EXERCISE
1) Calculate the volume V of the Dumbbell Nebula in Km 3 , with its diameter D and its height L such as: D =9.5*10 15 m and L =1.4*10 16 m.
We can consider the nebula as a double paraboloïd, the formula for the volume V of a paraboloïd is V =1.5708* R 2 *L ,so the formula of the volume of Dumbbell is : V=2*1.5708*R 2 *L
2) Calculate its mass M in Kg, with its volume V and its density N such as: N =1.7*10 -7 g/km 3
3) Compare its mass M with the mass m of our Sun ( you can use caution Dumbbell's mass/ Sun's mass ) such as: m =2*10 36 mg.
What can you say of this result?
CORRECTION :
1) It's necessary to convert D and L in Km: D =9.5*10 12 km and L =1.4*10 13 km. Next, we have to calculate the radius : R = D/2 = 4.75*10 12 km.
Then V =2*1.5708*(4.75*10 12 ) 2 *(1.4*10 13 ) =9.94*10 38 Km 3
2) We have to convert its density in Kg/Km 3 : N =1.7*10 -10 Kg/Km 3
If V=M/N then M=V*N
Then M =6.7*10 38 *1.7*10 -10 =1.7*10 29 Kg
3) We convert the Sun's mass in Kg: m =2*10 30 Kg.
Then M/m =(1.7*10 29 )/(2*10 30 ) =0.08
The mass of Dumbbell nebulary is around 0.1 mass of the sun !! But incertitudes of this calculation are very larges, so we have to be cautious...