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Answer: 88 Earth days
Explanation:
According to the Kepler Third Law of Planetary motion <em>“The square of the orbital period of a planet is proportional to the cube of the semi-major axis (size) of its orbit”. </em>
<em />
In other words, this law states a relation between the orbital period of a body (moon, planet, satellite) orbiting a greater body in space with the size
of its orbit:
(1)
If we assume the orbit is circular and apply Newton's law of motion and the Universal Law of Gravity we have:
(2)
Where is the mass of the massive object and
is the universal gravitation constant. If we assume
constant and larger enough to consider
really small, we can write a general form of this law:
(3)
Where is in units of Earth years,
is in AU (<u>1 Astronomical Unit is the average distane between the Earth and the Sun)</u> and
is the mass of the central object in units of the mass of the Sun.
This means when we are making calculations with planets in our solar system .
Hnece, in the case of Mercury:
(4)
Isolating :
(5)
(6)
This means the period of Mercury is 88 days.
To solve this problem it is necessary to apply the concepts concerning the conservation of both potential and thermodynamic energy of the body. That is to say that as the body has a loss of potential energy it is gained in the form of thermal energy on water. If the potential energy is defined as
Where,
m= mass
g = Gravitational acceleration
h = Height
And thermal energy is obtained as
Where,
= Change in Temperature
Specific Heat
m = Mass
We can equate this equation and rearrange to find the change at the Temperature, then
Our values are given as,
Specific Heat Water
Using energy conservation
Replacing,
Therefore the temperature increase in a 1kg sample of water is 1.89K