Question

Pluto moves in a fairly elliptical orbit around the sun. Pluto’s speed at its closest approach of $4.43\times {10}^9$km is 6.12 km/s. What is Pluto’s speed at the most distant point in its orbit, where it is$7.30\times {10}^9$km from the sun?

Short answer

The Pluto's speed at the most distant point in its orbit is$3.71km/s$.

Step-by-step solution

Step 1. Given information

Here,

$$\begin{gathered} r_1={\text{closestdistance=4.43×10}}^9\text{km} \\ {\text{v}}_1\text{=speedatclosestdistance=6.12km/s} \\ {\text{r}}_2{\text{=farthestdistance=7.30×10}}^9\text{km} \\ {\text{v}}_2\text{=?} \end{gathered}$$

Step 2. Formula used

Angular momentum, L=mvr

where,

m=mass of planet

r=distance from sun

v=speed of planet

Step 3. Calculation

As angular momentum should remain constant.

$$\begin{gathered} {\text{mv}}_1{\text{r}}_1{\text{=mv}}_2{\text{r}}_2 \\ {\text{⇒v}}_2{\text{=v}}_1{\text{r}}_1{\text{/r}}_2 \\ \Rightarrow {\text{v}}_2\text{=}\frac{4.43\times {10}^9\times 6.12}{7.30\times {10}^9}\text{km/s} \\ \Rightarrow {\text{v}}_2\text{=3.71km/s} \end{gathered}$$

Step 4. Conclusion

The speed of pluto at most distant point is 3.71km/s.