The mass of Kepler is what fraction of the mass of BEE106.
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there was a new planet discovered in 2017 names Kepler, it is about 300 light years from Earth. Compared to the expo planet BEE106 that was discovered in 2014, Kepler has 3 times less radius. The acceleration due to gravity on BEE106 is 3 times the gravitational acceleration on Kepler. The mass of Kepler is what fraction of the mass of BEE106.
Let an object of mass lies on the surface of a planet of mass of radius . The force of attraction between the planet and the object is given by Newton's Law of Universal Gravitation
is the universal gravitational constant. This force is equal to the weight of the object on the planet. Let the acceleration due to the gravity is then the weight of the object on the planet is
Thus we get
Let the mass and radius of Kepler be and respectively and the mass and radius of planet BEE106 be and .
It is given that the radius of Kepler is three times less than that of BEE106. Thus
Let the acceleration due to gravity on Kepler be and that of BEE106 be , it is given in the question that
Therefore the acceleration due to gravity on Kepler
Acceleration due to gravity on BEE106
Taking the ratio
This shows that the mass of Kepler is times the mass of BEE106.
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