One way to attack a satellite in Earth orbit is to launch a swarm of pellets in
ID: 1460475 • Letter: O
Question
One way to attack a satellite in Earth orbit is to launch a swarm of pellets in the same orbit as the satellite but in the opposite direction. Suppose a satellite in a circular orbit 510 km above Earth's surface collides with a pellet having mass 3.3 g. (a) What is the kinetic energy of the pellet in the reference frame of the satellite just before the collision? (b) What is the ratio of this kinetic energy to the kinetic energy of a 3.3 g bullet from a modern army rifle with a muzzle speed of 580 m/s?
Explanation / Answer
(a)
The pellet and the satellite must travel at the same speed to be in orbit at the same altitude.
Therefore relative to the satellite, the pellet approaches at twice it's speed.
r = Re + 510 km =
r = 6400 + 510 Km
r = 6910 * 10^3 m.
Force of gravity to the mass(centripetal acceleration) gives
G*M*m/ r^2 = m*v^2/r
v^2 = G*M/r
K.E Of Pellet = 1/2 * m*(2v)^2
K.E Of Pellet = 1/2 *3.3*10^-3*(2v)^2
K.E Of Pellet = 2 *3.3*10^-3* (G*M/r)
K.E Of Pellet = (2 *3.3*10^-3* 6.67 * 10^-11 * 5.972 * 10^24)/ (6910 * 10^3)
K.E Of Pellet = 380.5 KJ
(b)
The bullet speed is given as 580m/s
K.E of Bullet -
K.E = 0.5*3.3*10^-3*580^2 J
K.E = 555.1 J
The ratio = 380.5 *10^3 / 555.1
Ratio = 685.5 / 1
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