A satellite circling the earth completes each orbit in 5.10 x 10^3 s. What is the gravitational field strength @ the location of the satellite's orbit?
To calculate the gravitational field strength at the location of the satellite's orbit, we can use the formula for the gravitational field strength:
g = GM / r^2
Where:
g is the gravitational field strength,
G is the gravitational constant (6.67430 × 10^-11 N(m/kg)^2),
M is the mass of the Earth,
and r is the radius of the satellite's orbit.
To find the radius of the satellite's orbit, we need to know its period or the time it takes to complete one orbit around the Earth. In this case, the period is given as 5.10 x 10^3 s.
The period (T) of an orbit is related to the radius (r) by the formula:
T = 2π √(r^3 / GM)
Rearranging the above formula to solve for the radius (r):
r = (T^2 GM) / (4π^2)
Now, we can substitute the given values into the formula and calculate the radius of the satellite's orbit:
r = [(5.10 x 10^3 s)^2] × [6.67430 × 10^-11 N(m/kg)^2 × (5.97 × 10^24 kg)] / (4π^2)
After calculating for r, we can then substitute it back into the formula for gravitational field strength:
g = [(6.67430 × 10^-11 N(m/kg)^2) × (5.97 × 10^24 kg)] / (r^2)
Simplifying the equation will give us the value for the gravitational field strength at the location of the satellite's orbit.
Note: Since we've been given the value for the satellite's period, we've assumed that the satellite's orbit is circular and not elliptical.