# P5a(i) Satellites, Gravity and Circular Motion

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P5a(i) Satellites, Gravity and Circular Motion
P5a(i) Satellites, Gravity and Circular Motion You will find out about Natural and Artificial Satellites Gravity as a force of attraction The velocities of comets How a planet’s orbital velocity changes

Gravity www.PhysicsGCSE.co.uk
This apple falls towards Earth’s centre of mass. It is attracted to Earth. The Earth is also attracted to the apple. But the Earth has a much higher mass. So the apple moves towards it. This force of attraction is called gravity. The Moon and a satellite are kept in orbit due to gravity. This is going to sound strange. Every object in the Universe attracts every other object. That means you are right now being attracted to every single star, planet, black hole and everything else. It means that over 7 billion humans on Earth are all attracted to one another, gravitationally speaking. So why can’t we feel it? Well, the effects are only felt on truly astronomical scales. Mass plays an important role. The bigger the mass the stronger the effect of gravity. As humans we simply do not contain enough mass.

Satellites www.PhysicsGCSE.co.uk
A satellite stays in orbit around the Earth due to gravity. Since 1957 thousands of satellites have been sent into Earth’s orbit. These type are called artificial satellites. The picture shows some satellites closer to the Earth than others. IMPORTANT: The closer satellites orbit the Earth faster than the satellites further away. Satellites In 1957 the first satellite was sent into space to orbit Earth. It was called Sputnik I and was sent by the Soviet Union. It took just 98 minutes to complete one orbit. The Moon also orbits the Earth like a satellite. The Moon is an example of a natural satellite. GEO (Earth) STATIONARY (not moving) A geostationary satellite orbits above the Earth’s equator. It takes exactly 24 hours to orbit the Earth. Its ORBITAL PERIOD is therefore 24 hours. One axial spin (rotation) of the Earth is also 24 hours. This means that the satellite stays over the same point of Earth the whole time. This is useful for communication as a direct link is always available. Orbital periods are not all the same. The higher the satellite the longer the orbital period. For exactly 24 hours the satellite needs to be 36,000km above the Earth’s equator. If it was closer it would orbit too fast. The geostationary satellite stays above the same point as Earth rotates

Gravitational Force www.PhysicsGCSE.co.uk A B B A 1 2 3
These masses are gravitationally attracted to one another. Mass B is larger so it exerts a larger gravitational pull. A B If the masses are separated by a larger distance then the force of gravity is less. B A When the planet is 3 times further away then the gravitational attraction is 1 3² as strong. So 3x further = 1/9 attraction 1 2 3 The further a planet is the weaker the gravitational attraction. This can be expressed as a 𝟏 𝒅² relationship. When the planet is 2 times further away then the gravitational attraction is 1 2² as strong. So 2x further = ¼ attraction

Orbital periods www.PhysicsGCSE.co.uk
Recall that to maintain a circular path there must be a centripetal force acting towards the centre of mass IMPORTANT: Planets closer to the Sun have less distance to travel. The attractive force of gravity is stronger so they have a faster orbital period. Artificial satellites in low orbits also have short orbital periods. Gravity causes the satellite to accelerate towards it. BUT it moves at a tangent and due to earth being curved it maintains a near-circular orbit. Comets have very elongated elliptical orbits. This means its speed changes considerably. When the comet is closer to the Sun, gravitational force is stronger so the comet orbits much faster. When the comet is furthest away the gravitational force is much weaker so the comet orbits much slower. Planets have near-circular orbits because their distance form the Sun is almost constant all the way round. CLOSE = FAST FAR = SLOW

Planetary Orbital Speed Calculation
Planetary Orbital Speed Calculation It is possible to calculate the orbital speed of any object that has a circular or near-circular orbit. The distance between Mercury and the Sun is 58 million km. This is the RADIUS Mercury’s orbital period is 0.24 Earth years. Sun Careful with capitals: D = Diameter d = distance Mercury The distance that Mercury travels is a circular path. So we need to use π x Diameter to work that out. Distance = π x Diameter The distance between Mercury and the Sun is the RADIUS. So we need to DOUBLE that to get the DIAMETER. To calculate speed we use: Speed = 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑡𝑖𝑚𝑒 Speed = π𝑥 2𝑥58𝑚𝑖𝑙𝑙𝑖𝑜𝑛𝑘𝑚 0.24𝑥(365𝑥24𝑥60𝑥60) The time is measured in Earth years. So all we need to do is work out how many seconds there are in one Earth year and multiply by how many Earth years it takes Mercury to orbit the Sun. 2 x radius to get diameter That’s REALLY fast!! = km/s Number of Earth years Mercury’s orbital period is Number of seconds in one EARTH year

Questions The Moon is kept in orbit around the Earth by a force. In which direction is this force? Name a similarity and a difference between natural and artificial satellites. A geostationary satellite is 36,000km above the Earth’s surface. If the radius of Earth is 6,400km how far does the geostationary satellite travel in one day? Compare the orbital period of Mercury to Earth. Mars has two moons – Phobos and Deimos. Which force keeps them in orbit around Mars? Earth is 58 million km from the Sun. It takes one year to orbit the Sun. Calculate Earth’s orbital speed. Why is Earth’s orbital speed almost constant? Why are comets not?

Questions www.PhysicsGCSE.co.uk
The Moon is kept in orbit around the Earth by a force. In which direction is this force? Towards the mass Name a similarity and a difference between natural and artificial satellites. Similarity – both orbit the Earth or both are kept in orbit by Earth’s gravitational force. Difference – artificial is man-made whereas natural is not or artificial satellites are used for communication and receive and send information. A geostationary satellite is 36,000km above the Earth’s surface. If the radius of Earth is 6,400km how far does the geostationary satellite travel in one day? Distance = circumference of a circle = π x D = π x 2x(36,000km + 6,400km) = 266,407km or 2.7Mm Compare the orbital period of Mercury to Earth. Mercury’s orbital period is much faster due to the orbital distance being much smaller ad the gravitational force of the Sun being stronger. Mars has two moons – Phobos and Deimos. Which force keeps them in orbit around Mars? Centripetal force Earth is 150 million km from the Sun. It takes one year to orbit the Sun. Calculate Earth’s orbital speed Speed = 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑡𝑖𝑚𝑒 = π 𝑥 𝐷 𝑡𝑖𝑚𝑒 𝑖𝑛 𝑠𝑒𝑐𝑜𝑛𝑑𝑠 = π𝑥 2𝑥150𝑚𝑖𝑙𝑙𝑖𝑜𝑛𝑘𝑚 1𝑥365𝑥24𝑥60𝑥60 = 29.9km/s Why is Earth’s orbital speed almost constant? Why are comets not? Earth’s orbit is near-circular so the distance between Earth and Sun is almost constant. A comet’s orbit is elliptical so its distance varies which means that when it is close to the Sun it travels much faster and when it is far from the Sun it travels relatively slower..