Weight of a satellite

[mortho]

1. The problem statement, all variables and given/known data
A communications satellite with a mass of 240 kg is in a circular orbit about the Earth. The radius of the orbit is 41200 km as measured from the center of the Earth.
(a) Calculate the weight of the satellite on the surface of the Earth.
The final answer is in kN
2. Relevant equations
F=Gm1m2/r2


3. The attempt at a solution

So first i found out the gravitational force using the radius given and got 56.40 N and substituted tha for F and solved this time with the earth's radius. I got 5.74 N but was wrong.

[hotcommodity]

If you know the mass of the satellite, and you know the acceleration due to gravity at the Earth's surface, you don't need Newton's Universal Law of Gravitation to figure out its weight. With what equation would you calculate the weight of any object on Earth given some mass "m" ?

[mortho]

ok i think it's g=Gme\r2 so i subtracted the radius of the earth from the total distance and solved for m and got 5.12e18 kg . Correct?

[hotcommodity]

Are you not allowed to use the value of "g" in the cover of your textbook? You're solving for the weight of the satellite on Earth, correct? The mass is known, as is the value of "g". Do you follow?

[mortho]

oh..so i would do mg instead of g? and put in gravity but figure out the mass. But on the other side for mass, i use the mass of the satellite given right? and the earth also? so i solved and got 2.80e8 kg.

[hotcommodity]

The problem asks for the weight, call it "W". We know that the weight of an object on Earth is given by the product of its mass and the acceleration due to gravity at the surface of the Earth, W = mg. You were given the mass, and you know the value of g (9.81 m/s^2). Now just plug in values.

[mortho]

so what you're saying is (240)(9.81)=(6.67e-11)(m)\34830000squared ?? i solved and got 4.28e28 kg.

[hotcommodity]

You only need two values and one equation to solve this problem: 9.81 m/s^2, 240 kg, Weight of satellite = (mass)(acceleration due to gravity). Simply plug in the two values.

[mortho]

But isn't that f=ma which is force?

[hotcommodity]

Yes, it's a form of F = ma, where "m" is the mass, "a" would be the acceleration g, and the weight is the force.

[mortho]

so it's just 2354 kg?

[hotcommodity]

Yes, but it should be in units of Newtons, as weight is a force. Also, don't forget to place your answer into significant digits, using scientific notation. You only know the answer to 3 significant digits due to the accuracy of the mass.

[mortho]

Thanks! :)

[Steve0511]

You can use either F=ma or F= GmM/r^2. "a" is just the acceleration due to the gravitational force at the earth's surface. Thus "a" is GM/r^2 where G is the gravitiational constant, M is the mass of the earth, and r is the distance between the center of mass of the earth and the center of mass of the satellite. At the earth's surface, r is simply the earth's radius.