A planet p moves around the sun is in an elliptical orbit of eccentricity e
Answers
Answered by
0
We know that areal velocity of planet is constant.
The desired time is time taken to travel from A to B
The time taken to cover complete area of ellipse =T
∴
tAB
=(AreaofSAB. Areaofellipse)
∴tAB=(AreaofSAB. Areaofellipse)
TArea of ellipse = πab
=> tAB =πabArea of SAB
=14
=14πab−AreaofΔOSB
πab−AreaofΔOSB
=14
=14πab−12πab−12b×ae
b×ae
∴tAB=(πab4−12abe)Tπab
∴tAB=(πab4−12abe)Tπab
=T[14−e2π]
=T[14−e2π]
The desired time is time taken to travel from A to B
The time taken to cover complete area of ellipse =T
∴
tAB
=(AreaofSAB. Areaofellipse)
∴tAB=(AreaofSAB. Areaofellipse)
TArea of ellipse = πab
=> tAB =πabArea of SAB
=14
=14πab−AreaofΔOSB
πab−AreaofΔOSB
=14
=14πab−12πab−12b×ae
b×ae
∴tAB=(πab4−12abe)Tπab
∴tAB=(πab4−12abe)Tπab
=T[14−e2π]
=T[14−e2π]
Similar questions