MYTUTOR SUBJECT ANSWERS

516 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...

2 years ago

Answered by Dorian, an A Level Physics tutor with MyTutor


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

76 SUBJECT SPECIALISTS

Ethan R. A Level Maths tutor, GCSE Maths tutor
£20 /hr

Ethan R.

Degree: Maths and Physics (Masters) - Durham University

Subjects offered:Physics, Maths+ 1 more

Physics
Maths
Further Mathematics

“Hi, I'm Ethan. I like to take a friendly approach to tutoring and want to learn what works best for you. Maths can be easy, as long as you know how!”

£22 /hr

Dan B.

Degree: MPhys Physics (Masters) - Exeter University

Subjects offered:Physics, Maths

Physics
Maths

“Hi I'm Dan and I'm in the first year of a four-year MPhys Physics degree at the University of Exeter. I am very patient and will tailor the sessions' content and pace to suit your individual needs...”

£22 /hr

Chris P.

Degree: Mechanical Engineering (Masters) - Bristol University

Subjects offered:Physics, Maths+ 1 more

Physics
Maths
Further Mathematics

“Engineer from University of Bristol. Patient, understanding, knowledgeable, and ready to help you unlock your full potential and ace those exams.”

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

In still air an aircraft flies at 200 m/s . The aircraft is heading due north in still air when it flies into a steady wind of 50 m/s blowing from the west. Calculate the magnitude and direction of the resultant velocity?

What is damping in Simple Harmonic Motion?

How do I find the half-life of radioactive isotope?

What's the highest height a ball thrown straight up will reach?

View A Level Physics tutors

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

mtw:mercury1:status:ok