Well, well, well, looks like we have some space travelers here! Let's calculate the orbital speed of that second satellite, shall we?
To do this, we can use the principle of conservation of angular momentum. According to this principle, the product of an object's moment of inertia and its angular velocity is constant as long as no external torques are acting on it. In simpler terms, it means that as long as the radius of the orbit changes, the orbital speed will also change to keep that product constant.
In the case of the first satellite, we have a speed of 1.70 × 10^4 m/s and a radius of 5.80 × 10^6 m. We can calculate the angular momentum (L1) of the first satellite using the formula L = mvr, where "m" is the mass of the satellite, "v" is the speed, and "r" is the radius.
Now, let's move on to the second satellite, with a radius of 8.50 × 10^6 m. The angular momentum (L2) of the second satellite will be the same as the first one. We can use the same formula to find the orbital speed (v2) of the second satellite, but this time we have the radius (r2), and we need to solve for "v2."
So, we have L1 = L2, which means m1v1r1 = m2v2r2. As we can see, the mass of the satellites cancels out, leaving us with v1r1 = v2r2.
Now, we just need to plug in the values: (1.70 × 10^4 m/s)(5.80 × 10^6 m) = v2(8.50 × 10^6 m). Solving for v2, we get:
v2 = (1.70 × 10^4 m/s)(5.80 × 10^6 m) / (8.50 × 10^6 m)
And voila! You should be able to calculate the orbital speed of that second satellite. Just be careful not to get stuck in space traffic! Safe travels!