The escape(kinetic) energy is equal to the gravitational initial potentialenergy

Question

The escape(kinetic) energy is equal to the gravitational initial potentialenergy of the object. How does that potential energy depend on themass and radius of the astronomical body?
Section 13-6 GravitationPotential Energy
Calculate the amount of energy required to escape from the surfaceof the following bodies, relative to that required to escape fromthe surface of Earth. (a) the Sun 1x energy to escape Earth (b) Mercury 2 x energy to escape Earth The escape(kinetic) energy is equal to the gravitational initial potentialenergy of the object. How does that potential energy depend on themass and radius of the astronomical body? Section 13-6 GravitationPotential Energy

Explanation / Answer

(a)energy required to escape earth Ee= (GMem/r) =(GMem/Re + h) -------------(1) the energy required to escape Sun Es= (GMsm/r1) =(GMsm/Rs + h) -----------(2) from equation (1) we get m = (Re + h/GMe) * Ee-------------(3) from (2) and (3) we get Es= (GMs/Rs + h) *(Re + h/GMe) * Ee =(Ms/Me) * (Re + h/Rs +h) * Ee ------------(1) Ms(mass of Sun) = 1.98892 * 10^30 kg Me(mass of earth) = 5.9742 * 10^24 kg Re(radius of earth) = 6378.1 km = 6378.1 * 10^3m Rs(radius of sun) = 695500 km = 695500 * 10^3m h is the height of the mass above the surface of theearth (b)Similarly,when we consider Mercury then the energy requiredto escape from the surface of mercury is Em= (Mm/Me) * (Re+ h/Rm + h) * Ee (from equation (1)) Mm(mass of mercury) = 3.30200 * 10^23 kg Rm(radius of mercury) = 2439.7 km = 2439.7 * 10^3m Ms(mass of Sun) = 1.98892 * 10^30 kg Me(mass of earth) = 5.9742 * 10^24 kg Re(radius of earth) = 6378.1 km = 6378.1 * 10^3m Rs(radius of sun) = 695500 km = 695500 * 10^3m h is the height of the mass above the surface of theearth (b)Similarly,when we consider Mercury then the energy requiredto escape from the surface of mercury is Em= (Mm/Me) * (Re+ h/Rm + h) * Ee (from equation (1)) Mm(mass of mercury) = 3.30200 * 10^23 kg Rm(radius of mercury) = 2439.7 km = 2439.7 * 10^3m

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