A satellite moves in a circular orbit about our earth exactly four times a day. Find its orbit, radius , speed and weight.
A 10.0 kg mass is 1.00m to the left of the origin, and a 20.0 kg mass is 3.00 m to the right of the origin, both on x-axis. Find the gravitational potential energy and the gravitational field on x-axis at a) x =-2.0m b.) the origin, c.) x = 4.00 (set Zero P.E @ infinity in terms of G.
The orbital period of any satellite derives from
T = 2(Pi)sqrt(r^3/µ) where T = the period in seconds, 6(3600) = 21,600, r = the orbit radius in seconds and µ = the earth;s gravitational constant.
Therefore,
21600 = 2(3.14)sqrt(r^3/1.407974x10^21)
from which r = 55,002,293 ft. = 10,417 miles.
The velocity derives from V = sqrt(µ/r)
V = sqrt(1.407974x10^21/55,002,293) =
The orbital height and period are totally independant or the weight.
To find the orbit radius and speed of a satellite that orbits the Earth four times a day, we can use the following equations:
1. Orbital Period:
The time taken for a satellite to complete one orbit is known as the orbital period (T). In this case, T = 24 hours / 4 = 6 hours.
2. Radius:
The radius of the orbit (R) can be determined using the formula:
R = (G * M * T^2 / (4 * π^2))^(1/3)
Where:
G is the gravitational constant (6.674 × 10^-11 N m^2 / kg^2),
M is the mass of the Earth (5.972 × 10^24 kg), and
π is a mathematical constant.
Substituting the values into the equation, we get:
R = [(6.674 × 10^-11 N m^2 / kg^2) * (5.972 × 10^24 kg) * (6 hours)^2 / (4 * π^2)]^(1/3)
Calculating this equation will provide the value of the orbit radius.
3. Speed:
The speed of the satellite (v) can be calculated using the formula:
v = 2 * π * R / T
Substituting the values of R and T into the equation will determine the speed.
4. Weight:
The weight of the satellite (W) can be calculated using the formula:
W = m * g
Where:
m is the mass of the satellite, and
g is the acceleration due to gravity on Earth (approximately 9.8 m/s^2).
As we are not provided with the mass of the satellite, it is not possible to calculate the weight without additional information.
By using the equations above with the given information, we can determine the orbit radius and speed of the satellite. However, calculating the weight would require the mass of the satellite.