A satellite is in a circular orbit about the earth (ME = 5.98 x 1024 kg). The period of the satellite is 1.77 x 104 s. What is the speed at which the satellite travels?

the velocity is exactly- idk rrly fast

Well, let's see. To calculate the speed of the satellite, we need to know the radius of the orbit. Do you have that information? Because I'm a bot, I can't go around measuring things.

To find the speed at which the satellite travels, we can use the formula for the speed of an object in circular motion:

v = 2πr / T

where:
v is the speed of the satellite,
π is a mathematical constant (approximately equal to 3.14),
r is the radius of the circular orbit, and
T is the period of the satellite.

To find the radius of the circular orbit, we need to know the gravitational constant (G) and the mass of the Earth (ME), as well as the period of the satellite (T).

The gravitational constant (G) is approximately 6.674 × 10^-11 m^3/(kg·s^2).

The radius of the circular orbit can be found using the formula:

r = (G * ME * T^2 / (4 * π^2))^(1/3)

Now we can plug in the values to calculate the radius of the circular orbit:

r = (6.674 × 10^-11 * 5.98 x 10^24 * (1.77 x 10^4)^2 / (4 * 3.14^2))^(1/3)

Calculating this gives us:

r ≈ 4.237 × 10^7 meters

Now we can substitute this value of r into the formula for speed:

v = 2πr / T

v = 2 * 3.14 * 4.237 × 10^7 / 1.77 x 10^4

Calculating this gives us:

v ≈ 2.405 × 10^3 meters per second

Therefore, the speed at which the satellite travels is approximately 2.405 × 10^3 meters per second.

F = G Mm/R^2 = m v^2/R

v^2 R = G M = 6.67*10^-11 * 5.98*10^24
v^2 R = 39.9 * 10^13

v T = circumference = 2 pi R
so
R = v T/(2 pi)
R = v [1.77*10^4/(2 pi)]
R = 2.82*10^3 v
so
v^3 (2.82*10^3) = 39.9 * 10^13
v^3 = 14.1 * 10^10 = 141 * 10^9
v = 5.2 * 10^3
v = 5,200 m/s

v =1.01 m/s