Advertisements
Advertisements
प्रश्न
What is the direction of areal velocity of the earth around the sun?
Advertisements
उत्तर
Areal velocity of the earth around the sun is given by `(dA)/(dt) = L/(2m)` where L is the angular momentum and m is the mass of the earth.
But angular momentum `L = r xx p = r xx mv`
∴ Areal velocity `((dA)/(dt)) = 1/(2m) (r xx mv) = 1/2 (r xx v)`
Therefore, the direction of areal velocity `((dA)/(dt))` is the direction of `(r xx v)`, i.e., perpendicular to the plane containing r and v and directed as given by the right-hand rule.
APPEARS IN
संबंधित प्रश्न
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
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.
A Saturn year is 29.5 times the earth year. How far is the Saturn from the sun if the earth is 1.50 ×108 km away from 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.
Identify the law shown in the figure and state three respective laws.
Answer the following question in detail.
State Kepler’s three laws of planetary motion.
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.
- What is the conclusion about the orbit of a planet?
- What is the relation between velocity of planet and distance from sun?
- ASB, CSD and ESF relation between areas explain.
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 ______.
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 ______.
In our solar system, the inter-planetary region has chunks of matter (much smaller in size compared to planets) called asteroids. They ______.
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.
Draw areal velocity versus time graph for mars.
What is one practical use of Kepler’s laws?
