Let the speed of the planet at the perihelion $$P$$ in figure shown below be $$v_{_P}$$ and the Sun-planet distance $$\mathrm{SP}$$ be $$r_{_P}.$$ Relation between $$(r_{_P},~v_{_P})$$ to the corresponding quantities at the aphelion $$(r_{_A},~v_{_A})$$ is:

1. $$v_{_P} r_{_P} =v_{_A} r_{_A}$$
2. $$v_{_A} r_{_P} =v_{_P} r_{_A}$$
3. $$v_{_A} v_{_P} = r_{_A}r_{_P}$$
4. none of these

Subtopic:  Kepler's Laws |
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​Let the speed of the planet at the perihelion $$P$$ in the figure shown below be $$v_p$$ and the Sun-planet distance $$SP$$ be $$r_p$$. Will the planet take equal time to traverse $$BAC$$ and $$CPB?$$

 1 no 2 yes 3 depends on the mass of the planet 4 we can't say anything

Subtopic:  Kepler's Laws |
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Assume that earth and mars move in circular orbits around the sun, with the martian orbit being $$1.52$$ times the orbital radius of the earth. The length of the martian year in days is approximately:
(Take $$(1.52)^{3/2}=1.87$$)
1. $$344$$ days
2. $$684$$ days
3. $$584$$ days
4. $$484$$ days

Subtopic:  Kepler's Laws |
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