A satellite with a mass of 310 kg moves in a circular orbit 7.00*10^7 m above the Earth's surface.
(a) What is the gravitational force on the satellite?
(b) What is the speed of the satellite?
(c) What is the period of the satellite?
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To find the answers to these questions, we'll need to use the formulas related to circular motion and gravitational force. I'll explain step by step how to solve each part of the problem.
(a) To find the gravitational force on the satellite, we can use the formula for gravitational force:
F = (G * m1 * m2) / r^2
where F is the gravitational force, G is the gravitational constant (6.673 * 10^-11 N*m^2/kg^2), m1 and m2 are the masses of the two objects (in this case, the satellite and the Earth), and r is the distance between their centers.
In this case, the mass of the satellite is given as 310 kg, and the distance from the satellite to the Earth's surface is given as 7.00 * 10^7 m. We can assume the mass of the Earth is approximately 5.97 * 10^24 kg.
Plugging these values into the formula, we get:
F = (6.673 * 10^-11 N*m^2/kg^2) * (310 kg) * (5.97 * 10^24 kg) / (7.00 * 10^7 m)^2
Calculating this expression will give us the gravitational force on the satellite.
(b) To find the speed of the satellite, we can use the formula for centripetal force:
F = m * v^2 / r
where F is the centripetal force, m is the mass of the satellite, v is the speed of the satellite, and r is the radius of the circular orbit.
We already know the mass of the satellite (310 kg) and the radius of the orbit (7.00 * 10^7 m), and we need to find the speed v.
To find v, we can rearrange the formula as follows:
v = sqrt(F * r / m)
Plugging in the values we have, we can calculate the speed of the satellite.
(c) To find the period of the satellite, we can use the formula for the period of an object in circular motion:
T = 2 * pi * r / v
where T is the period, r is the radius of the orbit, and v is the speed of the satellite.
We already know the radius of the orbit (7.00 * 10^7 m) and we can use the value of v calculated in part (b) to find the period T.
Using these formulas, you can calculate the gravitational force, speed, and period of the satellite.