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T^2/r^3 =(4π^2)/(Gm_1 )

T^2/r^3 =(4π^2)/((6.67×〖10〗^(-11) )×(1.898×〖10〗^27))

T^2/r^3 =3.118×〖10〗^(-16)

r^3/T^2 =3.204×〖10〗^15 log⁡(r^3/T^2 )=log⁡(3.204 ×〖10〗^15)

log⁡(r^3 )-log⁡(T^2 )=log⁡(3.204 ×〖10〗^15)

3 log⁡(r)-2 log⁡(T)= log⁡(3.204 ×〖10〗^15)

log⁡(r)=2/3 log⁡(T)+(log⁡(3.204×〖10〗^15))/3

Kepler’s Third Law states that the gradient of the graph should be two thirds. Therefore because the graph shows the gradient of the moons is 0.6585 we can in fact confirm that Kepler’s Third Law is correct.
〖T_a〗^2/〖r_a〗^3 =〖T_b〗^2/〖r_b〗^3

〖1.77〗^2/〖(4.22×〖10〗^8)〗^3 =〖250.25〗^2/〖r_b〗^3



r_b=∛(1.502×〖10〗^30 )

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If an intervening mass can align perfectly with a background source then it will bend the light creating a ring of light around the object. This is known as Einstein’s ring and depending on the mass of the object will determine the size of the ring, a larger mass results in a larger ring. (Richmond, 2015)
Our universe is 85% dark matter, dark matter may be invisible but it still has mass and therefore when light travels towards it, it will bend around them matter causing gravitational lensing. All objects can bend light but usually the change is not measurable on smaller objects such as humans, for any substantial bend to occur it would take a huge mass and a light ray to travel extremely close to the matter. When the light bends it can alters the shape of the image, with a galaxy for example it can bend or warp the shape which is normally elliptical or spiral looking. (Grocutt, 2015)
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