radius R of the orbit of a geosynchronous satellite that circles the earth. (Note that R is measured from the center of the earth, not the surface.) You may use the following constants:
The universal gravitational constant G is 6.67×10−11N⋅m2/kg2.
The mass of the earth is 5.98×1024kg.
The radius of the earth is 6.38×106m.
T=8.64×10^4 s
4.23*10^7
Does this website even show answers?
The anonymous answer was right
Why did the geosynchronous satellite get a high T rating on its orbit around the Earth? Because it kept going around and around without missing a beat! Now, let's calculate the radius of its orbit.
To find the radius R, we can use the following equation:
T = 2π√(R^3 / GM)
Where:
T is the orbital period (in seconds)
G is the universal gravitational constant
M is the mass of the Earth
Plugging in the values:
8.64×10^4 = 2π√(R^3 / (6.67×10^(-11)(5.98×10^24)))
Now, let's solve this puzzle and find the value of R!
To find the radius R of the orbit of a geosynchronous satellite, we can use the formula for the period T of the satellite's orbit.
The period T is the time taken by the satellite to complete one full revolution around the Earth. In this case, the period T is given as 8.64×10^4 seconds.
The formula for the period of an object in circular orbit is:
T = 2π * √(R^3 / (G * Me))
where R is the radius of the orbit, G is the universal gravitational constant, and Me is the mass of the Earth.
Rearranging the formula, we can solve for R:
R = ((T^2 * G * Me) / (4π^2))^(1/3)
Now, let's substitute the given values into the formula and calculate the radius R:
G = 6.67×10−11 N⋅m^2/kg^2 (universal gravitational constant)
Me = 5.98×10^24 kg (mass of the Earth)
T = 8.64×10^4 s (period of the satellite)
R = ((8.64×10^4)^2 * (6.67×10−11) * (5.98×10^24)) / (4π^2))^(1/3)
Using a calculator, we can evaluate this expression to find the radius R.