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प्रश्न
Draw areal velocity versus time graph for mars.
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उत्तर
The areal velocity of a planet revolving around the sun is constant with time. Therefore, the graph between areal velocity and time is a straight line (AB) parallel to the time axis. ( Kepler's second law).
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संबंधित प्रश्न
A comet orbits the Sun in a highly elliptical orbit. Does the comet have a constant (a) linear speed, (b) angular speed, (c) angular momentum, (d) kinetic energy, (e) potential energy, (f) total energy throughout its orbit? Neglect any mass loss of the comet when it comes very close to the Sun.
Answer the following question in detail.
State Kepler’s three laws of planetary motion.
The square of its period of revolution around the sun is directly proportional to the _______ of the mean distance of a planet from the sun.
Write the Kepler's laws.
The third law of Kepler is also known as the Law of ______.
State Kepler’s laws.
If the distance between the sun and the earth is made three times, then attraction between the two will ______
To verify Kepler's third law graphically four students plotted graphs. Student A plotted a graph of T (period of revolution of planets) versus r (average distance of planets from the sun) and found the plot is straight line with slope 1.85. Student B plotted a graph of T2 v/s r3 and found the plot is straight line with slope 1.39 and negative Y-intercept. Student C plotted graph of log T v/s log r and found the plot is straight line with slope 1.5. Student D plotted graph of log T v/s log r and found the plot is straight line with slope 0.67 and with negative X-intercept. The correct graph is of student
Both earth and moon are subject to the gravitational force of the sun. As observed from the sun, the orbit of the moon ______.
If the sun and the planets carried huge amounts of opposite charges ______.
- all three of Kepler’s laws would still be valid.
- only the third law will be valid.
- the second law will not change.
- the first law will still be valid.
If the sun and the planets carried huge amounts of opposite charges ______.
- all three of Kepler’s laws would still be valid.
- only the third law will be valid.
- the second law will not change.
- the first law will still be valid.
Supposing Newton’s law of gravitation for gravitation forces F1 and F2 between two masses m1 and m2 at positions r1 and r2 read F1 = – F2 = `- r_12/r_12^3 GM_0^2 ((m_1m_2)/M_0^2)^n` where M0 is a constant of dimension of mass r12 = r1 – r2 and n is a number. in such a case.
- the acceleration due to gravity on earth will be different for different objects.
- none of the three laws of Kepler will be valid.
- only the third law will become invalid.
- for n negative, an object lighter than water will sink in water.
The centre of mass of an extended body on the surface of the earth and its centre of gravity ______.
- are always at the same point for any size of the body.
- are always at the same point only for spherical bodies.
- can never be at the same point.
- is close to each other for objects, say of sizes less than 100 m.
- both can change if the object is taken deep inside the earth.
Give one example each of central force and non-central force.
A star like the sun has several bodies moving around it at different distances. Consider that all of them are moving in circular orbits. Let r be the distance of the body from the centre of the star and let its linear velocity be v, angular velocity ω, kinetic energy K, gravitational potential energy U, total energy E and angular momentum l. As the radius r of the orbit increases, determine which of the above quantities increase and which ones decrease.
The maximum and minimum distances of a comet from the Sun are 1.6 × 1012 m and 8.0 × 1010 m respectively. If the speed of the comet at the nearest point is 6 × 104 ms-1, the speed at the farthest point is ______.
A planet revolving in an elliptical orbit has:
- a constant velocity of revolution.
- has the least velocity when it is nearest to the sun.
- its areal velocity is directly proportional to its velocity.
- areal velocity is inversely proportional to its velocity.
- to follow a trajectory such that the areal velocity is constant.
Choose the correct answer from the options given below:
Halley's Comet revolves around the sun for a time period of 76 years. The aphelion distance if perihelion is given by 8.9 × 1010 m, will be ______.
(Take, the mass of sun = 2 × 1030 kg and G = 6.67 × 10-11 Nm3/kg2)
