How Is Gravitational Force Calculated for a Satellite Near Earth?

[pookisantoki]

1.Calculate the magnitude of the graviational force exerted on 442kg satellite that is a distance of 1.87 times Earth radii from the center of the earth
Mass=442kg

For this I used the Newton's law of universal graviation formula: F=(g*m1*m2)/r^2
((6.67*10^-11)(442)(5.98*10^24))/(Radius of the earth(6.38*10^3) * 1.87=11930.6)^2
=1238581865N

a.) What is the magnitude of the gravitational force exerted on the Earth by the satellite?
I would think it's the same answer as number 1.

b.) Determine the magnitude of the satellite's acceleration
1238581865=Mass*acceleration
123858186=442*a
a=280222.1403

c.)What is the magnitude of the Earth's acceleration
123858186=(5.98*10^24)*a
a=2.0712 *10^-17

but it's wrong what am I doing wrong?
Thank you~!

 

[Redbelly98]

...Radius of the earth(6.38*10^3)...

What are the units in that value?

 

[tomcue]

I would like to point out that your calculations are correct but your units are not consistent. The gravitational constant (g) is in units of m^3/kg*s^2, the mass of the Earth is in kg, and the radius of the Earth is in meters. Therefore, your final answer for the magnitude of the Earth's acceleration should be in units of m/s^2, not in units of 10^-17. This is likely why you are getting a different answer. Additionally, it is important to note that the magnitude of the gravitational force on the Earth by the satellite is the same as the magnitude of the gravitational force on the satellite by the Earth, so your answer for part a) is also correct.