MYTUTOR SUBJECT ANSWERS

408 views

A satellite is in a stationary orbit above a planet of mass 8.9 x 10^25 kg and period of rotation 1.2 x 10^5 s. Calculate the radius of the satellite's orbit from the centre of the planet.

A body in a stationary orbit will always remain above the same point on the planet as it orbits. For a body to be in such an orbit, it must rotate around the planet in the same direction as the spin of the planet, and its orbital period must be equal to the period of rotation of the planet. In this question we are aksed to calculate the orbital radius at which the satellite will complete one orbital cycle in precisely the time that it will take the planet to complete one full revolution.

The satellite, mass m, will be undergoing uniform circular motion around the centre of mass of the planet at some radius r. The centripetal force, FC, required to keep the satellite moving at a constant angular speed w (where w=2*pi/T; T is the orbital period of the satellite), will be given by

FC=m*r*w2.

But what gives rise to this centripetal force? Recall that centripetal force is not a force in itself, but rather the name for a force which always acts centrally (towards the same point) on a body undergoing circular motion. In this case, the central force is the gravitational pull of the planet on the satellitle, FG, such that FC=FG. By Newton's universal law of gravitation,

FG=(G*M*m)/r2,

where M is the mass of the planet, and G is the gravitational constant 6.67*10-11 m3kg-1s-2.

Equating the two forces together, we get that

m*r*w2 = (G*M*m)/r2.

We wish to find r, so rearranging to make r the subject and noticing that the mass of the satellite cancels out, we get that

r3 = (G*M)/w2.

We know that w=(2*pi)/T, and we also know that T must be equal to the period of rotation of the planet for a stationary orbit, which we are given. Making this substitution for w, and performing a little algebra,

r3 = (G*M*T2)/4*pi2.

If we substitute in the values of G, M and T, and take the cubed root to get r, we get that

r = 1.3*108 m.

Thus, for our satellite to be in a stationary orbit around this planet it must be 1.3*108 m away from the centre of the planet.

Dorian A. A Level Physics tutor, A Level Maths tutor, A Level Further...

1 year ago

Answered by Dorian, an A Level Physics tutor with MyTutor


Still stuck? Get one-to-one help from a personally interviewed subject specialist

70 SUBJECT SPECIALISTS

£20 /hr

Nathan S.

Degree: Physics (Masters) - Durham University

Subjects offered: Physics, Maths+ 1 more

Physics
Maths
Chemistry

“I am xurrently a Physics student at Durham University. I achieved A*A*A in Maths, Physics and Chemistry respectively in my A level exams and can employ the skills I used to achieve those, to tutor others to hopefully achieve the same ...”

MyTutor guarantee

£36 /hr

Jacan C.

Degree: Theoretical Physics (Masters) - York University

Subjects offered: Physics, Science+ 3 more

Physics
Science
Maths
Further Mathematics
Chemistry

“Hi, my name is Jacan. I am a Theoretical Physics third year at the University of York. I have had a real excitement for gaining an understanding in science at all levels through my education. This was, however, not always facilitated...”

£20 /hr

Jake A.

Degree: Engineering (Masters) - Warwick University

Subjects offered: Physics, Maths+ 2 more

Physics
Maths
Further Mathematics
Chemistry

“Who am I? Hey! I’m a personal tutor, general maths enthusiast and am presently studying Engineering at Warwick University. I currently tutor students for Maths / Physics A-level along with Maths, Physics and Chemistry GCSE. I have a g...”

About the author

Dorian A.

Currently unavailable: for new students

Degree: Theoretical Physics (Masters) - Durham University

Subjects offered: Physics, Maths+ 1 more

Physics
Maths
Further Mathematics

“About Me As a Theoretical Physics student at Durham University, I am more than aware of all of the confusing turns that science can take. I have areal passion for my subject, and hope to show my students howbeautiful science can be.  ...”

You may also like...

Posts by Dorian

A satellite is in a stationary orbit above a planet of mass 8.9 x 10^25 kg and period of rotation 1.2 x 10^5 s. Calculate the radius of the satellite's orbit from the centre of the planet.

Two lines have equations r = (1,4,1)+s(-1,2,2) and r = (2,8,2)+t(1,3,5). Show that these lines are skew.

Use De Moivre's Theorem to show that if z = cos(q)+isin(q), then (z^n)+(z^-n) = 2cos(nq) and (z^n)-(z^-n)=2isin(nq).

Other A Level Physics questions

A stationary observer Bob, observes Alice take 5 seconds to travel from point A to B at 0.95c. How much time does Alice measure the journey from A to B to take?

Describe one technique you could use to measure the threshold voltage for LEDs.

Explain the difference between forced vibration and resonance in an oscillating object.

What is Coulomb's law

View A Level Physics tutors

Cookies:

We use cookies to improve our service. By continuing to use this website, we'll assume that you're OK with this. Dismiss

mtw:mercury1:status:ok