Finding the initial velocity

Estimate the initial velocity in meters/s that needs to be given to a spacecraft moving straight away from earth to make it reach the lunar orbit at 383000 km away from the centre of the earth.

The initial height of the spacecraft is H km above the surface of the earth. The radius of the earth is 6370 km.

H[km] = 6220;

Can someone help me please

Work done by gravitational force

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**m_i_k_o** Estimate the initial velocity in meters/s that needs to be given to a spacecraft moving straight away from earth to make it reach the lunar orbit at 383000 km away from the centre of the earth.

The initial height of the spacecraft is H km above the surface of the earth. The radius of the earth is 6370 km.

H[km] = 6220;

Can someone help me please

Here are the general principles to use:

- The gravitational pull exerted by the earth on the spacecraft is inversely proportional to the square of its distance from the centre of the earth. So if this force is $\displaystyle F$ N, the mass of the spacecraft is $\displaystyle m$ kg, and its distance is $\displaystyle x$ m from the centre of the earth,

$\displaystyle F = \frac{km}{x^2}$

- At the earth's surface this pull is equal to the weight of the spacecraft; i.e. when $\displaystyle x = 6370\times10^3, F = 9.8m$ N. This enables you to find $\displaystyle k$.

- When the spacecraft moves outwards from the earth from $\displaystyle x=x_0$ to $\displaystyle x=x_1$, the work done on it by the earth's gravitational pull is:

$\displaystyle \int_{x_0}^{x_1}-Fdx$

- Then use the Work-Energy Principle to find the initial velocity knowing that the final velocity is zero.

If it still doesn't work out, show us your working so far, and we'll have another look at it.

Grandad