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प्रश्न
Answer the following question in detail.
State Kepler’s three laws of planetary motion.
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उत्तर
1. Kepler’s law of orbits:
Statement:
All planets move in elliptical orbits around the Sun with the Sun at one of the foci of the ellipse.
2. Kepler’s law of equal areas:
Statement:
The line that joins a planet and the Sun sweeps equal areas in equal intervals of time.
3. Kepler’s law of periods:
Statement:
The square of the time period of revolution of a planet around the Sun is proportional to the cube of the semimajor axis of the ellipse traced by the planet.
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संबंधित प्रश्न
State Kepler's law of orbit and law of equal areas.
Let us assume that our galaxy consists of 2.5 × 1011 stars each of one solar mass. How long will a star at a distance of 50,000 ly from the galactic centre take to complete one revolution? Take the diameter of the Milky Way to be 105 ly
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.
Answer the following question.
State Kepler’s law of equal areas.
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.
State Kepler’s laws.
The mass and radius of earth is 'Me' and 'Re' respectively and that of moon is 'Mm' and 'Rm' respectively. The distance between the centre of the earth and that of moon is 'D'. The minimum speed required for a body (mass 'm') to project from a point midway between their centres to escape to infinity 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
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 ______.
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.
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.
Out of aphelion and perihelion, where is the speed of the earth more and why?
Earth’s orbit is an ellipse with eccentricity 0.0167. Thus, earth’s distance from the sun and speed as it moves around the sun varies from day to day. This means that the length of the solar day is not constant through the year. Assume that earth’s spin axis is normal to its orbital plane and find out the length of the shortest and the longest day. A day should be taken from noon to noon. Does this explain variation of length of the day during the year?
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]
lf the angular momentum of a planet of mass m, moving around the Sun in a circular orbit is L, about the center of the Sun, and its areal velocity is ______.
What is one practical use of Kepler’s laws?
How can an ellipse be drawn using pins and thread?
What is at one focus of the elliptical orbit of a planet?
The time taken by a planet to orbit the Sun depends on
