How do I go about in solving this?
A spy satellite is in circular orbit around Earth. It makes one revolution in 6.01 hours.
(a) How high above Earth's surface is the satellite?
___ km
(b) What is the satellite's acceleration?
___m/s2
(a) Set the centripetal force equal to the gravity force on the satellite, and solve for R, the distance from the center of the earth.
G*M*m/R^2 = m V^2/R
M is the mass of the Earth and G is the universal constant of gravity. The satellite mass m cancels out.
Once you have R, subtract the Earth's radius (Re) from that to get the altitude. You will need the speed V of the satellite. Express V in terms of the orbit radius (R) and the period (6.01 hours). Make sure the period is in seconds.
(b) The acceleration is V^2/R. Use the R and V that you get from part (a)
To solve this problem, we need to use the formulas for orbital motion. Let's break it down step by step:
(a) How high above Earth's surface is the satellite?
We can start by finding the radius of the satellite's orbit. The time it takes for one revolution is given as 6.01 hours. We know that the period of an object in circular motion (T) is related to the radius (r) of its orbit by the formula:
T = 2πr / v
where v is the orbital velocity of the satellite. Since we're given the period and we want to find the radius, we can rearrange the formula as follows:
r = (T * v) / (2π)
To find the orbital velocity, we can use the formula for the circumference (C) of a circle:
C = 2πr
The velocity is given by the formula:
v = C / T
Substituting the value of C, we get:
v = (2πr) / T
Now, we can substitute this value back into the equation for r:
r = (T * (2πr) / T) / (2π)
By canceling out the T terms:
r = (2πr) / (2π)
Simplifying further:
r = r
This means that the radius is equal to itself, which indicates that the satellite's height above Earth's surface is equal to the radius of Earth.
The average radius of Earth is approximately 6,371 kilometers. Therefore, the satellite's height above Earth's surface is 6,371 kilometers.
(b) What is the satellite's acceleration?
To find the satellite's acceleration, we can use the formula for centripetal acceleration:
a = v^2 / r
Since we know the orbital velocity (v) and the radius (r) from the previous calculations, we can substitute these values into the formula to find the acceleration.
It's important to note that the acceleration here represents the net force required to keep the satellite in orbit. This net force is provided by gravity.
Calculating the acceleration using the given values might be challenging as it depends on the specific values provided for the orbital velocity and radius. Please provide the specific values for the orbital velocity and we can substitute them into the formula to find the acceleration.