Answer: 6782 m/s
Explanation:
Given
Radius of the planet, r = 9*10^6 m
Mass of satellite 1, m1 = 68 kg
Radius of satellite 1, r1 = 6*10^7 m
Orbital speed of satellite 1, vs1 = 4800 m/s
Mass of satellite 2, m2 = 84 kg
Radius of satellite 2, r2 = 3*10^7 m
Orbital speed of satellite 2, vs2 = ?
We know that magnitude of gravitational force, F = (G.m.m•) / r²
Where,
m = mass of satellite
m• = mass of planet
r = radius of orbit
If we consider Newton's second law that states that, F = ma, thus
F(g) = ma(rad)
Where, a(rad) = v²/r
F(g) = mv²/r
Substituting in the initial equation
mv²/r = (G.m.m•) / r²
v² = (G.m•) / r
v = √[G.m•/r]
To find vs2, we first need to find mass of the planet, m• we know that G is a gravitational constant, so we plug in the values
vs1 = √[G.m•/r1]
4800 = √[(6.67*10^-11 * m•) / 6*10^7]
4800² = (6.67*10^-11 * m•) / 6*10^7
2.3*10^7 * 6*10^7 = 6.67*10^-11 * m•
1.38*10^15 = 6.67*10^-11 * m•
m• = 1.38*10^15 / 6.67*10^-11
m• =2.07*10^25 kg
Having found that, we use the value to find our vs2
vs2 = √[(G.m•) / r2]
vs2 = √[(6.67*10^-11 * 2.07*10^25) / 3*10^7]
vs2 = √(1.38*10^15 / 3*10^7)
vs2 = √4.6*10^7
vs2 = 6782.33 m/s
Therefore, the orbital speed of the second satellite is 6782 m/s
