(a) Find the speed of a satellite moving around the earth in a circular orbit that has a radius equal to five times the earth's radius of 6.38 106 m.



(b) Find the satellite's orbital period.

Please Help!

Earth’s mass is M = 5.97•10²⁴kg,

G =6.67•10⁻¹¹ N•m²/kg²,
R=5 • 6.378•10⁶ = ..
(a) mv²/R = G•m •M/R²
v=sqrt{ G •M/R) = …

(b) T=s/v =3πR/v

Sure! I'd be happy to help you with these questions.

(a) To find the speed of a satellite moving in a circular orbit, we can use the formula for the velocity of a satellite in circular motion:

v = √(G * M / r)

where:
v is the velocity of the satellite,
G is the gravitational constant (approximately 6.67430 × 10^-11 m^3 kg^-1 s^-2),
M is the mass of the Earth (approximately 5.972 × 10^24 kg),
and r is the distance from the center of the Earth to the satellite's orbit.

In this case, the radius of the satellite's orbit is equal to five times the Earth's radius, which is 6.38 × 10^6 m. So, we can calculate the speed using the formula mentioned above:

v = √((G * M) / (5 * r))

Substituting the known values, we get:

v = √((6.67430 × 10^-11 m^3 kg^-1 s^-2 * 5.972 × 10^24 kg) / (5 * 6.38 × 10^6 m))

Simplifying the equation gives us:

v = √(3.986292 × 10^14 m^2/s^2)

Calculating the square root of this value, we find that the speed of the satellite is approximately:

v ≈ 2.99 × 10^4 m/s

Therefore, the speed of the satellite moving around the Earth in a circular orbit is approximately 2.99 × 10^4 m/s.

(b) To find the satellite's orbital period, we can use the formula:

T = (2 * π * r) / v

where:
T is the orbital period (time taken for one complete revolution),
r is the radius of the satellite's orbit, and
v is the speed of the satellite.

Using the given radius of the satellite's orbit (5 times the Earth's radius) and the previously calculated speed, we can calculate the orbital period:

T = (2 * π * 5 * 6.38 × 10^6 m) / (2.99 × 10^4 m/s)

Simplifying the equation gives us:

T = 2.12 × 10^4 s

Therefore, the satellite's orbital period is approximately 2.12 × 10^4 seconds.

I hope this helps! Let me know if you have any further questions.