Question

Tidal friction is slowing the rotation of the Earth. As a result, the orbit of the Moon is increasing in radius at a rate of approximately 4.0 cm/yr. Assuming this to be a constant rate, how many years will pass before the radius of the Moon's orbit increases by 3.84x 10^7 m (10%)?

Answer 1

Answer:

967500000 years

Explanation:

The Speed at which the radius of the orbit of the Moon is increasing is 4 cm/yr

Converting to m

1 m = 100 cm

$1\ cm=\frac{1}{100}\ m$

$4\ cm\y=\frac{4}{100}=0.04\ m/yr$

The distance by which the radius increases is 3.84×10⁷ m

Time = Distance / Speed

$\text{Time}=\frac{3.87\times 10^7}{0.04}\\\Rightarrow \text{Time}=967500000\ yr$

967500000 years will pass before the radius of the orbit increases by 10%.