Calculating Satellite Orbit Period: A Misstep

[Punchlinegirl]

Consider a satellite, mass=85 kg, in a circular orbit about Earth. Calculate the period of the satellite given a radius r of its orbit of 2.04 x 10^7 m.

I used T^2= (4pi^2/ GM)r^3
Plugging in G= 6.67 x 10^-11
M= 85 kg
r= 2.04 x 10^7 and solving for T gave 7.69 x 10^15 s.
This wasn't right...

 

[whozum]

Pretty sure you use the mass of the earth, not the satelite, since it is what's providing the centripetal acceleration.

http://www.glenbrook.k12.il.us/gbssci/phys/Class/circles/u6l4c.html for more info.

 

[thepatientmental]

It seems like there may have been a mistake in the calculation. The formula used, T^2= (4pi^2/ GM)r^3, is the correct formula for calculating the orbital period of a satellite. However, the values used for the variables may not have been accurate.

Firstly, the mass of the satellite is given as 85 kg, which is an extremely low mass for a satellite. Most satellites have masses in the range of hundreds to thousands of kilograms. It is possible that this is a typo and the correct mass should have been given as 85,000 kg.

Secondly, the value of G used in the calculation is incorrect. The correct value for the gravitational constant is 6.67 x 10^-11 Nm^2/kg^2, not 6.67 x 10^-11 alone. This could have been a simple error in inputting the value into the calculator.

Lastly, it is important to note that the units used for the radius must be consistent with the units for G. In this case, the radius is given in meters, so the value of G should also be in meters. This could also have contributed to the incorrect result.

In order to accurately calculate the orbital period, it is important to double check all values and units before plugging them into the formula. It may also be helpful to use scientific notation to avoid any potential errors in calculation.