The area the radius vector will sweep is 0.889A
According to Kepler's second law, the radius vector <em>sweeps</em> out equal areas in equal times.
Let A = area and t = time period,
According to Kepler's law, A/t = constant
So, A₁/t₁ = A₂/t₂ where A₁ = area the radius vector sweeps at <em>slowest</em> orbital speed = A, t₁ = time period at <em>slowest </em>orbital speed = 45 days, A₂ = area the radius vector sweeps at<em> fastest</em> orbital speed, t₂ = time period at<em> fastest </em>orbital speed = 40 days.
Making A₂ subject of the formula, we have
A₂ = A₁t₂/t₁
Substituting the values of the variables into the equation, we have
A₂ = A₁t₂/t₁
A₂ = A × 40 days/45 days
A₂ = A × 40/45
A₂ = A × 8/9
A₂ = A × 0.889
A₂ = 0.889A
So, the area the radius vector will sweep is 0.889A
learn more about Kepler's second law here:
brainly.com/question/4639131
