An object of mass m is in a circular orbit another heavier object of mass M....

An object of mass m is in a circular orbit another heavier object of mass M. The radius of the orbit is R.
(a) Derive the speed of the orbiting object.
(b) Use this speed to derive the period of the circular orbit.
(c) Use your answer and the provided value to determine the period of Earth’s orbit around
the Sun based on our simplified circular motion model. Compare this to the actual value which you can look up.

Use the astronomical information below to solve the following problems. G = 6.67 x10-11 N m2/kg2
Mass of the Earth = 5.974 x1024 kg
Radius of the Earth = 6.3666x106 m
Mass of the Moon= 7.347x1022 kg Radius of the Moon = 1.737x106 m Earth - Moon distance = 3.816x108 m Mass of the Sun = 1.989x1030 kg Earth - Sun distance = 1.496x1011 m

Expert Solution

genius_generous answered 2 years ago

Problem 1. A particle is orbiting a star of mass M in a circular orbit. (a,...

Problem 1. A particle is orbiting a star of mass M in a circular orbit. (a, 2 POINTS) Find the equation that provides the orbital speed at a given distance r from the center of the star. (b, 1 POINT) From the result at (a), calculate at what distance rS the particle should be from the center of the star for its orbital speed to be equal to the speed of light, c (in this case, the particle would be...

A spaceship of mass ? is on a circular orbit around a planet of mass ?,...

A spaceship of mass ? is on a circular orbit around a planet of mass ?, and is moving with constant speed ?0. (a) What is the radius of the orbit of the spaceship? A sudden explosion tears the spaceship into two pieces of equal mass. Piece 1 leaves the explosion with speed 4?0/5 with its velocity is in the same direction of the velocity of the spaceship before the explosion. As ? ≪ ?, the gravitational attraction between the...

a) Consider an object of mass m=0.527kg rotates on circular path of radius r=1.82 m. Object...

a) Consider an object of mass m=0.527kg rotates on circular path of radius r=1.82 m. Object starts at rest and slowly increase its angular velocity at constant angular acceleration of 0.128 rad/s2. I. Find the angular velocity of the object after 35 seconds? II. Find the magnitude and direction of resultant linear acceleration after 35 seconds? III. Find the net force acting on the object after 35 seconds? b) Consider the same above object of mass m=0.527kg rotates around its...

Two stars of mass M?1 and M?2<M?1 are orbiting eachother in a circular orbit. The heavy...

Two stars of mass M?1 and M?2<M?1 are orbiting eachother in a circular orbit. The heavy star experiences a supernova explosion, losing most of its mass in a spherically symmetric outflow (i.e. without losing angular momentum) and leaving behind a small neutron star of mass M??NS. Show that if the mass lost is larger then half of the total mass of the system, the binary is disrupted.

A rocket with mass 5.00×103 kg is in a circular orbit of radius 7.30×106 m around...

A rocket with mass 5.00×103 kg is in a circular orbit of radius 7.30×106 m around the earth. The rocket's engines fire for a period of time to increase that radius to 8.70×106 m , with the orbit again circular. A)What is the change in the rocket's gravitational potential energy? Does the potential energy increase or decrease? B) How much work is done by the rocket engines in changing the orbital radius

A rocket with mass 4.00×103 kg is in a circular orbit of radius 7.40×106 m around...

A rocket with mass 4.00×103 kg is in a circular orbit of radius 7.40×106 m around the earth. The rocket's engines fire for a period of time to increase that radius to 8.90×106 m, with the orbit again circular. a) What is the change in the rocket's kinetic energy? Does the kinetic energy increase or decrease? b) What is the change in the rocket's gravitational potential energy? Does the potential energy increase or decrease? c) How much work is done...

A landing craft with mass 1.22×104 kg is in a circular orbit a distance 5.70×105 m...

A landing craft with mass 1.22×104 kg is in a circular orbit a distance 5.70×105 m above the surface of a planet. The period of the orbit is 5600 s . The astronauts in the lander measure the diameter of the planet to be 9.80×106 m . The lander sets down at the north pole of the planet. A. What is the weight w of an astronaut of mass 86.0 kg as he steps out onto the planet's surface?

A satellite has a mass of 6189 kg and is in a circular orbit 4.84 ×...

A satellite has a mass of 6189 kg and is in a circular orbit 4.84 × 105 m above the surface of a planet. The period of the orbit is 2.4 hours. The radius of the planet is 4.80 × 106 m. What would be the true weight of the satellite if it were at rest on the planet’s surface? W = ?

A satellite has a mass of 6255 kg and is in a circular orbit 4.30 ×...

A satellite has a mass of 6255 kg and is in a circular orbit 4.30 × 105 m above the surface of a planet. The period of the orbit is 2.2 hours. The radius of the planet is 4.49 × 106 m. What would be the true weight of the satellite if it were at rest on the planet’s surface?

An object of mass m1 approaches with velocity v1 another object of mass m2, which is...

An object of mass m1 approaches with velocity v1 another object of mass m2, which is at rest, next to a spring having force constant k. The spring is fixed to a wall and m2 can compress the spring. This is one-dim horizontal collision without friction. We consider two collision scenarios, one which is perfectly inelastic, and the other which is elastic. (a) In the first collision case the object m1 strikes m2 and sticks. Moving together, they compress the...

Question