Respuesta :
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
Answer:
The orbital speed of the second satellite is 6788.29 m/s
Explanation:
Given;
Radius of the planet, R = 9.00 × 10⁶ m
Mass of the first, m₁ = 68.0 kg
Speed of the first planet, v₁ = 4800 m/s
Radius of the first planet, r₁ = 6.00 x 10⁷ m
Mass of the second planet, m₂ = 84.0 kg
Radius of the second planet, r₂ = 3.00 × 10⁷ m
Let the speed of the second planet, = v₂
From Newton's gravitational law;
[tex]F = \frac{GM_pm}{r^2}[/tex] -------equation (i)
where;
G is universal gravitational constant, G = 6.67 x 10⁻¹¹ N.m²/kg²
[tex]M_p[/tex] is mass of the planet
m is mass of the satellite
r is radius of the satellite
From Newton's second law of motion;
[tex]F = ma=m\frac{v^2}{r}[/tex] -----------equation (ii)
Equate (i) and (ii)
[tex]\frac{GM_pm}{r^2} =\frac{mv^2}{r} \\\\\frac{GM_p}{r} =v^2\\\\v = \sqrt{\frac{GM_p}{r} }[/tex]
v is velocity of the satellite
r is radius of the satellite
Now, determine [tex]M_p[/tex], mass of the planet
[tex]v_1 =\sqrt{\frac{GM_p}{r_1} } \\\\v_1^2 = \frac{GM_p}{r_1}\\\\M_p = \frac{v_1^2r_1}{G} = \frac{(4800)^2(6*10^7)}{6.67*10^{-11}}=2.0726*10^{25} \ kg[/tex]
Finally, determine the speed of the second satellite;
[tex]v_2=\sqrt{\frac{GM_p}{r_2} }\\\\v_2=\sqrt{\frac{6.67*10^{-11}(2.0726*10^{25})}{3*10^7} }\\\\v_2 = 6788.29 \ m/s[/tex]
Therefore, the orbital speed of the second satellite is 6788.29 m/s
