# ? Earth's Gravitational Field Effect on space shuttles

1. Aug 29, 2005

### samaank

???? Earth's Gravitational Field Effect on space shuttles

Hi, i have a physics question in my physics portfolio, it goes as follows

Critically assess the following statement: ‘Astronauts in a space capsule orbiting the earth at a height of 900km experience weightlessness: hence the gravitational field due to the earth must be zero at that altitude'. Include calculations in your answer.

Can someone please help ?

2. Aug 29, 2005

### HallsofIvy

Staff Emeritus
Do you know the formula for the strength of earth's gravitational field?

$$F= \frac{GM}{r^2}$$

Where G is the "universal gravitational constant", M is the mass of the earth, and r is the distance from the center of the earth (radius of the earth plus altitude). For what value of r is that 0?

Whe DO astronauts experience weightlessness? (What weight would you feel if you jumped off the edge of the Grand Canyon?)

3. Aug 29, 2005

### samaank

thank you very much, your post made something click in my mind, i got it now. thanks

4. Aug 31, 2005

### samaank

ok i thought i had it but i didnt, could u please prove that theory mathematically, i tried inputting the numbers but ended up with 610.24234......

5. Aug 31, 2005

### Dr.Brain

Astronauts donot feel weightless because of earth's gravitational field =0 , infact the gravitational field due to earth is not zero by any means at a height of 900 km. Astronauts would feel weightless if their space-shuttles accelerated in such a way that it counterbalanced the earth's attraction.Astronauts could feelw eightless if they were under freefall in space , like in case of satellites orbiting earth, in this case earth's gravitational field helps in motion of satellite and is not zero.Earth's Gravitational field will be zero when r---> infinity.

BJ

6. Aug 31, 2005

### samaank

how would i prove that mathematically ?

7. Aug 31, 2005

### HallsofIvy

Staff Emeritus
I'll try one more time- the question asked whether the force of gravity was 0.

$$F= \frac{GMm}{r^2}$$

For what value of r is that 0?

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