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Homework Statement
Calculate the relative change in the distance of the Earth from the Sun, if the mass of the Sun is 15% lower than today weight of the Sun. Suppose that the Earth moves and will move along a circular path and will maintain its angular momentum.
Homework Equations
Equality of gravitational and centrifugal forces.
The Attempt at a Solution
For mass of the Sun today:
Valid for Earth: The centrifugal force = gravitational force
m_e*(v)^2/r=κ*m_e*m_s/(r)^2
(v)^2=κ*m_s/r
For mass of the Sun when is 15% lower than today weight of the Sun:
Valid for Earth: The centrifugal force = gravitational force
Mass and velocity of the Earth does not change because it does not change angular momentum.
m_e*(v)^2/r_1=κ*0,85m_s*m_e*/(r_1)^2
(v)^2=κ*0,85m_s/r_1
Equal squares of velocities:
κ*m_s/r=κ*0,85m_s/r_1
1/r=0,85/r_1
When is r=1 AU, then r_1=0,85AU
Why? I think it's stupid. Why the Earth is closer to the Sun, when the Sun is lighter? I think must be the Earth from the Sun farther, because the gravitational effects diminish. Why my ideas don't coincide with the results? How would you counted it?
Thanks very much.