Gravity,Orbits & Escape VelocityWhy does everything fall down? Why do the planets go around the Sun? Can the Earth stop circling the Sun and go somewhere else and how? These are some questions that can be answered and explained by using Gravity, Orbits and Escape Velocity. Here we will see how drastically would the orbits/velocities change from different factors. I want to know what and how factors or determinants affect orbits of objects and why do orbits exist and what math/formulas are used to calculate them.
First off let us see:What are Gravity, Orbits and Escape Velocity?Gravity is the force in which a planet or another body pulls objects toward its center. The force of gravity is what keeps all of the planets in orbit around the sun, the gravity of earth is what keeps us on the ground and what makes everything fall, which follows Newton’s Law of Universal Gravitation.An orbit is a regular, repeating path that an object in space takes around another object, an example are the planets in our solar system and the moon with the Earth as seen in Figure 1, they follow a certain path when circling and are in an orbit due to the gravity of the planet/star.
Currently we are in an orbit as well due to the Earth. Figure 1.Escape velocity is when an object reaches the minimum speed that it needs to be traveling to break free of a planet’s or moon’s gravitational attraction or gravity fully and leave it without further propulsion or being pulled back in. Essentially, escape velocity is the speed at which the sum of an object’s kinetic energy and its gravitational potential energy is equal to zero. For example the escape velocity from Earth is about 11.186 km/s (40,270 km/h / 25,020 mph) at the surface.Gravity affects orbits, in order for an object to have an orbit there needs to be gravity because without gravity, an example to show what would happen would be an Earth-orbiting satellite would go off into space along a straight line and that would also apply to the planets around the Sun. An object in an orbit is called a satellite, the moon is a satellite since in orbits the earth and a satellite as in space satellite – which is a machine – can also be called as this satellite since it is an object in an orbit.
DefinitionsKinetic Energy: the energy an object has because of its motion.Gravitational Potential Energy (GPE): The amount of gravitational potential energy an object on Earth has depends on its: mass and height above the ground. The energy is stored as the result of the gravitational attraction of the Earth for the object. For example if Person A (90 lbs) is standing on top of a 30-story building and Person B (90 lbs) and Person C (115 lbs) are standing on top of a 15-story building, Person A will have more gravitational potential energy than Person B and C but Person C will also have more GPE than Person B. All conservative forces have potential energy associated with them. Gravitational potential energy is often given the symbol Ug.
It represents the potential an object has to do work as the result of being located at a certain position in a gravitational field.The gravitational field strength on earth is about 10N (Newtons) on every mass of 1kg. This means an object with a mass of 1kg would be drawn towards the centre of the Earth by a force of 10N.
Gravitational field strength is represented by the letter ‘g’. On larger planets, like Jupiter where the gravitational field strength is greater, the gravitational potential energy would also be greater. Gravitational field strength in different placesPlaceGravitational Field StrengthEarth10N/kgMoon1.6N/kgJupiter26N/kgThe equation for gravitational potential energy (GPE) or Ug which is the symbol mentioned in the above is: Ug(J) = m g h. Joules or J is the unit for GPE.To further expand, consider a mass (m) being lifted through a height (h) against the force of gravity. The object is lifted vertically by a pulley and rope, so the force due to lifting the mass and the force due to gravity, Fg , are parallel. If ‘g’ is the immensity of the gravitational acceleration, we can find the work done by the force on the weight by multiplying the immensity of the force of gravity, Fg , and by the vertical distance, h, it has moved through.
This assumes the gravitational acceleration is constant over the height. Gravitational acceleration (g) is an expression used in physics to indicate the intensity of a gravitational field. It is indicated in meters per second squared (m/s2 ). At the surface of the earth, 1 g is about 9.8 m/s2 .Here is an example: On Jupiter, a ball of mass 0.8kg is kicked straight up.
How much GPE does it have at its highest point, 5m off the ground?Ug= mgh = 0.8265= 104J?the GPE at the highest point is 104J.Gravitational constant or universal gravitational constant/Newton’s constant: The gravitational constant denoted by letter G, it is an empirical physical constant involved in the calculations of the gravitational force between two bodies used in Sir Isaac Newton’s law of universal gravitation. The measured value of G is approximately 6.673×10?11 N(m2/kg2).The formula of Newton’s law of universal gravitation is: FGravity=Gm1m2r2FGravity represents the force of gravity between two objectsG represents the gravitational constantm1 & m2 represent mass of the first and second objectr is the distance between the two objectsHere is an example of the formula above, find the force of gravitational attraction between the earth (m = 5.
