Question

How much gravitational potential energy must a 3140-kg satellite acquire in order to attain a geosynchronous orbit?

The answer to the above question is 1.67x10^11 J.

How much kinetic energy must it gain? Note that because of the rotation of the Earth on its axis, the satellite had a velocity of 467 m/s relative to the center of the Earth just before launch.

Doing a 1/2mv^2 doesn't get the correct answer. The law of conservation of energy would state that KE = change in PE but KE = 1.67x10^11 J is not the correct answer either.

Answer #1

**time period of satellite**

**T = 24 hr = 24*60*60**

**T = 2*pi*r^(3/2)/sqrt(GM)**

**24*60*60 =
2*pi*r^(3/2)/sqrt(6.67*10^-11*5.98*10^24)**

**r = 4.22*10^7 m**

**In orbit Fg = Fc**

**GMm/r^2 = mv0^2/r**

**v0 = sqrt(GM/r)**

**KE due to orbital motion k2 = (1/2)*m*v0^2 =
(1/2)*m*GM/r**

**KE due to rotation of earth K1 = (1/2)*m*v^2**

**gain = k2 - k1**

**gain = (1/2)*m*GM/r - (1/2)*m*v^2**

**gain = (1/2)*m*( (GM/r) - v^2)**

**gain = (1/2)*3140*( (6.67*10^-11*5.98*10^24/(4.22*10^7))
- 467^2)**

**gain = 1.45*10^10 J**

Part A
How much gravitational potential energy must a 3200-kg satellite
acquire in order to attain a geosynchronous orbit?
Express your answer to three significant figures and include
appropriate units.
Answer : (Value) (Units)
Part B
How much kinetic energy must it gain? Note that because of the
rotation of the Earth on its axis, the satellite had a velocity of
469 m/s relative to the center of the Earth just before
launch.
Express your answer to three significant figures...

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 972-kg satellite orbits the Earth at a constant altitude of
99-km.
(a) How much energy must be added to the system to move the
satellite into a circular orbit with altitude 201 km?
____ MJ
(b) What is the change in the system's kinetic energy?
____MJ
(c) What is the change in the system's potential energy?
____ MJ
The answer is not 974.5 mi. Its marked wrong

A 969-kg satellite orbits the Earth at a constant altitude of
103-km.
(a) How much energy must be added to the system to move the
satellite into a circular orbit with altitude 208 km?
(b) What is the change in the system's kinetic energy?
(c) What is the change in the system's potential energy?

A 984-kg satellite orbits the Earth at a constant altitude of
110-km.
(a) How much energy must be added to the system to move the
satellite into a circular orbit with altitude 198 km? MJ
(b) What is the change in the system's kinetic energy? MJ
(c) What is the change in the system's potential energy? MJ

QUESTION 1
Part 1
Engineers wish to launch a satellite from the surface of the
Moon. What is the minimum speed the satellite must have to escape
the Moon’s gravity – that is, what is the escape velocity at the
surface of the Moon? The Moon has a mass of 7.3x10^22 kg and a
radius of 1.7x10^6 m.
a.
1700 m/s
b.
5.7x10^6 m/s
c.
It depends on the mass of the satellite.
d.
2400 m/s
Part 2
The satellite...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 12 minutes ago

asked 40 minutes ago

asked 56 minutes ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 3 hours ago

asked 4 hours ago

asked 4 hours ago

asked 4 hours ago