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