#### Question

A communications satellite weighs $4400$N on Earth where $g=9.81 \frac{m}{s^2}$ . What is the weight of the satellite, in N, as it orbits Earth where the acceleration of gravity is $0.224 \frac{m}{s^2}$. Express each weight in lbf.

#### Solutions

Verified#### Step 1

1 of 5Data:

$F_{earth} = 4400 N$ - The weight of the satellite on Earth

$g_{earth} = 9,81 m/s^2$ - Gravitational acceleration on Earth

$g_{orbit} = 0,224 m/s^2$ - Gravitational acceleration in orbit

#### Step 1

1 of 3Information:

$F_{S}=4400\hspace{1mm}\text{N}$ (weight of the satellite resting on the surface of the Earth)

$g_{S}=9.81\hspace{1mm}\dfrac{\text{m}}{\text{s}^{2}}$ (gravitational acceleration on the surface)

$g_{O}=0.224\hspace{1mm}\dfrac{\text{m}}{\text{s}^{2}}$ (gravitational acceleration while in orbit)

$F_{O}=?$ (weight of the satellite while in orbit)

Weight of the satellite equals its mass multiplied by the local gravitational acceleration: $F=m\cdot g$, therefore

#### Step 1

1 of 3$\rule{430pt}{1pt}$

$\text{\textcolor{#4257b2}{Given}}$

-Weight on earth $(W_{earth})=4400\mathrm{N}$

-gravitational acceleration on earth $(g_{earth})=9.81\mathrm{m/s^{2}}$

- Gravitational acceleration while orbiting $(g_{orbit})=.224\ \mathrm{m/s^{2}}$

$\text{\textcolor{#4257b2}{Required}}$

- Weight while orbiting $W_{orbit}$ in $\mathrm{N}$ and in $\mathrm{Ibf}$

$\text{\textcolor{#4257b2}{Assumption}}$

- The mass is constant and doesn't change with gravity.