Calculating the distance to the moon based on given parameters.

[tgitatif]

Homework Statement

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.

On your first attempt you leave the surface of the Earth at v = 5534 m/s. How far from the center of the Earth will you get?

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

Homework Equations

PE = GM_Em/r

KE₁ + PE₁ = KE₂ + PE₂

The Attempt at a Solution

\frac{1}{2}m (5534)² = GM_Em/r

r = 2.6 x 10⁷

 

[lendav_rott]

If you get 26 000km away fromt he Earth into space traveling at 5.5 km/s then you would have escaped the Earth's gravity. Thing is, you need to be faster to escape.

If this is like a slingshot thing where you are given the initial velocity of 5534 m/s, then you definitely can't escape. Since you said you don't have rockets, you need to be atleast AT the same speed as escape velocity for a, what are youmacallit, unpowered ship? You need to be faster than the escape velocity if you want to make it to the Moon, much faster if you want to make it in a reasonable amount of time.

gravity is decelerating your ship by g m/s² , find the time it takes for the ship's vertical velocity become 0.

 

[tgitatif]

So since you don't escape the Earth's gravity, I just used mgh for PE instead of the universal gravitation and was able to get the correct answer. Thanks for pointing that out.

 

[voko]

KE₁ + PE₁ = KE₂ + PE₂

The Attempt at a Solution

\frac{1}{2}m (5534)² = GM_Em/r

Why do you think PE₁ = 0?

If you get 26 000km away fromt he Earth into space traveling at 5.5 km/s then you would have escaped the Earth's gravity.

No, you would not. Geostationary satellites are at about 36,000 km, but they are pretty much bound to the Earth.

gravity is decelerating your ship by g m/s² , find the time it takes for the ship's vertical velocity become 0.

That is only true when you are close to the Earth, which is not obvious in this case.

 

[phinds]

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.

I assume this is just a set-up for a math problem, not an actual ENGINEERING thought experiment, but just in case it IS intended to be an engineering concept, what DO you plan on using for the launch? Since once it leaves the launch mechanism, it will be on a purely ballistic trajectory, you have to gain all your needed speed in a short amount of space/time. How are you going to keep the astronauts from being crushed by the G forces? A big enough explosion on the ground works for a math problem, but obviously not for an engineering problem since it would likely turn the astronauts into a crushed blob.