मराठी
महाराष्ट्र राज्य शिक्षण मंडळएस.एस.सी (इंग्रजी माध्यम) इयत्ता १० वी

Write the Kepler’s laws.

Advertisements
Advertisements

प्रश्न

Write the Kepler’s laws.

नियम
Advertisements

उत्तर

  1. Kepler’s first law: The orbit of a planet is an ellipse with the sun at one of the foci.
  2. Kepler’s second law: The line joining the planet and the sun sweeps equal areas in equal intervals of time.
  3. Kepler’s third law: The square of the orbital period of revolution of a planet around the Sun is directly proportional to the cube of the mean distance of the planet from the Sun.
shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1: Gravitation - Answer the Following [पृष्ठ ३३]

संबंधित प्रश्‍न

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.


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.


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.

  1. What is the conclusion about the orbit of a planet?
  2. What is the relation between velocity of planet and distance from sun?
  3. ASB, CSD and ESF relation between areas explain.

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


A planet revolves in an elliptical orbit around the sun. The semi-major and minor axes are a and b, then the time period is given by:


Both earth and moon are subject to the gravitational force of the sun. As observed from the sun, the orbit of the moon ______.


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.

  1. the acceleration due to gravity on earth will be different for different objects.
  2. none of the three laws of Kepler will be valid.
  3. only the third law will become invalid.
  4. for n negative, an object lighter than water will sink in water.

Give one example each of central force and non-central force.


Out of aphelion and perihelion, where is the speed of the earth more and why?


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]


What is one practical use of Kepler’s laws?


The time taken by a planet to orbit the Sun depends on ______.


When is a planet moving fastest in its orbit?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×