ceres orbits the sun every 1680 days. calculate how many seconds it takes for ceres to complete one orbit.
1 answer:
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Answer:
Explanation:
We are told both planets describe a circular orbit around the star S. So, let's approach this problem begining with the angular velocity of the planet P1 with a period
:
(1)
Where:
is the velocity of planet P1
is the radius of the orbit of planet P1
Finding :
(2)
(3)
(4)
On the other hand, we know the gravitational force between the star S with mass
and the planet P1 with mass
is:
(5)
Where is the Gravitational Constant and its value is
In addition, the centripetal force exerted on the planet is:
(6)
Assuming this system is in equilibrium:
(7)
Substituting (5) and (6) in (7):
(8)
Finding :
(9)
(10)
Finally:
(11) This is the mass of the star S