Advertisements
Advertisements
Question
Out of aphelion and perihelion, where is the speed of the earth more and why?
Advertisements
Solution
Aphelion is the location of the earth where it is at the greatest distance from the sun and perihelion is the location of the earth where it is at the nearest distance from the sun. According to the diagram given below point A represents aphelion and point P perihelion.

According to Kepler's second law, a real velocity is constant. So, `r_p xx v_p = r_A xx v_A`
⇒ `r_A/r_p = v_p/v_A`
Therefore, `r_A > r_p`. So `v_p > v_A`
Therefore, the speed of the earth is more at the perihelion than at the aphelion.
APPEARS IN
RELATED QUESTIONS
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.
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.
Answer the following question in detail.
State Kepler’s three laws of planetary motion.
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 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 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 ______.

Both earth and moon are subject to the gravitational force of the sun. As observed from the sun, the orbit of the moon ______.
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.
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 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:
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 ______.
Two planets A and B of equal mass are having their period of revolutions TA and TB such that TA = 2TB. These planets are revolving in the circular orbits of radii rA and rB respectively. Which out of the following would be the correct relationship of their orbits?
