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ACS Without an Attitude

Apr 14, 2017 ... spacecraft onboard attitude and orbit applications in favor of a more quali- tative ... Satellite Technology and Its Applications, by P.R.K. Chetty, TAB Profes- ... cluded, and the same rotation is applied to each vector in the GSFC FDF ... axes are equal to the Earth's equatorial radius (about 6,378 km) while their.

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A 10kg satellite circles earth once every 2hr in an orbit havi

Jul 26, 2020 ... In fact for such large quantum numbers the results of quantisation conditions tend to those of classical physics. ... Assuming that Bohr's angular momentum postulate applies to satellites just as it does to an electron in the hydrogen atom, find the quantum number of the orbit of the satellite. check-circle.

For more information, see A 10kg satellite circles earth once every 2hr in an orbit havi


Given that

Mass of satellite m = 10 kg

Radius of orbit r = 8000 km = 8 * 10^{6} m

Time period T = 2 h = 7200 seconds

Assuming that the angular momentum postulate of Bohr applies to the satellite

Step 1: Using the Bohr's postulate to get an expression for quantum number

The second postulate of Bohr describes certain stable orbits. This postulate states that the electron revolves around the nucleus only in certain orbits where the angular momentum is some integral multiple of \frac{h}{2 \pi} .

L = m v_n r_n = \frac{nh}{2 \pi} ..................(1)

Relation between the angular and linear velocity

Velocity v_n = \omega r_n = \frac{2 \pi r_n}{T}       

Substituting v_n . value in equation (1)

[math] m [\frac{2 \pi r_n}{T}] r_n = \frac{nh}{2 \pi} [/math]

n = m \frac{4 \pi^2 r_n^2}{T * h}         

Thus, Quantum number of the satellite orbit n = m \frac{4 \pi^2 r_n^2}{T * h}


Step 2: Substitute the known values in the above equation

n = 10 \frac{4 * (3.14)^2 * (8 * 10^{6})^2 }{7200 * 6.63 * 10^{-34}}

n = 5.3 * 10^{45}       

Hence, Quantum number of the satellite orbit   n = 5.3 * 10^{45}   

The quantum number of the motion of the satellite is extremely high! In reality, the effects of quantization conditions are more likely to be classical physics for such large numbers.