is highest when it is: —
Closest to the Sun
16.
Gravitational potential is a scalar quantity, while gravitational field is a vector quantity. The relationship between them is: —
Field = -Gradient of Potential
17.
Gravitational potential energy of a system of two point masses m1 and m2 separated by a distance r is given by: —
-G * m1 * m2 / r
18.
The gravitational potential energy of a system of two particles of masses m1 and m2 at infinite separation is defined as: —
0
19.
The gravitational potential energy of a system of two identical masses 'm' separated by a distance 'r' is: —
-Gm^2/r
20.
The gravitational potential at the surface of the Earth (mass M, radius R) is: —
-GM/R
21.
The gravitational potential due to a point mass 'M' at a distance 'r' is given by: —
-GM/r
22.
If a body of mass 'm' is moved from infinity to a point at distance 'r' from a mass 'M', the change in its gravitational potential energy is: —
-GMm/r
23.
If the Earth were to collapse to a point mass, its gravitational potential at its surface would: —
Remain the same
24.
If the distance between two masses is doubled, their gravitational potential energy: —
Becomes one-fourth
25.
If the semi-major axis of a planet's orbit is doubled, how does its orbital period change according to Kepler's Third Law? —
It becomes approximately 2.8 times larger (2^1.5)
26.
If the Earth's mass is doubled and its radius is halved, what happens to the gravitational potential at its surface? —
It becomes four times
27.
What is the unit of gravitational potential? —
Joule/kg
28.
The path of a planet around the Sun is an ellipse, with the Sun at one of the foci. This is a statement of: —
Kepler's First Law
29.
Which law states that the line joining a planet and the Sun sweeps out equal areas in equal intervals of time? —
Kepler's Second Law
30.
Which of Kepler's laws states that the square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit? —
Kepler's Third Law (Law of Periods)
31.
The gravitational potential at a point is the potential energy per unit: —
Mass
32.
Gravitational potential at a point is defined as the work done per unit: —
Mass in bringing a unit mass from infinity to that point
33.
The gravitational potential energy of an object of mass 'm' at a height 'h' above the Earth's surface (mass M, radius R) is approximately: —
-GMm/(R+h)
34.
If we define the gravitational potential energy of an object to be zero at the Earth's surface, then at a height 'h' above the surface, it would be: —
mgh
35.
The gravitational potential at a point P is V. If a mass 'm' is brought from infinity to P, the work done by the gravitational field is: —
-mV
36.
The work done in moving a particle of mass 'm' from a point A to a point B in a gravitational field is independent of the path taken if the gravitational force is: —
Conservative
37.
Which of the following is NOT a direct consequence of Kepler's laws? —
The force causing planetary motion is attractive
38.
The work done by the gravitational force as a planet moves from perihelion to aphelion in its orbit is: —
Zero
39.
The gravitational potential at a distance 'r' from a point mass 'M' is numerically equal to the work done per unit mass in bringing the mass from infinity to that point. This work done is: —
Negative
40.
What is the gravitational potential at infinity? —
Zero
41.
If a planet has a larger semi-major axis, its orbital period will be: —
Longer
42.
If T is the orbital period and R is the radius of a circular orbit (approximating semi-major axis), Kepler's Third Law can be expressed as: —
T^2 ∝ R^3
43.
Kepler's Third Law is often used to determine the mass of a central body if the orbital parameters of a satellite are known. If a satellite's period is T and its orbital radius is R (for a circular orbit), the mass of the central body is proportional to: —
R^3 / T^2
44.
The work done to bring a unit positive test mass from infinity to a point in a gravitational field is equal to: —
The gravitational potential at that point
45.
Consider a planet moving in an elliptical orbit around the Sun. Its angular momentum is conserved because: —
The gravitational force is a central force
46.
The gravitational potential energy of a system is the energy stored in the system due to: —
The positions of the objects
47.
The gravitational potential energy of a system of N particles is the sum of the potential energies of all possible pairs of particles. For a system of three particles, it is: —
U12 + U23 + U31
48.
The gravitational potential energy of a system of particles is defined as the work done by an external agent against the gravitational force to assemble the system from a configuration where the potential energy is zero. This zero potential energy configuration is typically: —
When the particles are at infinite separation
49.
The gravitational potential energy is taken to be zero when the separation between the masses is: —
Infinite
50.
If the Sun suddenly vanished, the gravitational potential energy of the Earth would become: —
Zero