Calculating the Period of an Earth Satellite

[Chica1975]

Homework Statement

What is the period of an Earth satellite orbiting at a height of 1.80 x 10^7m above the surface of the earth? Use G = 6.67 x 10^-11 N.m2 Kg-2

Homework Equations

T = SQRT 4*pi^2 * R^3/G*Mass of the earth

The Attempt at a Solution

I added the Earth mass and the height and got = 5.98 x 10^24
Then I plugged everything into the equation but cannot get the answer out. I am not so great on this scientific notation addition etc calculations on the calculator.

the answer is 10.5 but I can't get it out.

PLEASE HELP!

 

[joeghal87]

hello there,

please provide some details about your calculations and about the units of the answer.

It's 10.5 what ? (mention the units)

 

[Chica1975]

the units in the answer are hours - the answer was given by the lecturer.

I plugged in the formulae as per above and got

sqrt of 39.4784176 * 3.97471 * E33/ 1764366 =38.379 hours

 

[Borek]

above the surface of the earth

It means orbit radius is not 1.80x10⁷.

Edit: I see you posted in the meantime. Numbers you show don't make much sense, please elaborate what they are.

 

[Chica1975]

yes that is the height I multiplied the radius of the Earth and the height of satellite

 

[Chica1975]

I meant to say I added not multiplied

 

[Borek]

3.97471E33/ 1764366

Neither of these numbers is correct. I guess first one should be R³ and the other one GM.

 

[Chica1975]

It means orbit radius is not 1.80x10⁷.

Edit: I see you posted in the meantime. Numbers you show don't make much sense, please elaborate what they are.

I have basically looked at the formula and plugged in what it says. Radius is the radius of Earth (6.38 x 10^6) plus the height of satellite. Then the gravitational constant is given. and pi we know. and then mass of the Earth (5.98x 10^24)

 

[joeghal87]

Borek is right. Your calculations are actually very strange

As for the radius, it must be the sum of the radius of Earth + the height of the satellite

 

[joeghal87]

then there is no way you can get that crazy E33 number ! u'll get smth around E21

 

[Borek]

Chica - please explain how do you enter these numbers into your calculator. Key by key.

 

[Chica1975]

exactly - my calculator is driving me crazy - every time I use E anything it spits out something I cannot fathom I am so over it you have no idea I have doing this for 3 hours now.

 

[Chica1975]

I type it like this for eg the radius of the earth
(6.38 shift e (6)) + (1.80 shift e (7)) and press the equals sign

 

[Chica1975]

radius of the Earth + height of satellite is what I meant - am frazzled! :)

 

[Chica1975]

despite being told not to use the x10^X on my calculator - I tried it with that and I got it out. so much for my tutor being on the ball! Thanks everyone.

 

[Borek]

No idea what calculator you use, most of those I know don't require something like "shift e", they have just a separate key for exponents. For example EE on TI calculators, or EXP on old Casio.