# Is related to its mass m by the formula r 2 gm c 2

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) is related to its mass,M, by the formula:R= 2GM/cwhereG= 6.674×1011m3/kg·s2andc= 2.998×108Let’s look at the units:R= (m3/kg·s2)×(kg)÷(m/s)2. The units ofGcan be rewritten as m3kg1s2.The mass of the object is kg.The units for the speed of lightccan be rewritten as m·s1; the units for the speed of light squared (c2) will then be m2·s2. Lookingat the full equation, kilograms will cancel. Seconds squared (s2) in the denominator ofGwill cancel with the seconds squared (s2in the denominator ofc2because we are dividing: s2÷s2= s2×s2. Meters cubed (m3) fromGdivided by meters squared (m2fromc2will leave meters (m), which makes sense as the radius of an object will be in meters.Given that the mass of the Earth is 5.973×1024kg, determine its Schwarzchild radius if it somehow collapses into a black hole.Do the same for the Sun (the mass of the Sun is 1.989×1030kg). Show your work in the box.[60 pts total]Schwarzchild radius of Earth: (a) _____________________________ m [Write in scientific notation; round to2decimals.](b) _____________________________ cm [Convert to cm; write in scientific notation;2decimals.](c) _____________________________ cm [Write as aREGULARNUMBER; round to1decimal.]Schwarzchild radius of Sun: (d) _____________________________ m [Write in scientific notation; round to2decimals.](e) _____________________________ km [Convert to km; write as aREGULAR NUMBER; round to1decimal.][Parts a, b, c, d, e each worth 10 pts; work = 10 pts]8.87 x 10^-30.88650.892.95 x 10^32.952m/s.))a.2GM/c^2= 2x6.674 x10^-11 x 5.973 x10^24/(2.998 x 10^8)^2= 0.8865m=mb.SN= 8.87 x 10^-2c. RN= 0.887d.Rs=2GM/c^2= 2x 6.67 x 10^-11 x 1.989 x 10^30/ (2.998 x 10^8)^2=2 x 6.67 x 1.989 x10^19/8.988 x 10^16= 2.952 x10^3 or2.95 x 10^3e.RN= 2.95
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