Two satellites are in circular orbits around a planet that has radius 9.00×106m. One satellite has mass 68.0 kg, orbital radius 6.00×107 m , and orbital speed 4800 m/sm/s. The second satellite has mass 84.0 kg and orbital radius 3.00×107 m. What is the orbital speed of this second satellite?v=?

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;

-------equation (i)

where;

G is universal gravitational constant, G = 6.67 x 10⁻¹¹ N.m²/kg²

is mass of the planet

m is mass of the satellite

r is radius of the satellite

From Newton's second law of motion;

-----------equation (ii)

Equate (i) and (ii)

v is velocity of the satellite

r is radius of the satellite

Now, determine , mass of the planet

Finally, determine the speed of the second satellite;

Therefore, the orbital speed of the second satellite is 6788.29 m/s

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