An artificial satellite circles the Earth in a circular orbit at a location where the acceleration due to gravity is 8.26 m/s2. Determine the orbital period of the satellite.

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Ive tried everything I can think of the value im getting through the equations though isn't giving me the right answer it keeps saying within 10%?

To determine the orbital period of the satellite, we can use the formula:

T = 2π * √(r³ / GM)

where:
T is the orbital period,
π is the mathematical constant pi (approximately equal to 3.14159),
r is the radius of the satellite's circular orbit,
G is the gravitational constant (approximately equal to 6.67430 × 10⁻¹¹ m³/(kg·s²)),
M is the mass of the Earth.

First, we need to find the radius of the satellite's orbit. We can use the acceleration due to gravity and the formula for centripetal acceleration:

a = (v²) / r

where:
a is the acceleration due to gravity (8.26 m/s²),
v is the orbital speed of the satellite,
r is the radius of the satellite's orbit.

Since the satellite is in a circular orbit, the centripetal acceleration is equal to the acceleration due to gravity. Hence, we can rewrite the equation as:

8.26 m/s² = (v²) / r

Solving this equation for v², we get:

v² = 8.26 m/s² * r

Next, we can use the formula for the orbital speed of a satellite:

v = √(GM / r)

By substituting the value of v² from the previous equation, we get:

√(8.26 m/s² * r) = √(GM / r)

Squaring both sides of the equation, we have:

8.26 m/s² * r = GM / r

Now we can rearrange this equation to solve for r:

r² = GM / 8.26 m/s²

Finally, substituting the values for G and M and solving for r, we can determine the radius of the satellite's orbit.

Once you have the radius, you can substitute it into the formula for the orbital period mentioned at the beginning to calculate the orbital period of the satellite.

If you've tried different calculations and are still not getting the correct answer, please double-check your calculations and make sure you've used the correct values for G and M. Also, pay attention to the units of measurement to avoid any conversion errors.