M5 Flashcards
Describe Newton’s thought experiment and how this contributed to the definition of a satellite
Newton proposed that the moon was falling to Earth without getting closer, through his thought experiment where he compared the motion of the Moon with a cannonball fired horizontally from the top of a mountain. If the cannonball was fired fast enough it could travel around the earth and reach the place where it was fired from, at this speed it would circle the earth. Hence Newton proposed the notion of an artificial satellite a hundred years before one was actually launched. Any object placed at the right altitude with enough speed would simply continue in its orbit.
What distinguishes a geostationary orbit? (A type of geosynchronous orbit)
They are satellites that are always located at a fixed point on the Earth’s equator. They do not orbit around Earth’s equator. They orbit for a period of 24 hours.
what is a geosynchronous orbit?
Satellites located in geosynchronous orbit move in time with the rotation of the earth
What are Kepler’s three laws?
- The planets move in elliptical orbits with the sun at one focus
- The line connecting a planet to the Sun sweeps out equal areas in equal intervals of time
- For every planet, the ratio of the cube of the average orbital radius to the square of the period (T) of revolution is the same, i.e. r^3/T^2 = k (where k is a constant)
Explain what is escape velocity and derive an expression for it
the minimum initial velocity required by a projectile to just escape the gravitational field of a planet such that the object is given an initial launch but has no further forces acting upon it.
Since an object that has escaped a gravitational field has a potential energy of U = 0, due to the conservation of mechanical energy the escape velocity occurs when the kinetic energy of the object is equal in magnitude to its gravitational potential energy.
In other words, when K = U.
1/2mv(escape)^2 = GMm/r
What is the design speed of a track? What happens when the car is faster than the design speed?
At the design speed of a track, a car can travel around a corner with no friction at all, this is the real advantage of banked tracks, there is a speed at which you can travel and not require friction. if the car is travelling faster than the design speed the car would travel higher up the slope as the greater speed means that a greater radius is required in the circular path. Above the design speed, the normal force is not enough to keep the car in a circle, hence it moves outwards from the centre.
If the v > design speed then friction acts
down the slope to keep the vehicle from skidding out
If v < design speed, then friction acts
up the slope to stop the vehicle from spiralling inwards
Explain in detail Newton’s thought experiment
Newton conducted a thought experiment regarding the consequences of launching a projectile with different horizontal velocities from a high tower. PATH A: If a projectile is launched with a low horizontal velocity, it will follow a parabolic path before hitting the ground. PATH B: if the projectile was fired faster, it would strike the ground at a point further away whilst still maintaining a parabolic path. PATH C: If the projectile was launched at an even faster horizontal velocity where the projectile falls due to gravity at the same rate the Earth’s surface curves away, it will undergo a circular orbit at a fixed altitude, known as orbital velocity. PATH D: At horizontal velocities faster than this, the orbit will be elliptical. PATH E: At horizontal velocities faster than this, the object will follow a parabolic path and escape the earth’s gravitational field entirely.
