When we think of gravitation most people think immediately of Isaac Newton's understanding Gravitation,
which he developed in the late 17th century.
This is often referred to as the force at a distance and one of the non-contact forces.
However, it was Albert Einstein who gave us a fuller a picture of gravitation,
not as a force but as a distortion of space-time and comes out of his General Theory of Relativity.
which he developed in the late 17th century.
This is often referred to as the force at a distance and one of the non-contact forces.
However, it was Albert Einstein who gave us a fuller a picture of gravitation,
not as a force but as a distortion of space-time and comes out of his General Theory of Relativity.
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Nonetheless, Newton's understanding of gravitation is an appropriate model, relevant to most situations : it's still is good enough to get us to the moon and back These series of lessons will cover of the classical understanding of gravitation, and its consequences, as developed by Isaac Newton |
1. Understanding Law of Gravity
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This video covers the Law of Gravitation, as Newton understood it. Check out also the sample problem and the interactive from pHET is useful to help consolidate your understanding. |
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It is always helpful to attempt the problem first before looking at the sample solution
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- The radius of the earth is about 6400 km. What would be the earths gravitational attraction on a 75 kg astronaut in an orbit of 6400 km above the earth surface? (183.75N)
- The mass of Mars is about 6.6×10^23 kg, and the acceleration due to gravity is 3.7 m/s/s. What is the radius of Mars?(3450km)
- Two objects with the same mass are placed 60 cm apart. If the gravitational force between the objects is 7×10^-9 N, what is the mass of each object? (6.15 kg)
- Add what altitude above earths surface of the acceleration due to gravity before .9 m/s per second? (2670km)
- A sphere of mass 85 kg is 12 m from a second sphere of mass 65 kg. What is the gravitational force of the attraction between then? (1.01 x 10^-8 N)
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This great pHET interactive allows to explore the Law of Gravitation
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Gravity Variation
The value of acceleration due to gravity at the surface of the Earth varies from the usually accepted value of 9.81 m/s/s, due to a number of factors:
As a result of the above, the value of g at the surface of the Earth varies between 9.782 m/s/s at the equator and 9.832 m/s/s at the poles.
The value of acceleration due to gravity at the surface of the Earth varies from the usually accepted value of 9.81 m/s/s, due to a number of factors:
- The Earth’s lithosphere varies in structure, thickness and density. Thickness variations are a product of the source and history of the material. Oceanic crust is thinner than continental crust. Continental crust is thickest under mountain ranges. Density variations occur due to the presence of concentrated and large mineral deposits or petroleum gas and related liquids trapped in sedimentary rocks and structures. All of these variations can influence local values of g.
- The Earth’s globe is flattened at the poles. This means that the distance of the surface from the centre of the Earth is less at the poles, which increases the local value of g.
- The spinning Earth also affects the value of g. At the equator, the spin effect is greatest resulting in a lowering of the value of g. As you travel from the equator to the poles, the spin effect on g shrinks to zero.
As a result of the above, the value of g at the surface of the Earth varies between 9.782 m/s/s at the equator and 9.832 m/s/s at the poles.
2. Gravity and Orbital Velocity
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If the satellite is in orbit around a larger object it generally follows either an elliptical path or a circular path. This could be a case of an artificial satellite around the planet, or a plant around a star.
The reason it stays in orbit is simply because the gravitational force holds it there, and this gravitational force ends up being the centripetal force. As a result, we are able to establish mathematical relationships between how fast the satellite is going and how high the satellite is, as well as the mass of the central object. This video examines the physics principles for circular orbits. |
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It is always helpful to attempt the problem first before looking at the sample solution
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- A satellite is in orbit at an altitude of 500 km. What is the velocity of this satellite? (7.63 km/s)
- The moon is 384,000 km away from the earth, Measure from their respective centres. How fast is a travelling? (1.02 km/s)
- The sun is part of the Milky Way Galaxy and rotates about the centre of this galaxy. The sun is radius of rotation is about 2.7×10^20 m and its period is about 6.3 x 10^15 seconds. If our son has a mass of approximately 2 x 10^30 kg, calculate the number of similar suns or stars that make the mass of the Milky Way [we assume most of the galaxy's mass is located centrally] (number of 'suns' = 1.47 x 10^11)
- NROL – 76 is a military satellite launched in 2017, that has one of the lowest orbits. If its period is 90.5 minutes determine its altitude? (317.4 km)
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Use this interactive to explore how gravity affect orbital motion
3. Understanding Gravitational Potential energy
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Gravitational potential energy, or simply Gravitational energy is due to the work done by a gravitation field. This video discusses this concept, allowing for change in gravitational fields and shows, in a simple way how the formula is determined. All this in the context of a teddy bear |
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A brief review of gravitational potential energy, useful for review
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- And Earth satellite has a mass of 100 kg and is at an altitude of 2000 km. What is its gravitational energy? (-20.01 GJ)
- The gravitational energy of a Russian Mars orbiter is 4.1 x 10^12 J. It orbits Mars at a distance of 4.8×10^3 km from the centre. What is the mass of the orbiter? (462 kg)
4. What are Kepler's Three Laws?
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Between 1609 and 1619, Johannes Kepler published his planetary laws of motion. He did this based on the data he received from his mentor, Tycho Brahe. As he studied the data he discovered that the planets revolved around the sun, not in circular orbits as many believed, but in elliptical orbits. He also noted that the speed at which the planets moved varied depending on the distance away from the sun. This video discusses his three laws and also examines Isaac Newton's analysis which validated Kepler's work.
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A brief summary of Keplers Laws , useful for review
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It is always helpful to attempt the problem first before looking at the sample solution
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Use the sliders to adjust the initial speed of the planet, the initial distance from the center of the planet to the center of the sun, and the mass of the sun. Hit run to see the orbit animate. The orbit will be with elliptical, circular, parabolic, or hyperbolic, depending on the initial conditions. Show the Kepler's 2nd Law of planetary motion trace to see the elliptical orbit broken into eight wedges of equal area, each swept out in equal times. By Tom Walsh
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- A satellite is placed in a circular orbit of 1.0×10^7 m radius with a period of 9900 seconds. Calculate the mass of the earth. (6.04 x 10^24 kg)
5. Examine satellite motion in terms of their energy
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A satellite in orbit is in motion. This means it has both gravitational potential energy (U) and kinetic energy (K). So how are they related? IF an object increases its gravitational energy , does that mean it will lose kinetic energy? Well that depends - is it in a new orbit, is their work done on it? This video explores the key concepts. |
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It is always helpful to attempt the problem first before looking at the sample solution
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Coming Soon
6. Examining physics of satellites using ©Spacebook
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©Spacebook is a great online tool that examines real satellites in earth's orbit. This video explains how you can use it to get a better understating of the physics involved
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7. The physics of rocket launching
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Using a Saturn V rocket and simulation data online, I examine the physics of launching, specifically acceleration, force and momentum |
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