A satellite is in a circular orbit around an unknown planet. The satellite has a speed of 1.70 104 m/s, and the radius of the orbit is 5.30 106 m. A second satellite also has a circular orbit around this same planet. The orbit of this second satellite has a radius of 8.70 106 m. What is the orbital speed of the second satellite?

A = v^2/r

A = (1.70*10^4)^2/(5.30*10^6)
A = 54.53
A = G(m/r^2)
m = A*r^2/G
G = 6.67*10^-11
m = 54.53*(5.30*10^6)^2/6.67*10^-11
m = 2.30*10^25
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A = G(m/r^2)
A = 6.67*10^-11(2.30*10^25/(8.70*10^6)^2)
A = 20.27
A = v^2/r
(A*r)^(1/2) = v
v = 13279.6 m/s^2

V = sqrt[µ/r]

µ = V^2(r) = (1.7x10^4)^2(5.3x10^6) = 1.5317x10^15

V2 = sqrt[1.5317^15/8.7x10^6] = 1.3268x10^4m/s

To find the orbital speed of the second satellite, we can use Kepler's Third Law of planetary motion. According to Kepler's Third Law, the square of the orbital period of a satellite is directly proportional to the cube of its average orbital radius.

Let's denote the orbital speed of the second satellite as V2. We can set up a proportion using the known information:

(V1 / V2)^2 = (R1 / R2)^3

where V1 is the orbital speed of the first satellite, R1 is the radius of the orbit of the first satellite, R2 is the radius of the orbit of the second satellite, and V2 is the unknown orbital speed of the second satellite.

Substituting the given values:
(1.70 * 10^4 / V2)^2 = (5.30 * 10^6 / 8.70 * 10^6)^3

To simplify, we can cross-multiply and solve for V2:

(1.70 * 10^4)^2 * (8.70 * 10^6)^3 = V2^2 * (5.30 * 10^6)^3

Find the value of V2 by taking the square root of both sides of the equation:

V2 = √((1.70 * 10^4)^2 * (8.70 * 10^6)^3 / (5.30 * 10^6)^3)

Calculating on a calculator, we get:

V2 ≈ 1.65 * 10^4 m/s

Therefore, the orbital speed of the second satellite is approximately 1.65 * 10^4 m/s.

To find the orbital speed of the second satellite, we can make use of the concept of conservation of angular momentum. According to this principle, the product of the moment of inertia and angular velocity of a system remains constant as long as no external torques act on it.

For satellites in circular orbits, the moment of inertia can be approximated as m * r^2, where m is the mass of the satellite and r is the radius of the orbit. The angular velocity, on the other hand, is related to the orbital speed (v) by the equation v = ω * r, where ω is the angular velocity.

Since the two satellites are in circular orbits around the same planet, the product of their moment of inertia and angular velocity remains the same. Therefore, we can write:

(m1 * r1^2) * ω1 = (m2 * r2^2) * ω2

Now, rearranging the equation to solve for ω2:

ω2 = (m1 * r1^2 * ω1) / (m2 * r2^2)

Since the mass of the satellites is not provided, it cancels out in the calculation. Thus, we can write:

ω2 = (r1^2 * ω1) / r2^2

Finally, we substitute v1 = ω1 * r1 and solve for v2:

v2 = (r1^2 * ω1) / r2

Given that r1 = 5.30 × 10^6 m, ω1 = v1 / r1 = 1.70 × 10^4 m/s / 5.30 × 10^6 m, and r2 = 8.70 × 10^6 m, we can plug in the values to find the orbital speed of the second satellite:

v2 = (5.30 × 10^6 m)^2 * (1.70 × 10^4 m/s / 5.30 × 10^6 m) / (8.70 × 10^6 m)

Calculating this expression will give us the orbital speed of the second satellite.