![The Law of Universal Gravitation
● Determine the gravitational field strength at:
– a point 6000km above the Moon surface.
– a point 36000km above Earth
– a point 750000000km from the Sun's surface
– A point 750000000km from the Earth's surface
● Determine the point where Earth's gravitational field is balanced by:
[Quite Hard]
– The Sun
– The Moon
● Data:
M⊙=1.99 x1030kg M=5.97 x1024 kg M=7.35 x1022 kg
R⊙=6.96 x108m R=6.38 x106m R=1.74 x106m
Distance→⊙=150000000km Distance→=384500km](https://image.slidesharecdn.com/1-140909184824-phpapp01/85/1-4-1-gravity-again-8-320.jpg)
1.4.1 gravity again
- 1. Topic 9.2 1.4.1 – Gravity Again
- 2. Gravitational Field Lines • The gravitational field surrounding an object with mass can be represented by field lines (just like electric field lines around a negative charge) • The closer the field lines are together the stronger the field • The further away from the mass generating the field, the weaker the field gets • Around a single object, the lines are always perpendicular to the surface.
- 3. Gravitational Field Lines ● Gravitational Field lines around Earth are radial ● BUT close to the surface they appear to be uniform and parallel
- 4. The Law of Universal Gravitation ● The law of universal gravitation mathematically describes the force of attraction between two objects. ● In a system where there are more than 2 gravitational fields, the overall (net) effect is the vector sum of the individual forces. F=G M1m2 r2
- 5. The Law of Universal Gravitation ● The r in Newton's Law of universal gravitation refers to the centre of the point mass. ● In reality, the mass is usually a planet which has a real radius. ● The denominator is often replaced with (R0 + h) where h is the altitude. F=G M1m2 (R0+h)2
- 6. The Law of Universal Gravitation ● Determine the gravitational force felt by: – A 150kg satellite placed 6000km from the Moon. – A 25T space capsule 30000km from Earth – The Moon placed 385000km from Earth – The Earth placed 150000000km from the Sun – A 250kg satellite at an altitude of 400km above the Earth – A 250kg satellite at an altitude of 30000km above the Earth – A 250kg satellite at an altitude of 30000km above the Moon – A 250kg satellite at an altitude of 30000km above the Sun – Data: M⊙=1.99 x1030kg M=5.97 x1024 kg M=7.35 x1022 kg R⊙=6.96 x108m R=6.38 x106m R=1.74 x106m
- 7. Gravitational Field Strength ● The correct name for weight is “weight force due to gravity” ● Therefore – Weight force = Gravitational Force ● Given that the Earth has a radius of 6.38x106 m and g=9.81 Nkg-1 determine the mass of the Earth. FW=FG mg=G M1m2 (r )2 g= Fm =G M1 (r )2
- 8. The Law of Universal Gravitation ● Determine the gravitational field strength at: – a point 6000km above the Moon surface. – a point 36000km above Earth – a point 750000000km from the Sun's surface – A point 750000000km from the Earth's surface ● Determine the point where Earth's gravitational field is balanced by: [Quite Hard] – The Sun – The Moon ● Data: M⊙=1.99 x1030kg M=5.97 x1024 kg M=7.35 x1022 kg R⊙=6.96 x108m R=6.38 x106m R=1.74 x106m Distance→⊙=150000000km Distance→=384500km
- 9. Gravitational Potential Energy ● On Earth, we experience that whenever we place an object in a gravitational field, its gravitational potential energy is converted into other forms e.g. Kinetic – That is the object will always fall down towards the Earth! ● When an object is allowed to move under the influence of a gravitational force, its gravitational potential energy will decrease.
- 10. Gravitational Potential Energy ● We recall that work done by a force is given by Force x Displacement. ● In a uniform field, this force is the weight. FW=mg Δ EG=mg Δr g m Δr
- 11. Gravitational Potential Energy ● However, this formula gives the change in gravitational potential energy relative to some point. ● This is fine on Earth, but in space there is no reference point! – Which way is UP?
- 12. Gravitational Potential Energy ● Scientists have agreed that the edge of space has an absolute gravitational potential energy of 0J ● All other absolute gravitational energies are relative to this AND must be therefore be negative.
- 13. Gravitational Potential Energy ● Also, experience shows that work must be done to move objects against the field. ● If zero is the edge of the field, and work is added to move the object to the edge, then all other values must be negative
- 14. Gravitational Potential Energy ● In a radial field the same rules hold. EG=mg Δ r=−G M1m2 (r )2 ×r=−G ● Calculate the energy required to just move: – A 10T rocket from Earth to infinity. – A 750kg satellite from the Sun to infinity. M1m2 r M⊙=1.99 x1030kg M=5.97 x1024 kg M=7.35 x1022 kg R⊙=6.96 x108m R=6.38 x106m R=1.74 x106m
- 15. Gravitational Potential Energy ● Therefore in a radial field moving a body from point 1 to point 2... Δ EG=mg Δr=−(G M1 m2 (r2) −G M1m2 (r1) )=G M1m2×( 1 r1 − 1 r2 ) ● Calculate the energy required to move a rocket from the surface of the Earth to an orbit of altitude 36000km ● Calculate the energy required to move a satellite from an orbit of altitude 30000km to an orbit of altitude 400km above the Earth. M=5.97 x1024 kg R=6.38 x106m
- 16. Gravitational Potential ● Gravitational Potential is the energy required per unit mass to move an object from infinity to a point in a field. ● Like gravitational Field Strength, it is a property of the field. U= EG m −G M1 (r )
- 17. Gravitation Summary ● All masses cause a gravitational field around themselves. ● This attracts all other objects with mass towards them. – G is the Universal Gravitational Constant = 6.67x10-11 Nm2kg-2 U=−G M1 (r ) g=−G M1 (r 2) EG=−G M1m2 (r ) F=−G M1m2 (r2) Force and acceleration Potential Energy and Potential Properties of Objects in the Field Properties of the Field