Answer:
Eccentricity = 0.0557
Semi-major axis = 9,095 km
Angular momentum/mass = 60,116 [tex]\frac{km^{2} }{Sec}[/tex]
Kinetic energies/mass = 24,500 KJ
Potential energies/mass = 21,673 KJ
Explanation:
Eccentricity
To find the eccentricity use the following formula
Eccentricity = [ Altitude from the earth x ( [tex]Velocity^{2}[/tex] / Gravitational parameter for the Earth ) ] - 1
Where
Altitude from the earth radius = Radius of the earth + Altitude of the earth from radius = 6,378 km + 2,210 km = 8,588 km
Velocity = 7,000 m/s
Gravitational parameter for the Earth = 3.986004418 × [tex]10^{14}[/tex]
Eccentricity = ?
Placing values in the formula
Eccentricity = [ ( 8,588 km x 1000 ) x ( [tex]7000^{2}[/tex] / 3.986004418 × [tex]10^{14}[/tex] ) ] - 1
Eccentricity = 0.0557
Semi-major axis
Total Distance = Semi-major axis x ( 1 - Eccentricity )
Where
Total Distance = 8,588 km
Eccentricity = 0.0557
8,588 x 1,000 m = Semi-major axis x ( 1 - 0.0557 )
8,588,000 m = Semi-major axis x 0.9443
Semi-major axis = 8,588,000 m / 0.9443
Semi-major axis = 9,094,567.40 m
Semi-major axis = 9,094.56740 km
Semi-major axis = 9,095 km
Angular momentum/mass
L = MVR
L/M = VR
Where
V = Velocity = [tex]\frac{7,000 m/s}{1000}[/tex] = 7 km/s
R = Total Radius = Radius of Earth + Altitude = 6,378 km + 2,210 km = 8,588 km
Placing values in the formula
L/M = 7 km/s x 8,588 km = 60,116 [tex]\frac{km^{2} }{Sec}[/tex]
Kinetic energies/mass
Ke = I [tex]W^{2}[/tex]
Ke = [tex]\frac{1}{2} mr^{2}[/tex] [tex]W^{2}[/tex] ( Where I = [tex]mr^{2}[/tex] )
[tex]\frac{ke}{m}[/tex] = [tex]\frac{r^2}{2}[/tex] [tex]W^{2}[/tex]
[tex]\frac{ke}{m}[/tex] = [tex]\frac{r^2}{2}[/tex] [tex]\frac{V^2}{r^2}[/tex] ( [tex]W^{2}[/tex] = [tex]\frac{V^2}{r^2}[/tex] )
[tex]\frac{ke}{m}[/tex] = [tex]\frac{V^2}{2}[/tex]
[tex]\frac{ke}{m}[/tex] = [tex]\frac{7000^2}{2}[/tex]
[tex]\frac{ke}{m}[/tex] = 24,500,000 J
[tex]\frac{ke}{m}[/tex] = 24,500 KJ
Potential energies/mass
PE = mgh
[tex]\frac{PE}{m}[/tex] = gh
Where
g = 9.807 [tex]\frac{m}{s^2}[/tex]
h = 2,210 km x 1,000 = 2,210,000 m
Placing values in the formula
[tex]\frac{PE}{m}[/tex] = 9.807 [tex]\frac{m}{s^2}[/tex] x 2,210,000 m
[tex]\frac{PE}{m}[/tex] = 21,673,470 J
[tex]\frac{PE}{m}[/tex] = 21,673.470 KJ
[tex]\frac{PE}{m}[/tex] = 21,673 KJ
