Two galaxies of masses 9 billion solar
mass and 4 billion solar mass are 5
million light years apart. If, the Sun has
to cross the line joining them, without
being attracted by either of them, through
what point it should pass?
Answers
If, the Sun has to cross the line joining them, without being attracted by either of them, through it should pass through the point which is at a distance of 3million light years from the 1st galaxy and at a distance of 2 million light years from the 2 million light years.
For this to happen the total gravitational force on the sun from either of the mass should be zero. That is they should cancel out.
Gravitational force is given by GM1M2/r^2.
Let M be mass of sun.
M1 be the mass of the 9billion solar mass galaxy.
M2 be the mass of the 4 billion solar mass galaxy.
Distance between 2 galaxies is 5 million light years = r1 + r2
We know 1 billion is 1000 millions.
- Now force on sun from galaxy 1 is : GM1M/r1^2
- F1 = GM x 9000 million M / r1^2
- Now force on sun from galaxy 2 is : GM2M/r2^2
- F2 = GM x 4000 million M /r2^2
For sun to pass through without being attracted,
- F1 = F2
- GM x 9000 million M /r1^2 = GM x 4000million M / r2^2
- 9/r1^2 = 4/r2^2
- r2 = 2r1/3
Therefore, r1 + r2 = 5million light years.
- 5r1/3 = 5million light years.
- r1 = 3 million light years
- r2 = 2 million light years.
Therefore the sun should pass through the point which is at a distance of 3million light years from the 1st galaxy and at a distance of 2 million light years from the 2 million light years.