Question

GPS (Global Positioning System) satellites orbit at an altitude of 2.4×107 m .

A) Find the orbital period.
B) Find the orbital speed of such a satellite.

Answer 1

To find the orbital period, use Kepler's Third Law. To find the orbital speed, use the equation for orbital speed.

Step-by-step explanation:

The orbital period of a satellite can be found using Kepler's Third Law, which states that the square of the orbital period is proportional to the cube of the radius of the orbit.

A) To find the orbital period, we can use the formula T^2 = (4*pi^2*r^3) / (G*M), where T is the period, r is the radius of the orbit, G is the gravitational constant, and M is the mass of the Earth.

B) The orbital speed of a satellite can be found using the equation v = (2*pi*r) / T, where v is the orbital speed, r is the radius of the orbit, and T is the period.

Plugging in the values for the altitude, radius of Earth, and other constants, we can find the answers to both questions.

Answer 2

To find the orbital period of a satellite, use Kepler's third law. To find the orbital speed, use v = √(GM/r).

Step-by-step explanation:

In order to find the orbital period of a satellite at an altitude of 2.4x107 m, we can use Kepler's third law. This law states that the square of the orbital period is proportional to the cube of the orbital radius. The equation for the orbital period is T = 2π√(r3/GM), where T is the orbital period, r is the orbital radius, G is the gravitational constant, and M is the mass of the Earth. Plugging in the given values, we have T = 2π√((2.4x107)3/(6.67x10-11)(5.97x1024)).

To find the orbital speed of the satellite, we can use the formula v = √(GM/r), where v is the orbital speed. Plugging in the given values, we have v = √((6.67x10-11)(5.97x1024)/(2.4x107)).