Question

Two satellites are in orbit around the same planet. Satellite A has a mass of 1.5 x 10^2 kg and satellite B has a mass of 4.5 x 10^3 kg. The mass of the planet is 6.6 x 10^24 kg. Both satellites have the same orbital radius of 6.8 x 10^6 m. What is the difference in the orbital periods of the satellites?

Answer 1

The orbital period of a satellite is determined by the mass of the planet it orbits and the radius of its orbit. The formula for the orbital period of a satellite is T = 2π√(r³/GM). By calculating the orbital periods using the given information, we can find the difference between them.

Step-by-step explanation:

The orbital period of a satellite is determined by the mass of the planet it orbits and the radius of its orbit. The formula for the orbital period of a satellite is T = 2π√(r³/GM), where T is the period, r is the orbital radius, G is the gravitational constant, and M is the mass of the planet.

For satellite A, T₁ = 2π√((6.8 x 10⁶ m)³/(6.67 x 10⁻¹¹ Nm²/kg²)(6.6 x 10²⁴ kg)), and for satellite B, T₂ = 2π√((6.8 x 10⁶ m)³/(6.67 x 10⁻¹¹ Nm²/kg²)(6.6 x 10²⁴ kg)).

Substituting the values into the formulas, we can calculate the orbital periods of the satellites and find the difference between them.

Answer 2

The difference in the orbital periods of the satellites is zero.

Step-by-step explanation:

Given data,

The mass of the planet A is, m = 1.5 x 10² kg

The mass of the planet B is, m' = 4.5 x 10³ kg

The mass of the planet is, M = 6.6 x 10²⁴ kg

The orbital radius of the satellites are, R = 6.8 x 10⁶ m

The orbital period of the satellite is given by,

`T=\frac{2\pi R}{\sqrt{(GM)/(R)}}`

From the above equation, it is evident that the period of the satellite is independent of the mass of the satellite.

Since the radius of the orbit of the satellites A and B are the same, the difference in the orbital periods of the satellites is zero.