Question

Two satellites are in circular orbits around a planet that has radius 9.00×106 m. One satellite has mass 68.0 kg, orbital radius 8.00×107 m , and orbital speed 4800 m/s. The second satellite has mass 84.0 kg and orbital radius 7.00×107
What is the orbital speed of this second satellite?

Answer 1

Answer:

v₂ = 5131.42 m/s

Explanation:

given,

radius of the planet = r₁ = 9.00×10⁶ m

mass of the satellite = m₁ = 68 Kg

orbital radius = r₁ = 8 x 10⁷ m

orbital speed = v₁ = 4800 m/s

mass of second satellite = m₂ =  84.0 kg

orbital radius = r₂ = 7.00×10⁷ m

orbital speed of second satellite = v₂ = ?

using orbital speed of satellite

            $v = \sqrt{\dfrac{GM}{r}}$

     so,

            $v \alpha \dfrac{1}{\sqrt{r}}$

now,

            $\dfrac{v_1}{v_2} =\sqrt{\dfrac{r_2}{r_1}}$

            $\dfrac{v_2}{4800} =\sqrt{\dfrac{8\times 10^7}{7 \times 10^7}}$

                v₂ = 5131.42 m/s

The orbital speed of second satellite is equal to v₂ = 5131.42 m/s