Question

A satellite of mass m is in an elliptical orbit around the Earth, which has mass...

A satellite of mass m is in an elliptical orbit around the Earth, which has mass Me and radius Re. The orbit varies from closest approach of distance a at point A to maximum distance of b from the center of the Earth at point B. At point A, the speed of the satellite is v0. Assume that the gravitational potential energy Ug = 0 when masses are an infinite distance apart. Express your answers in terms of some or all the variables a, b, m, Me, Re, v0, and G.

Write the expression for the total mechanical energy of the satellite when it is at point A.

Write the expression for the speed of the satellite as it passes point B in its orbit.

As the satellite passes point A, a rocket engine on the satellite is fired so that its orbit is changed to a circular orbit of radius a about the center of the Earth. Write the expression for the speed of the satellite for this circular orbit.

Write the expression for the work done by the rocket engine to effect this change.

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Consider a satellite of mass m in a circular orbit of radius r around the Earth...
Consider a satellite of mass m in a circular orbit of radius r around the Earth of mass ME and radius RE. 1. What is the gravitational force (magnitude and direction) on the satellite from Earth? 2. If we define g(r) to be the force of gravity on a mass m at a radial distance r from the center of the Earth, divided by the mass m, then evaluate the ratio g(r)/g(RE)to see how g varies with radial distance. If...
A satellite of mass 1525 kg is in circular orbit around Earth. The radius of the...
A satellite of mass 1525 kg is in circular orbit around Earth. The radius of the orbit of the satellite is equal to 1.5 times the radius of Earth (RE = 6.378*106 m, ME = 5.98*1024 kg, G = 6.67*10-11 Nm2/kg2). (a) Find the orbital period of the satellite? (b) Find the orbital (tangential) velocity of the satellite.  (c) Find the total energy of the satellite?
A satellite of mass m = 2.00 ×103 kg is launched into a circular orbit of...
A satellite of mass m = 2.00 ×103 kg is launched into a circular orbit of orbital period T = 4.00 hours. Newton's gravitational constant is G = 6.67 ×10−11 N∙m2/kg2, and the mass and radius of the Earth are respectively M⨁ = 5.97 ×1024 kg and r⨁ = 6.37 ×106 m. Answer the following questions. What is the total mechanical energy (kinetic energy + potential energy) of the satellite in orbit? Take the gravitational potential energy of the satellite...
A satellite is in a circular orbit around the Earth at an altitude of 3.84  106 m....
A satellite is in a circular orbit around the Earth at an altitude of 3.84  106 m. (a) Find the period of the orbit. (Hint: Modify Kepler's third law so it is suitable for objects orbiting the Earth rather than the Sun. The radius of the Earth is 6.38  106 m, and the mass of the Earth is 5.98  1024 kg.) h (b) Find the speed of the satellite. km/s (c) Find the acceleration of the satellite. m/s2 toward the center of the...
A satellite is put into an elliptical orbit around the Earth. When the satellite is at...
A satellite is put into an elliptical orbit around the Earth. When the satellite is at its perigee, its nearest point to the Earth, its height above the ground is ℎp=241.0 km,hp=241.0 km, and it is moving with a speed of ?p=7.850 km/s.vp=7.850 km/s. The gravitational constant ?G equals 6.67×10−11 m3·kg−1·s−26.67×10−11 m3·kg−1·s−2 and the mass of Earth equals 5.972×1024 kg.5.972×1024 kg. When the satellite reaches its apogee, at its farthest point from the Earth, what is its height ℎaha above...
A satellite (mass m) is in circular orbit around Earth (mass M) with orbital period T....
A satellite (mass m) is in circular orbit around Earth (mass M) with orbital period T. What is the satellite’s distance r from the Earth’s center? Group of answer choices
A satellite is in a circular orbit around the Earth at an altitude of 3.32 106...
A satellite is in a circular orbit around the Earth at an altitude of 3.32 106 m. (a) Find the period of the orbit. (Hint: Modify Kepler's third law so it is suitable for objects orbiting the Earth rather than the Sun. The radius of the Earth is 6.38 106 m, and the mass of the Earth is 5.98 1024 kg.) h (b) Find the speed of the satellite. km/s (c) Find the acceleration of the satellite. m/s2 toward the...
A satellite in a circular orbit around the earth with a radius 1.019 times the mean...
A satellite in a circular orbit around the earth with a radius 1.019 times the mean radius of the earth is hit by an incoming meteorite. A large fragment (m = 69.0 kg) is ejected in the backwards direction so that it is stationary with respect to the earth and falls directly to the ground. Its speed just before it hits the ground is 367.0 m/s. a)Find the total work done by gravity on the satellite fragment. RE 6.37·103 km;...
A satellite is in a circular orbit around the Earth at an altitude of 1.66 106...
A satellite is in a circular orbit around the Earth at an altitude of 1.66 106 m. (a) Find the period of the orbit (in hrs). (Hint: Modify Kepler's third law: T2 = (4π2/GMS)r3 so it is suitable for objects orbiting the Earth rather than the Sun. The radius of the Earth is 6.38 106 m, and the mass of the Earth is 5.98 1024 kg.) (b) Find the speed of the satellite (in km/s). (c) Find the acceleration of...
A satellite is in a circular orbit around the EArth at a distance equal to twice...
A satellite is in a circular orbit around the EArth at a distance equal to twice the radius of the Earth RE, as measured from the center of the Earth, how does its speed v relate to the Earth's radius RE, and the magnitude g of the acceleration due to gravity on the Earth's surface? I know that I use the equation F = Gm * ME / 2R2. F = Gm * ME / 2R2, where F = ma...