Presentation Transcript

1. HSC Space: Section 3

2. Gravitational Field The gravitational field around a massive object is radial in shape, with the direction of the field being towards the massive body The strength of the gravitational field obeys an inverse square law i.e. the gravitational field strength decreases in proportion the the reciprocal of the square of the distance from the object’s centre of mass
3. Gravitational Field The gravitational field of the Earth is not uniform... … unless just a small region of the total field is considered uniform field The gravitational field of a massive body such as the Earth causes objects near the surface to undergo projectile motion, and more distant objects to undergo orbital motion
4. FactorsAffecting Fg The strength of the gravitational force between two masses is proportional to the mass of each object inversely proportional to the square of the distance between the centres of mass of the two objects The force is also dependent on the Universal Gravitational Constant - it is believed that this is a fixed quantity for our Universe
5. Newton’s Law of Universal Gravitation Every particle in the universe attracts every other particle in the universe with a force that is proportional to the product of the masses and inversely proportional to the square of the distance between the particles.
6. d m m M E Newton’s Law of Universal Gravitation Calculate the gravitational force between the Earth and the Moon. The mass of the Moon is 7.3483 x 1022 kg and the mass of the Earth is 5.98 x 1024 kg. The distance between the Earth and the Moon is 384,402 km. G = 6.67300 x 10-11 m3 kg-1 s-2
7. Newton’s Law of Universal Gravitation mEarth=5.97 x 1024 kg mSun=1.99 x 1030 kg distance from the Sun to the Earth = 150 million km What is the gravitational force between the Earth and the Sun?
8. Newton’s Law of Universal Gravitation What would be the gravitational force between you and and a 20 000 tonne ship 2 km away? m1 = 65 kg m2 = 20 000 000 kg distance between neighbours = 2000 m
9. Newton’s Law of Universal Gravitation Isaac Newton proposed the Law of Gravity – a universal force that governed both projectile motion on the Earth, the motion of the Moon around the Earth and the motion of the planets around the Sun Newton’s three laws of motion apply to planetary motion as they do to motion on the Earth’s surface Law of inertia F = ma Forces act in pairs
10. Newton’s Law of Universal Gravitation Before Newton, nobody understood what force kept the planets moving in their orbits. Newton realised that the same force of gravity governed the motion of projectiles on the Earth and the motion of planets around the Sun Gravitational forces act between all objects having mass The gravitational pull of the Sun provides the required centripetal force
11. The SlingShotEffect The slingshot effect is used to increase - or sometimes to decrease - the the speed, and to change the direction of motion of an interplanetary spacecraft. Three bodies must always be involved for the slingshot effect to operate. The satellites (usually a planet and an artificial one) must both be in orbit around a third central body. As a result of the slingshot effect, the satellite gains momentum relative to the central body. Successive positions of the Earth and a passing satellite interacting gravitationally. T1 shows the path of the satellite altered by the slingshot effect. T2 shows the path had there been no interaction.
12. The SlingShotEffect The momentum gained by the satellite is not transferred back to the planet after the satellite-planet interaction. Momentum is transferred between the two because of the gravitational interaction between them. To gain momentum the satellite must approach the planet so that it passes on the side of the planet away from the Sun.
13. The SlingShotEffect Interplanetary satellites use the slingshot effect to reach their destinations without requiring large amounts of fuel. Looping orbits take the satellite close to the planet from which momentum is transferred, increasing the velocity. The trade-off is a journey which takes a long time, since several orbits around the Sun may be necessary to achieve the final goal.
14. The SlingShotEffect The Cassini spacecraft was launched in 1997, flew twice by Venus, and then passed 1200 km from the Earth. On Dec. 30th 2000, it passed Jupiter, and finally arrived at Saturn in July 2004. Cassini, increased its speed by 5.5 kilometres per second as it passed Earth. And the total effect of the probe's four planetary flybys was 21.44 kilometres per second.
15. End of Section 3