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The Earth is nearest the Sun, at 1.471 × 10¹¹ m, in January, and farthest, at 1.521 × 10¹¹ m, in…

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

The Earth is nearest the Sun, at $1.471 \times 10^{11}\ \text{m}$ , in January, and farthest, at $1.521 \times 10^{11}\ \text{m}$ , in July. In January it moves at $30.3\ \text{km/s}$ . How fast does it move in July?

Need a reminder? The key ideaShow

Kepler's laws. Orbits are ellipses with the Sun at a focus. The line to the Sun sweeps equal areas in equal times, so at the nearest and farthest points $v_1r_1 = v_2r_2$ . And $T^2 \propto a^3$ : for bodies around the Sun, $T^2 = a^3$ with $T$ in years and $a$ in AU.

The worked solution

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Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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