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Standard IX

Physics

Introduction to Gravitation : Kepler's Laws

In the figure...

Question

In the figure Area 1 is equal to Area 2 . Time taken by the planet in moving from $P_{1}$ to $P_{2}$ is t1 and from $P_{3}$ to $P_{4}$ is $t_{2}$ . Relation between $t_{1}$ and $t_{2}$ is

t_{1} = t_{2}

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t_{1} > t_{2}

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t_{1} < t_{2}

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t_{1} = 2 t_{2}

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Solution

The correct option is A $t_{1} = t_{2}$
According to Kepler's second law, planets in orbits sweep equal areas in equal intervals of time therefore $t_{1} = t_{2}$ .

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Similar questions

Q. Figure (11-Q2) 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,
(a) t₁ < t₂
(b) t₁ = t₂
(c) t₁ > t₂
(d) insufficient information to deduce the relation between t₁ and t₂.
Figure

Q. The areas

A_{1}, A_{2}

, and

A_{3}

are equal. Time taken for a planet to move from point M to N is

T_{1}

, and from point O to Q is

T_{2}

. Find the ratio of

T_{1}

and

T_{2}

The following figure shows the elliptical path of a planet about the sun. The two shaded parts have equal areas. If $t_{1}$ , $t_{2}$ be the time taken by the planet to go from A to B and from C to D respectively.

For an ideal gas, an illustration of three different paths

A

(B + C)

and

(D + E)

from an initial state

P_{1}

V_{1}

T_{1}

to a final state

P_{2}

V_{2}

T_{1}

is shown in the given figure.
Path

A

represents a reversible Isothermal expansion from

P_{1}

V_{1}

P_{2}, V_{2}

. Path

(B + C)

reperesents a reversible adiabatic expansion

(B)

from

P_{1} V_{1}

T_{1}

P_{3}

V_{2}

T_{2}

followed by reversible heating the gas at constant volume

(C)

from

P_{3}

V_{2}

T_{2}

P_{2}

V_{2}

T_{1}

. Path

(D + E)

represents a reversible expansion at constant pressure

P_{1} (D)

from

P_{1}

V_{1}

T_{1}

P_{1}

V_{2}

T_{3}

followed by a reversible cooling at constant volume

V_{2} (E)

from

P_{1}

V_{2}

T_{3}

P_{2}

V_{2}

T_{1}

. What is

Δ S

for path

(D + E) ?

Q. The following figure shows the elliptical path of a planet about the Sun. The two shaded parts,

S 1

and

S 2

, have equal areas. If

t_{1}

and

t_{2}

be the time taken by the planet to go from

A

B

and from

C

D

respectively, then:

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In the figure Area 1 is equal to Area 2 . Time taken by the planet in moving from P1 to P2 is t1 and from P3 to P4 is t2. Relation between t1 and t2 is

The correct option is A t1=t2According to Kepler's second law, planets in orbits sweep equal areas in equal intervals of time therefore t1=t2.

In the figure Area 1 is equal to Area 2 . Time taken by the planet in moving from $P_{1}$ to $P_{2}$ is t1 and from $P_{3}$ to $P_{4}$ is $t_{2}$ . Relation between $t_{1}$ and $t_{2}$ is

The correct option is A $t_{1} = t_{2}$
According to Kepler's second law, planets in orbits sweep equal areas in equal intervals of time therefore $t_{1} = t_{2}$ .