A satellite is in circular orbit at a height R above earth's surface.
a)find orbital period.
b)what height is required for a circular orbit with a period double that found in part (a)?
A satellite is in circular orbit at a height R above earth's surface.
a)find orbital period.
b)what height is required for a circular orbit with a period double that found in part (a)?
Allow me to modify your terms.
a) The orbit radius R = Re + h where Re = the earth's radius and h = the altitude of the satellite in feet.
The orbital period of a satellite derives from
T = 2(Pi)sqrt(R^3/µ) where T = the orbital period in seconds, R = the radius of the satellite orbit and µ = the earth's gravitational constant = 1.407974x10^16 ft^3/sec^2.
b) For T = 4(Pi)sqrt[(Re + h)^3/µ)
h = R - Re = [(Tµ)/(16Pi^2)]^(1/3) - Re
To find the orbital period of a satellite in a circular orbit, you need to use the formula:
T = 2π√(r³/GM),
where T is the orbital period, r is the distance from the center of the Earth to the satellite (which is the sum of the radius of the Earth and the height of the satellite above the Earth's surface), G is the gravitational constant (approximately 6.67430 × 10^(-11) N m²/kg²), and M is the mass of the Earth (approximately 5.972 × 10^24 kg).
a) To find the orbital period, we assume R is the radius of the Earth (6,371 km) and the height, h, above the Earth's surface is given. The distance, r, can be calculated as follows:
r = R + h
Substituting the values into the formula, we get:
T = 2π√((R+h)³/GM)
Calculating this will give you the orbital period of the satellite.
b) To find the height required for a circular orbit with a period double the one found in part (a), you can use the formula:
T' = 2T
Substituting T' and T into the formula, we get:
2π√((R+h')³/GM) = 2π√((R+h)³/GM)
Simplifying and solving for h', we get:
(R+h')³ = 2³(R+h)³
Taking the cube root and rearranging, we get:
h' = [2³(R+h)³ - R³]^(1/3) - R
Calculating this will give you the height required for the circular orbit with a period double the one found in part (a).