# Astronaut releasing apple - Find acceleration

1. Aug 5, 2009

### dance_sg

1. The problem statement, all variables and given/known data
In a space shuttle orbiting 6.40 x 103 km above the surface of Earth, an astronaut releases
a 325 g apple. If the radius of Earth is 6.40 x 103 km, what is the acceleration of the apple?

A. 2.45 m/s2
B. 4.90 m/s2
C. 9.80 m/s2
D. 19.6 m/s2

2. Relevant equations

g=GM/r^2

3. The attempt at a solution
i converted grams to kg whihc gave me 0.325kg. then i multiplied that number by the universal gravitational constant. then i divided that number by two times the radius. what am i doing wrong?

2. Aug 5, 2009

### kuruman

Re: gravitation/acceleration

What did you use for the radius? It should be the distance from the center of the Earth not the distance above the surface of the Earth.

3. Aug 5, 2009

### Pengwuino

Re: gravitation/acceleration

Two times the radius? Do you mean the radius squared? 2 x R is not hte same as R^2, which is R * R.

4. Aug 5, 2009

### ideasrule

Re: gravitation/acceleration

And also, "M" is Earth's mass, not the apple's mass. Think about it: gravitational acceleration does not depend on mass.

5. Aug 8, 2009

### dance_sg

Re: gravitation/acceleration

sorry yes, i meant the radius squared. and so the earths mass is 5.97 x 10^24, but dont i need to use the mass of the apple at all?

6. Aug 8, 2009

### Pupil

Re: gravitation/acceleration

F = ma

Fg = GMm/r^2

GMm/r^2 = ma <--- Cancel little m.

GM/r^2 = a

7. Aug 10, 2009

### dance_sg

Re: gravitation/acceleration

so 6.67 x 10^-11 (0.325)/6.40 x 10^3^2. that gives me some huge big number like 5.29 x 10^ -19 and that is not one of the options.

8. Aug 10, 2009

### dance_sg

Re: gravitation/acceleration

even when i use earths mass (5.97 x 10^ 24) it still gives me a huge number.

9. Aug 10, 2009

### rock.freak667

Re: gravitation/acceleration

r=2R

so g=GM/4R2

That shouldn't give you that big of a number

10. Aug 10, 2009

### bm0p700f

Re: gravitation/acceleration

You need to make sure r is in m not km then it will work.

11. Aug 10, 2009

### dance_sg

Re: gravitation/acceleration

so u guys gave me two equations: g=GM/4R2, GM/r^2 = a. which one is right? and thanks bm0p700f for telling me to convert!

12. Aug 10, 2009

### Pupil

Re: gravitation/acceleration

The former equation is an application of the latter equation. The distance from the center of the earth to the ground is R. The distance from the ground to the satellite is R. R + R = 2R. 2R is the thing getting squared in the denominator. Distinguish between the capital Rs and the lower case rs. Think of the lower case r as the general distance, and the big R as an actual measurement.