You plan to take a trip to the moon. Since you do not have a traditional spaceship with rockets, you will need to leave the earth with enough speed to make it to the moon. Some information that will help during this problem: mearth = 5.9742 x 1024 kg rearth = 6.3781 x 106 m mmoon = 7.36 x 1022 kg rmoon = 1.7374 x 106 m dearth to moon = 3.844 x 108 m (center to center) G = 6.67428 x 10-11 N-m2/kg2

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aristocles aristocles · Answer 1 · 2019-10-11T04:00:43+02:00

Answer:

[tex]v = 3.5 \times 10^5 m/s[/tex]

Explanation:

At some distance from the Earth the force of attraction due to moon is balanced by the force due to Moon

so we will have

[tex]\frac{GM_em}{r^2} = \frac{GM_m}{(d-r)^2}[/tex]

now we have

[tex]\frac{d - r}{r} = \sqrt{\frac{M_m}{M_e}}[/tex]

[tex]\frac{3.844\times 10^8 - r}{r} = \sqrt{\frac{7.36 \times 10^{22}}{5.9742\times 10^{24}}}[/tex]

so we will have

[tex]r = 3.46 \times 10^8 m[/tex]

Now by energy conservation

[tex]-\frac{GM_e}{R_e} - \frac{GM_m}{d - (R_e + R_m)} + \frac{1}{2}v^2 = -\frac{GM_e}{r} - \frac{GM_m}{d - r}[/tex]

[tex]-6.26 \times 10^{8} - 13046 + \frac{1}{2}v^2 = -1.15 \times 10^6 - 1.28 \times 10^5[/tex]

[tex]v = 3.5 \times 10^5 m/s[/tex]