A satellite is in a circular orbit around an unknown planet. The satellite has a speed of 1.80 104 m/s, and the radius of the orbit is 5.45 106 m. A second satellite also has a circular orbit around this same planet. The orbit of this second satellite has a radius of 8.60 106 m. What is the orbital speed of the second satellite?

centripetal force = gravitational force

m V^2/R = GMm/R^2

m is the satellite mass, which cancels out. M is the planet mass. G is the universal gravity constant.

Note that R*V^2 = G M, which is the same for both satellites
Use that fact to answer your question.

To find the orbital speed of the second satellite, we can use the concept of conservation of angular momentum.

The angular momentum of an object in circular orbit is given by the equation:

L = mvr

Where L is the angular momentum, m is the mass of the satellite, v is the orbital speed, and r is the radius of the orbit.

Since both satellites are orbiting the same planet, the product of mass and radius will be the same for both satellites. Thus, we can equate the angular momentum of the two satellites:

m1v1r1 = m2v2r2

Where v1 and r1 are the orbital speed and radius of the first satellite, and v2 and r2 are the orbital speed and radius of the second satellite.

We are given v1 = 1.80 x 10^4 m/s and r1 = 5.45 x 10^6 m. Let's substitute these values into the equation:

m1(1.80 x 10^4 m/s)(5.45 x 10^6 m) = m2v2(8.60 x 10^6 m)

Now, we know that the mass of an object cancels out when equating angular momentum. So we can eliminate m1 and m2 from the equation:

(1.80 x 10^4 m/s)(5.45 x 10^6 m) = v2(8.60 x 10^6 m)

Now we can solve for v2:

v2 = (1.80 x 10^4 m/s)(5.45 x 10^6 m)/(8.60 x 10^6 m)

v2 = 1.14 x 10^4 m/s

Therefore, the orbital speed of the second satellite is 1.14 x 10^4 m/s.