What would be the orbital speed and period of a satellite in orbit 0.88 multiplied by 108 m above the Earth?
Orbital Speed___m/s
Period___s
Thanks!
start with Newtons law of gravity
F=GMem/(re+.88E8)^2
that has to equal centripetal force
GMe m /(re+.88E8)^2= m v^2/(re+.88E8)
solve for v
period? well 2PI(re+.88E8)/period= v
solve for period.
To find the orbital speed and period of a satellite, we can use the following formulas:
1. Orbital Speed (V):
The orbital speed of a satellite can be calculated using the following formula:
V = sqrt(G * M / r)
where:
- V is the orbital speed in meters per second (m/s).
- 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).
- r is the distance between the center of the Earth and the satellite in meters (m).
2. Period (T):
The period of a satellite is the time taken for one complete orbit around the Earth. It can be calculated using the formula:
T = 2 * π * sqrt(r^3 / (G * M))
where:
- T is the period of the satellite in seconds (s).
- π is a mathematical constant (approximately 3.14159).
- 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).
- r is the distance between the center of the Earth and the satellite in meters (m).
Now, let's calculate the orbital speed and period for a satellite 0.88 * 10^8 m above the Earth:
Given:
r = 0.88 * 10^8 m
1. Orbital Speed (V):
Substituting the given values into the formula, we get:
V = sqrt(G * M / r)
V = sqrt((6.67430 * 10^-11 m^3 kg^-1 s^-2) * (5.972 × 10^24 kg) / (0.88 * 10^8 m))
Calculating this expression will give us the value for the orbital speed in m/s.
2. Period (T):
Substituting the given values into the formula, we get:
T = 2 * π * sqrt(r^3 / (G * M))
T = 2 * π * sqrt((0.88 * 10^8 m)^3 / ((6.67430 * 10^-11 m^3 kg^-1 s^-2) * (5.972 × 10^24 kg)))
Calculating this expression will give us the value for the period in seconds (s).
By substituting the given values into the formulas and performing the necessary calculations, you will find the exact values for the orbital speed and period of the satellite.