Net gravitational force

**Yonkersnerd** · February 23rd 2008, 05:38 AM

Hey:
I am trying to solve this problem, but getting nowhere, any help would be greatly appreciated!

What is the net gravitational force exerted on a 3.00 X 10^4 kg spaceship halfway between the Earth and the Moon. The average distance between the Earth and the Moon is 384,000 km. The Earth's mass is 5.98 X 10^24 kg, and the Moon's mass is 7.36 X 10^22 kg.

I am confused.

Thanks!

**TheEmptySet** · February 23rd 2008, 07:08 AM

The Force of Gravity between two objects is given by
$F_g=G\frac{m_1m_2}{r^2}$

So the force of the earth on the ship is

$F_g=G\frac{m_sm_e}{d^2}$

and the force of the moon on the ship is

$F_g=G\frac{m_sm_m}{d^2}$

where $m_s$ is the mass of the ship

and where $m_e$ is the mass of the earth

and where $m_m$ is the mass of the moon

and where $d$ is the distance half way inbetween

and $G$ is gravitational constant

so $F_{net}=G\frac{m_sm_e}{d^2}-G\frac{m_sm_m}{d^2}=G\frac{m_s}{d^2}(m_e-m_m)$

Just plug in the numbers to finish...

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