A satellite is in a circular orbit around an unknown planet. The satellite has a speed of 1.60 104 m/s, and the radius of the orbit is 5.50 106 m. A second satellite also has a circular orbit around this same planet. The orbit of this second satellite has a radius of 8.50 106 m. What is the orbital speed of the second satellite?

Please help! I used the equation v=sqr root over G(m/r) and I can't get the right answer. Thanks:)

GMm1/r1^2=m1 v1^2/r1

GM=v1^2 r1

but
GMm2/r2^2=m2 v2^2/r2

GM=v2^2 r2

set them equal
V2^2=v1^2*r1/r2

v2= v1 sqrt (r1/r2) check my math...

To solve this problem, you can use the equation for orbital speed v = √(GM/r), where G is the gravitational constant (6.67430 × 10^-11 N(m/kg)^2), M is the mass of the planet, and r is the radius of the orbit.

In this case, you have the values for the first satellite's speed and radius, but you want to find the second satellite's orbital speed. Let's call it v2. You already know the radius of the second orbit, which is 8.50 × 10^6 m.

To find the orbital speed of the second satellite, you need to determine the mass of the planet. Unfortunately, you don't have enough information to directly find the mass of the planet. However, you can use the fact that the two satellites are orbiting the same planet, meaning that the mass of the planet is the same for both satellites.

Therefore, you can set up a ratio of the speeds and radii to find the ratio of the masses. In this case:

(v1^2 / v2^2) = (r1/r2)^3

where v1 is the speed of the first satellite (1.60 × 10^4 m/s), r1 is the radius of the first orbit (5.50 × 10^6 m), and r2 is the radius of the second orbit (8.50 × 10^6 m). We are solving for v2, the speed of the second satellite.

Rearranging the equation, we have:

v2 = v1 * √(r2/r1)^3

Plugging in the values:

v2 = (1.60 × 10^4 m/s) * √((8.50 × 10^6 m)/(5.50 × 10^6 m))^3

Calculating this expression, we find:

v2 ≈ 2.03 × 10^4 m/s

So the orbital speed of the second satellite is approximately 2.03 × 10^4 m/s.