Taking into account the gravitational pull of the sun , how much work is require

Question

Taking into account the gravitational pull of the sun , how much work is required to send a rocket ship of mass m from the surface of the earth to the surface of the sun? Additional data: Mass of the sun = 1.99*10^30 kg Radius of the sun =6.95*10^8m Distance from the earth to the sun =1.49*10^11m Gravitational constant =6.67*10^(-11) Mass of the earth =5.98*10^24 kg Radius of the earth =6.38*10^6
a) Find the point between the earth and the sun where the pull of the earth's Gravity matches that of the sun. b) Calculate the initial velocity of a cannonball fired from the surface of the earth if it is to land on the surface of the sun . Taking into account the gravitational pull of the sun , how much work is required to send a rocket ship of mass m from the surface of the earth to the surface of the sun? Additional data: Mass of the sun = 1.99*10^30 kg Radius of the sun =6.95*10^8m Distance from the earth to the sun =1.49*10^11m Gravitational constant =6.67*10^(-11) Mass of the earth =5.98*10^24 kg Radius of the earth =6.38*10^6
a) Find the point between the earth and the sun where the pull of the earth's Gravity matches that of the sun. b) Calculate the initial velocity of a cannonball fired from the surface of the earth if it is to land on the surface of the sun . Additional data: Mass of the sun = 1.99*10^30 kg Radius of the sun =6.95*10^8m Distance from the earth to the sun =1.49*10^11m Gravitational constant =6.67*10^(-11) Mass of the earth =5.98*10^24 kg Radius of the earth =6.38*10^6
a) Find the point between the earth and the sun where the pull of the earth's Gravity matches that of the sun. b) Calculate the initial velocity of a cannonball fired from the surface of the earth if it is to land on the surface of the sun .

Explanation / Answer

Mass of the sun = 1.99*10^30 kg

Radius of the sun =6.95*10^8m

Distance from the earth to the sun =1.49*10^11m

Gravitational constant =6.67*10^(-11)

Mass of the earth =5.98*10^24 kg

Radius of the earth =6.38*10^6

a)   the point between the earth and the sun where the pull of the earth's Gravity matches that of the sun.

(1.99*10^30 )/R12  =  5.98*10^24 / R22

R12 /  R22 = (1.99/5.98)*106

R1 / R2 = 576.87

And R1 + R2 = 1.49*10^11m

or 576.87R2 + R2 = 1.49*10^11m

or R2  = 2,58 * 108   m from Earth

b)  the initial velocity of a cannonball fired from the surface of the earth if it is to land on the surface of the sun

(1/2) V2 - [6.67*10^(-11)][5.98*10^24]/[6.38*10^6] = -[6.67*10^(-11)][5.98*10^24]/[6.38*10^6 + 2,58 * 108]

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