Newton's Law of Universal Gravitation
- F = G ( Mm / r^2 )
- F is proportional to 1 / r^2
- By Newton's Second Law,
Fg = Fc
Formulas One System
- T = 2π ( √ ( r^3 / GM ) )
- V = 2πr / T
- V = √ ( GM / R )
- 2πr / T = √ ( GM / R )
- V is proportional to 1 / √ r
- ( V2 / V1) = √( R1 / R2)
Binary System
- Fx = G ( MxMy) / ( Rxy)^2
- Net Moment = 0
- G (Mm) / r^2 = m(r/2)ω^2
Geostationary Satellites Period
- 24 hours
- Same direction of rotation as Earth
- Same plane as Equator
Advantages
- Require no tracking as they are stationary
- Able to view the whole Earth due to high altitude
Disadvantages - Spatial Resolution not that good
- Limited view, unable to see the poles
Gravitational Field Strength
- Defined as gravitational field force per unit mass acting on a small mass placed on the point
- g = Fg / m
- g = GM / r^2
Variation of field strength with respect to distance
- g is proportional to 1/ r^2 when R >= Rearth
- g is proportional to r when R < Rearth
Reasons for Variation of G
- Earth is not a perfect sphere
- Density of Earth is not constant
- Earth is rotating about its own axis
Weightlessness True weightlessness
- No net gravitational force acting upon it
False weightlessness
- Object exerts no contact force on its support
- F = G ( Mm / r^2 )
- F is proportional to 1 / r^2
- By Newton's Second Law,
Fg = Fc
Formulas
One System
- T = 2π ( √ ( r^3 / GM ) )
- V = 2πr / T
- V = √ ( GM / R )
- 2πr / T = √ ( GM / R )
- V is proportional to 1 / √ r
- ( V2 / V1) = √( R1 / R2)
Binary System
- Fx = G ( MxMy) / ( Rxy)^2
- Net Moment = 0
- G (Mm) / r^2 = m(r/2)ω^2
Geostationary Satellites
Period
- 24 hours
- Same direction of rotation as Earth
- Same plane as Equator
Advantages
- Require no tracking as they are stationary
- Able to view the whole Earth due to high altitude
Disadvantages
- Spatial Resolution not that good
- Limited view, unable to see the poles
Gravitational Field Strength
- Defined as gravitational field force per unit mass acting on a small mass placed on the point
- g = Fg / m
- g = GM / r^2
Variation of field strength with respect to distance
- g is proportional to 1/ r^2 when R >= Rearth
- g is proportional to r when R < Rearth
Reasons for Variation of G
- Earth is not a perfect sphere
- Density of Earth is not constant
- Earth is rotating about its own axis
Weightlessness
True weightlessness
- No net gravitational force acting upon it
False weightlessness
- Object exerts no contact force on its support