Question

In: Physics

A 778 kg satellite is in a circular orbit about the Earth at a height above...

A 778 kg satellite is in a circular orbit about the Earth at a height above the Earth equal to the Earth's mean radius.

(a) Find the satellite's orbital speed.

(b) Find the period of its revolution.

(c) Find the gravitational force acting on it.

Solutions

Expert Solution

The mass of the satellite is given as 778kg.

Required constants:

1. Earth mass, M =5.972e24 kg

2. Earth radius, R = 6.371e6 m

3. Gravitational constant, G = 6.674e-11 Nm2kg-2

a) Orbital speed, v is given by the equation

=

= 7.909e3 ms-1

Satellite's orbital speed = 7.909e3 ms-1

b) To find the period of revolution, we use the equation for speed = distance/ time

Here the speed --> orbital speed,v

distance --> 2R, since the satellite is travelling in a circular path around the Earth

time --> T, period of revolution, which we have to calculate

So v = 2R/T

==> T = 2R / v = 2 * 3.14 * 6.371e6 / 7.909e3 = 5058.78 s 1.405 hrs (1 hr = 3600s)

Period of revolution = 5058.78 s or 1.405 hrs

c) The gravitational force equation is

Fgrav = GMm/R2

= 6.674e-11 * 5.972e24 * 778 / (6.371e6)

= 7,639.6 N

Alternatively, the centripetal force equation, mv2/R can also be used since the centripetal force is balanced by the gravitational force acting on the satellite. The final answer will differ by a small unit. However I suggest you use the gravitational force equation.

Gravitational force = 7,639.6 N


Related Solutions

A 590-kg satellite is in a circular orbit about Earth at a height above Earth equal...
A 590-kg satellite is in a circular orbit about Earth at a height above Earth equal to Earth's mean radius. (a) Find the satellite's orbital speed. m/s (b) Find the period of its revolution. h (c) Find the gravitational force acting on it. N
A satellite of mass 1,500 kg is placed in a circular Earth orbit at a height,...
A satellite of mass 1,500 kg is placed in a circular Earth orbit at a height, h, above the surface. It is launched from Treasure Island in the SF Bay at 37 degrees latitude (north of the equator). 2465.98 10 , 6.37 10EarthEarthMxkgRx==ma) Derive Kepler’s Thrid Law from Newton’s Universal Law of gravity. b) If the orbital period of the satellite is 12 hrs, find the distance h above the Earth. c) What is the minimum energy required to put...
A satellite moves in orbit about the Earth at a height of 9500 km above Earth's...
A satellite moves in orbit about the Earth at a height of 9500 km above Earth's surface. Find a) the velocity of the satellite; b) it's period of rotation; c) the magnitude of the Earth's gravitational force on the satellite if it's mass is 2500 kg; d) if the satellite's velocity is increased by 20% at what height must it now orbit the Earth? Explain D step by step please.
A satellite is in a circular orbit about the earth (ME = 5.98 X10^24 kg). The...
A satellite is in a circular orbit about the earth (ME = 5.98 X10^24 kg). The period of the satellite is 1.40X10^4 s. What is the speed at which the satellite travels?
A satellite of mass 220 kg is placed into Earth orbit at a height of 150...
A satellite of mass 220 kg is placed into Earth orbit at a height of 150 km above the surface. (a) Assuming a circular orbit, how long does the satellite take to complete one orbit? h (b) What is the satellite's speed? m/s (c) Starting from the satellite on the Earth's surface, what is the minimum energy input necessary to place this satellite in orbit? Ignore air resistance but include the effect of the planet's daily rotation. J
A satellite of mass 180 kg is placed into Earth orbit at a height of 850...
A satellite of mass 180 kg is placed into Earth orbit at a height of 850 km above the surface. (a) Assuming a circular orbit, how long does the satellite take to complete one orbit? ans)_____h (b) What is the satellite's speed? 7558.5 Correct: Your answer is correct. m/s (c) Starting from the satellite on the Earth's surface, what is the minimum energy input necessary to place this satellite in orbit? Ignore air resistance but include the effect of the...
A 425 kg satellite is in a circular orbit at an altitude of 400 km above...
A 425 kg satellite is in a circular orbit at an altitude of 400 km above the Earth's surface. Because of air friction, the satellite eventually falls to the Earth's surface, where it hits the ground with a speed of 2.00 km/s. How much energy was transformed to internal energy by means of friction? J
An Earth satellite moves in a circular orbit 924 km above Earth's surface with a period...
An Earth satellite moves in a circular orbit 924 km above Earth's surface with a period of 103.3 min. What are (a) the speed and (b) the magnitude of the centripetal acceleration of the satellite?
(a) A 374 kg satellite orbits the Earth at a height of 3197 km above the...
(a) A 374 kg satellite orbits the Earth at a height of 3197 km above the Earth's surface. Assume the Earth has a mass of 5.98 x 1024 kg and a radius of 6,380 km. Find the velocity (in m/s) of the satellite in its orbit. (b) Calculate the period of the satellite's orbit when it orbits the Earth at a height of 3197 km above the Earth's surface. State your answer in minutes.
Consider a satellite of mass ms in circular orbit around Earth, a distance h above Earth's...
Consider a satellite of mass ms in circular orbit around Earth, a distance h above Earth's surface. Assume the Earth is a sphere with radius Re and mass Me. (a) As the satellite travels in circular orbit, will its speed increase, decrease, or remain constant? Explain. (b) The only force acting on the satellite is gravity, so the satellite is in freefall. Why doesn't the satellite get closer to Earth's surface? (c) Determine the ratio of the force of gravity...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT