The earth revolves around the sun in a circular path with a speed of 30 \mathrm{~km} / \mathrm{s}. What is the radial acceleration directed towards the sun?
The earth revolves around the sun in a circular path with a speed of 30 \mathrm{~km} / \mathrm{s}. What is the radial acceleration directed towards the sun?

    \[\begin{array}{c} \text { Speed of revolution }=30 \mathrm{Km} / \mathrm{s} \\ =3 \times 10^{4} \mathrm{~m} / \mathrm{s} \end{array}\]

Time of revolution = One year =356 days (convert into seconds)

    \[=365 \times 24 \times 60 \times 60=3.5 \times 10^{7} \text { seconds }\]

The formula of radial acceleration:

    \[\mathrm{ac}=\mathrm{V}^{2} / \mathrm{r}\]

Distance covered by the earth around the sun will be equal to the circumference of orbit.

    \[\begin{array}{l} \text { Speed } \times \text { Time }(\mathrm{V} \cdot \mathrm{T})=2 \pi \mathrm{r} \\ \mathrm{r}=\mathrm{V} \cdot \mathrm{T} / 2 \pi \\ \mathrm{a}_{\mathrm{c}}=\mathrm{V}^{2} / \mathrm{r}=\mathrm{V}^{2} \times 2 \pi / \mathrm{V} \times \mathrm{T} \\ \mathrm{a}_{\mathrm{c}}=2 \pi \mathrm{V} / \mathrm{T} \\ a_{c}=\frac{2 \times 3.14 \times 3 \times 10^{4}}{3.5 \times 10^{7}} \\ \left.\$ \$ \mathrm{a}_{-} \mathbf{c}=\mathbf{5} \cdot 98 \times 10^{\wedge} \mathrm{\{}-3\right\} \mathrm{m} / \mathrm{s}^{\wedge} \mathbf{2} \$ \$ \end{array}\]