Question

What is the true weight of an object in a geostationary satellite that weighed exactly 10.0 N at the north pole?

Answer 1

For a geostationary satellite, we have:
R = 6.4 × 10³ km
h = 3.6 × 10³ km
Given: mg = 10 N

The true weight of the object in the geostationary satellite is given by

\[\text { mg' = mg }- \frac{R^2}{\left( R + h \right)^2}\]

\[ = 10 - \frac{\left( 6400 \times {10}^3 \right)^2}{\left( 6400 \times {10}^3 + 3600 \times {10}^3 \right)}\]

\[ = 10 - \left[ \frac{\left( 64 \times {10}^5 \right)^2}{\left( 6 . 4 \times {10}^6 + 36 \times {10}^5 \right)} \right]\]

\[ = 10 - \left[ \frac{4096 \times {10}^{10}}{\left( 42 . 4 \right)^2 \times {10}^{12}} \right]\]

\[ = \frac{4096}{17980} = 0 . 227 N\]