Question

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

Answer 1

`v = 3.5 * 10^5 m/s`

Step-by-step 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

`(GM_em)/(r^2) = (GM_m)/((d-r)^2)`

now we have

`(d - r)/(r) = \sqrt{(M_m)/(M_e)}`

`(3.844* 10^8 - r)/(r) = \sqrt{(7.36 * 10^(22))/(5.9742* 10^(24))}`

so we will have

`r = 3.46 * 10^8 m`

Now by energy conservation

`-(GM_e)/(R_e) - (GM_m)/(d - (R_e + R_m)) + (1)/(2)v^2 = -(GM_e)/(r) - (GM_m)/(d - r)`

`-6.26 * 10^(8) - 13046 + (1)/(2)v^2 = -1.15 * 10^6 - 1.28 * 10^5`

`v = 3.5 * 10^5 m/s`