(i) Planets move faster at perihelion and slower at aphelion.
(ii) A line joining a planet to the sun sweeps out equal areas in equal intervals of time.
(iii) Planets moves slower at perihelion and faster at aphelion.
Understanding Kepler's Laws of Planetary Motion
Kepler's laws describe the motion of planets around the Sun. There are three main laws. Let's examine the given statements in the context of these laws.
Analyzing Statement (i): Speed Variation
Statement (i) says: "Planets move faster at perihelion and slower at aphelion."
- Perihelion is the point in a planet's orbit where it is closest to the Sun.
- Aphelion is the point where it is farthest from the Sun.
This statement relates to Kepler's Second Law, which is about the conservation of angular momentum. For a planet's orbit, angular momentum is conserved. This means that as the distance from the Sun decreases (moving towards perihelion), the planet's speed must increase to keep the angular momentum constant. Conversely, as the distance increases (moving towards aphelion), the speed must decrease.
Therefore, statement (i) is correct.
Analyzing Statement (ii): Equal Areas in Equal Times
Statement (ii) says: "A line joining a planet to the sun sweeps out equal areas in equal intervals of time."
This is the precise mathematical statement of Kepler's Second Law of Planetary Motion. It directly follows from the conservation of angular momentum. Imagine a line connecting the planet to the Sun; over any given time period (e.g., one hour), the area this line 'draws' or 'sweeps' through space is constant, regardless of whether the planet is near or far from the Sun.
Therefore, statement (ii) is correct.
Analyzing Statement (iii): Speed at Perihelion and Aphelion
Statement (iii) says: "Planets moves slower at perihelion and faster at aphelion."
As explained when analyzing statement (i), this contradicts the principle derived from Kepler's Second Law. Planets move faster when they are closer (perihelion) and slower when they are farther away (aphelion). This statement is the exact opposite of what happens.
Therefore, statement (iii) is incorrect.
Conclusion on Valid Statements
Based on the analysis:
- Statement (i) is valid.
- Statement (ii) is valid.
- Statement (iii) is invalid.
Thus, the valid statements are (i) and (ii) only.
Important Questions from Miscellaneous
A stone is thrown horizontally from the top of a 20 m high building with a speed of 12 m/s. It hits the ground at a distance R from the building. Taking g = 10 m/s2 and neglecting air resistance will give :
A mass is attached to a spring that hangs vertically. The extension produced in the spring is 6 cm on Earth. The acceleration due to gravity on the surface of the Moon is one-sixth of its value on the surface of the Earth. The extension of the spring on the Moon would be:
Directions: Each item in this section consists of a sentence with an underlined word followed by four words (a), (b), (c), and (d). Select the option that is opposite in meaning to the underlined word and mark your response in your Answer Sheet accordingly.
The deluge affected the population.The major source of vitamins and minerals for vegetarians is
Which of the following statements about the Deccan Riots Commission is/are correct?
1. The Commission did not hold enquiries in the districts which were not affected.
2. The Commission did record the statements of ryots, sahukars and eye-witnesses.
Select the correct answer using the code given below:
