keplers third law states that the square of the period of any planets orbit is proportional...

keplers third law states that the square of the period of any planets orbit is proportional to the cube of the semimajor axis of the orbit. for the following, show all your work and dont skip steps

derive the exact expression relating the period (T) and the radius (r) for a planet in circular orbit by applying newtons second law for circular motion.

the orbital period of mars in its revolution around the sun is 1.88 years what average distance from the sun does the keplers thirdlaw predict for mars?

Expert Solution

genius_generous answered 5 months ago

Explain how Newton’s Law of Universal Gravitation can be used to explain how the planets orbit...

Explain how Newton’s Law of Universal Gravitation can be used to explain how the planets orbit the Sun (or satellites orbit the Earth) and use the law to derive Kepler’s third law for planets orbiting their sun in a circular orbit. For the 6 planets closest to the sun find, from the internet or elsewhere, the mean distance from the sun (in astronomical units) and their orbital period (in years). Use this information to plot, using a software package, an...

(a) A fundamental law of motion states that the acceleration of an object is directly proportional...

(a) A fundamental law of motion states that the acceleration of an object is directly proportional to the resultant force exerted on the object and inversely proportional to its mass. If the proportionality constant is defined to have no dimensions, determine the dimensions of force. (Use the following as necessary: M, L, and T.) (b) The newton is the SI unit of force. According to the results for (a), how can you express a force having units of newtons using...

Coulomb’s Law states that the force is directly proportional to the size of the charges and...

Coulomb’s Law states that the force is directly proportional to the size of the charges and inversely related to the distance between them. Considering the total charge for the nucleus and the total charge for the electrons, explain why the unexpected trend

Newton's law of cooling states that the temperature of an object changes at a rate proportional...

Newton's law of cooling states that the temperature of an object changes at a rate proportional to the difference between its temperature and that of its surroundings. Suppose that the temperature of a cup of coffee obeys Newton's law of cooling. If the coffee has a temperature of 205 degrees Fahrenheit when freshly poured, and 1 minutes later has cooled to 190 degrees in a room at 64 degrees, determine when the coffee reaches a temperature of 150 degrees. The...

Newton's Law of Cooling states that the rate at which and objects cools is directly proportional...

Newton's Law of Cooling states that the rate at which and objects cools is directly proportional to the difference in temperature between the object an the surrounding medium. if an object cools from 125F to 100F in half an hour when surrounded by air at a temperautre of 75F, find it's temperature at the end of the next half hour. (Hint: we wrote a differenial equation involving a proportional relationship before in lecture)

It seems the universe is full of angular momentum. Planets revolve and orbit stars, stars revolve...

It seems the universe is full of angular momentum. Planets revolve and orbit stars, stars revolve and orbit galactic centres even sub atomic particles spin. Yet the origin of the universe was the big bang where everything exploded outward froma point source. As I understand it there is a law of conservation of angular momentum saying it cannot be created or destroyed onlt transferred. So I am puzzled where did all the angular momentum come from?

Hooke's Law Objective: To verify Hooke’s law that the extension of a spring is proportional to...

Hooke's Law Objective: To verify Hooke’s law that the extension of a spring is proportional to the stretching force applied once the elastic limit is not exceeded. a) Mention at least three important precautions that you take while performing the experiment? b)Give one example where Hooke’s law can be applied. c) Draw the forces experienced by the mass spring system. d) Name the forces and state the law applicable here. e) If a mass of 250 grams is suspended, then find...

Two planets P1 and P2 orbit around a star S in circular orbits with speeds v1...

Two planets P1 and P2 orbit around a star S in circular orbits with speeds v1 = 42.6 km/s, and v2 = 56.0 km/s respectively. (a) If the period of the first planet P1 is 780 years what is the mass, in kg, of the star it orbits around? (b) Determine the orbital period, in years, of P2.

1. The time rate of change of a rabbit population P is proportional to the square...

1. The time rate of change of a rabbit population P is proportional to the square root of P. At time t = 0 (months) the population numbers 100 and after 8 months there are 196 rabbits. How many rabbits will be two years later (find P(t) for t = 24 months)?

The temperature T at a point (x,y,z) in space is inversely proportional to the square of...

The temperature T at a point (x,y,z) in space is inversely proportional to the square of the distance from (x,y,z) to the origin. It is known that T(0,0,1) = 500. a. [2] Compute T(2,0,0). b. [3] Find the rate of change of T at the point (2,3,3) in the direction of the point (3,1,1). c. [3] What is the maximal rate of change of T at the point (2,3,3)?

Question