The answer is; Irregular.
If the period of a satellite is T=24 h = 86400 s that means it is in geostationary orbit around Earth. That means that the force of gravity Fg and the centripetal force Fcp are equal:
Fg=Fcp
m*g=m*(v²/R),
where m is mass, v is the velocity of the satelite and R is the height of the satellite and g=G*(M/r²), where G=6.67*10^-11 m³ kg⁻¹ s⁻², M is the mass of the Earth and r is the distance from the satellite.
Masses cancel out and we have:
G*(M/r²)=v²/R, R=r so:
G*(M/r)=v²
r=G*(M/v²), since v=ωr it means v²=ω²r² and we plug it in,
r=G*(M/ω²r²),
r³=G*(M/ω²), ω=2π/T, it means ω²=4π²/T² and we plug that in:
r³=G*(M/(4π²/T²)), and finally we take the third root to get r:
r=∛{(G*M*T²)/(4π²)}=4.226*10^7 m= 42 260 km which is the height of a geostationary satellite.
Answer: 3 radians/meter.
Explanation:
The general sinusoidal function will be something like:
y = A*sin(k*x - ω*t) + C
Where:
A is the amplitude.
k is the wave number.
x is the spatial variable
ω is the angular frequency
t is the time variable.
C is the mid-value.
The rule that we can use to solve this problem, is that the argument of the sin( ) function must be in radians (or in degrees)
Then if x is in meters, the wave-number must be in radians/meters, so when these numbers multiply the "meters" part is canceled.
Then for the case of the function:
y(x,t) = 0.1 sin(3x + 10t)
Where x is in meters, the units of the wave number (the 3) must be in radians/meters. Then the angular wave number is 3 radians/meter.
