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Questions
State Kepler’s laws.
State Kepler's three laws of motion.
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Solution
- Kepler's first Law: The orbit of a planet is an ellipse with the Sun at one of the foci.
- Kepler's second Law: The line joining the planet and the Sun sweeps equal areas in equal intervals of time.
- Kepler's third Law: The square of its period of revolution around the Sun is directly proportional to the cube of the mean distance of a planet from the Sun.
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State Kepler's law of orbit and law of equal areas.
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.
State Kepler's laws of planetary motion.
Let the period of revolution of a planet at a distance R from a star be T. Prove that if it was at a distance of 2R from the star, its period of revolution will be \[\sqrt{8}\] T.
Identify the law shown in the figure and state three respective laws.
In the Following figure shows the elliptical path of a planet about the sun. The two shaded parts have equal area. If t1 and t2 be the time taken by the planet to go from a to b and from c to d respectively,
Answer the following question.
State Kepler’s law of the period.
Observe the given figure showing the orbit of a planet moving around the Sun and write the three laws related to it:
The orbit of a planet moving around the Sun
The orbit of a planet revolving around a star is _______.
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.
Observe the given figure and answer these following questions.
The orbit of a planet moving around the Sun
- What is the conclusion about the orbit of a planet?
- What is the relation between velocity of planet and distance from sun?
- Explain the relation between areas ASB, CSD and ESF.
Write the Kepler's laws.
The third law of Kepler is also known as the Law of ______.
The earth moves around the sun in an elliptical orbit as shown in the figure. The ratio, `"OA"/"OB"` = x. The ratio of the speed of the earth at Band at A is ______.
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 ______.
In our solar system, the inter-planetary region has chunks of matter (much smaller in size compared to planets) called asteroids. They ______.
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.
Draw areal velocity versus time graph for mars.
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.
A satellite is in an elliptic orbit around the earth with aphelion of 6R and perihelion of 2 R where R= 6400 km is the radius of the earth. Find eccentricity of the orbit. Find the velocity of the satellite at apogee and perigee. What should be done if this satellite has to be transferred to a circular orbit of radius 6R ?
[G = 6.67 × 10–11 SI units and M = 6 × 1024 kg]
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)
What is one practical use of Kepler’s laws?
How can an ellipse be drawn using pins and thread?
