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.

Expert Solution
Step 1

Let an object of mass m lies on the surface of a planet of mass M of radius R. The force of attraction between the planet and the object is given by Newton's Law of Universal Gravitation

F=GMmR2

G 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 g then the weight of the object on the planet is

F=mg

Thus we get

mg=GMmR2g=GMR2

Step 2

Let the mass and radius of Kepler be M and R respectively and the mass and radius of planet BEE106 be M' and R'.

It is given that the radius of Kepler is three times less than that of BEE106. Thus

R'=3R

Let the acceleration due to gravity on Kepler be g and that of BEE106 be g', it is given in the question that

g'=3g

Therefore the acceleration due to gravity on Kepler

g=GMR2

Acceleration due to gravity on BEE106 

g'=GM'R'2=GM'3R2

Taking the ratio

gg'=GMR2GM'3R2g3g=MM'9R2R2MM'=13×9=127M=127M'

This shows that the mass of Kepler is 127 times the mass of BEE106. 

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