98 x 1024 kg) and a 80-kg student if the student is standing at sea level, a distance of 6.38 x 106 m from earth’s center: FGravity=(6.673×10-11 N(m2/kg2)(5.98 x 1024kg)(80kg)(6.38106m)2=784.279N? the force of gravity between the student and the earth is 784.279N.
Here is a question to think about, it is one of the questions from the beginning, What would happen if Earth stopped orbiting the Sun? If Earth did stop orbiting the Sun we’d only have about 64 days before our world became inhospitable during its inexorable plunge into the Sun. This phenomenon is known as Earthfall. A brief explanation would be that on the first day of Earthfall, we’d begin our direct descent into the Sun, accelerating due to its gravity on the way and picking up quite a bit of heat due to the increasing intensity of sunlight which will eventually cause increases to Earth’s average temperature. About 41 days in, we will cross Venus’ orbit. Our waterways are now literally boiling since the average global temperature exceeds the boiling point of water and on the final day of Earthfall ends after only 13 hours thanks to the Sun’s immense gravity causing the tidal force to pull the planet into an ovoid shape, allowing magma to erupt through cracks in the Earth’s crust, Earth’s surface will soon be liquid hot magma. The Sun itself soon fills most of the sky. Earth passes the point of no-return, a line called the Roche radius which, having crossed it, sees the tidal forces overcome Earth’s own gravity, ripping the planet into chunks of melted rock and magma. Good news is Earthfall is unlikely to happen.
The planet’s orbit is really stable; not even a collision from an asteroid would stop Earth’s revolution dead or knock enough mass from the planet to bring about a full-stop. It would be relatively easier to increase our speed to an orbital escape velocity of 42.1 km/s and shoot off into space as a rogue planet. To further explain escape velocity, I will give an example with Earth. Earth’s orbital velocity is 30 km/s and that is the exact speed that it needs to counteract the force of gravity from the Sun, pulling it inwards. Theoretically if the Sun were to disappear, Earth would travel in a perfectly in a straight line at 30 km/s.
If the Earth’s orbital velocity sped up, then it would go into a higher and larger orbit to compensate and if the orbital velocity slowed down, then it will fall to a lower orbit. If the Earth stopped revolving around the Sun as in 0 km/s then Earthfall will occur. In order for the Earth to stop revolving around the Sun and go somewhere else, the Earth have to reach the escape velocity of 42.1 km/s, and that is to escape the gravity of the Sun and have no orbit. Once escape velocity is achieved, the Earth will move away from the Sun to infinity without extra force having its speed slowing down forever but never reaching zero, therefore without ever coming back.
This applies to everything that has orbits, but the escape velocities will differ between each mass.The formula to find/calculate escape velocity is: Vescape=2Gmr Vescape= escape velocity (m/s) – r = radius of planet of moonG is the Universal Constant ( 6.673×10?11 N(m2/kg2) )m = mass of planet and moonHere is an example for finding the escape velocity: The radius of Earth is 6.38×106 m, and the mass of the Earth is 5.98x1024kg. What is the escape velocity from Earth?Vescape=2Gmr = 2(6.673×10?11 N(m2/kg2))5.98x1024kg6.38×106 m= 11184 m/s or ? 11.2km/s? the escape velocity from Earth is 11184 m/s or ? 11.2km/sCitationshttps://www.nasa.gov/audience/forstudents/5-8/features/nasa-knows/what-is-orbit-58.htmlhttps://www.khanacademy.org/science/physicshttps://en.wikipedia.org/wiki/Escape_velocityhttp://www.qrg.northwestern.edu/projects/vss/docs/space-environment/2-whats-escape-velocity.htmlhttp://www.bbc.co.uk/schools/gcsebitesize/science/add_gateway_pre_2011/forces/themeridesrev1.shtmlhttp://www.bbc.co.uk/schools/gcsebitesize/science/add_ocr_gateway/forces/themeridesrev1.shtmlhttps://www.nasa.gov/audience/forstudents/k-4/stories/nasa-knows/what-is-a-satellite-k4.htmlhttps://www.khanacademy.org/science/physics/work-and-energy/work-and-energy-tutorial/a/what-is-gravitational-potential-energyhttp://whatis.techtarget.com/definition/gravitational-accelerationhttps://nerdist.com/spooky-science-what-happens-if-the-earth-stops-orbiting-the-sun/