Geostationary satellites are placed in orbits of radius 4.2×10^4 km. Use this information to deduce g at that height
[(Earth radius) / 4.2E4]^2 * 9.8 m/s^2 = ?
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To deduce the value of g at the height of a geostationary satellite orbit, we can use the formula for gravitational acceleration:
g = (G * M) / r^2
Where:
- G is the gravitational constant (approximately equal to 6.67430 × 10^-11 N m^2/kg^2)
- M is the mass of the Earth (approximately 5.972 × 10^24 kg)
- r is the distance from the center of the Earth to the satellite orbit
In this case, the radius of the geostationary satellite orbit is given as 4.2 × 10^4 km. However, we need to convert this to meters in order to use the formula.
1 km = 1000 m
Therefore, the radius in meters is:
4.2 × 10^4 km = 4.2 × 10^4 × 1000 m = 4.2 × 10^7 m
Now, we can plug these values into the formula to find the value of g:
g = (6.67430 × 10^-11 N m^2/kg^2 * 5.972 × 10^24 kg) / (4.2 × 10^7 m)^2
Calculating this expression will give us the value of g at the height of a geostationary satellite orbit.