Keplers Laws

The figure shows the elliptical orbit of a planet about the sun The shaded area is twice the shaded area If is the time for the planet to move from to and is the time to move from to then:

1.		2.
3.		4.

A planet moving along an elliptical orbit is closest to the sun at a distance r₁ and farthest away at a distance of r₂. If v₁ and v₂ are the linear velocities at these points respectively, then the ratio $\frac{{\mathrm{v}}_1}{{\mathrm{v}}_2}$ is:

1. ${\mathrm{r}}_2/{\mathrm{r}}_1$

2. ${\left({\mathrm{r}}_2/{\mathrm{r}}_1\right)}^2$

3. ${\mathrm{r}}_1/{\mathrm{r}}_2$

4. ${\left({\mathrm{r}}_1/{\mathrm{r}}_2\right)}^2$

The kinetic energies of a planet in an elliptical orbit around the Sun, at positions are respectively. is the major axis and is perpendicular to at the position of the Sun , as shown in the figure. Then:

1.
2.
3.
4.

The radius of Martian orbit around the sun is about times the radius of the orbit of mercury. The Martian year is earth days. Then which of the following is the length of year on mercury?
1. earth days
2. earth days
3. earth days
4. earth days