Final answer:
To determine the radius of the circular orbit, use the formula for centripetal force. The speed of the satellite can be found using the formula for orbital speed. The period of the orbit can be determined using the formula for period.
Step-by-step explanation:
To determine the radius of the circular orbit, we can use the formula for centripetal force:
Fc = (m × v2) / r
We know that the satellite has a mass of 500 kg and experiences a gravitational force of 3000 N.
Rearranging the formula, we can solve for the radius:
r = (m × v2) / Fc
Substituting the given values, we get:
r = (500 kg × (v2)) / 3000 N
Next, to determine the speed of the satellite, we can use the formula for orbital speed:
v = sqrt((G × M) / r)
We know that the mass of the Earth (M) is approximately 5.98 × 1024 kg and the gravitational constant (G) is approximately 6.67 × 10-11 N · (m/kg)2.
Substituting the values, we can solve for v:
v = sqrt((6.67 × 10-11 N · (5.98 × 1024 kg)) / r)
Finally, to determine the period of the orbit, we can use the formula:
T = (2 × π × r) / v
Substituting the given values, we can solve for T:
T = (2 × π × r) / sqrt((6.67 × 10-11 N · (5.98 × 1024 kg)) / r))