How High Must a Rocket Travel for Gravity to Halve?

[Hannahj1]

A rocket ship is moving away from the Earth after having been fired from a launch pad in Florida. At what point above the Earth's surface will the force of gravity be reduced to ½ of its original value?
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Prior to this question I was given the equations to calculate the Force of Gravity (Fg = GMm/R^2) and the Gravitational Field Strength (g = GM/R^2).

At first, I thought you would use the Force of Gravity equation due to what the question is asking but am I mistaken in thinking that the correct answer is gotten by using the Gravitational Field Strength equation?

I'm also not too sure about whether or not the original force of gravity would be 9.8m/s^2.

Using the given value G = (6.67 x 10^-11) and letting d = distance above the Earth's surface.. (0.5)g = GM/(R+d)^2, I just plugged the values in and ended up with a distance of (2.6 x 10^6) meters above the Earth's surface.

 

[berkeman]

A rocket ship is moving away from the Earth after having been fired from a launch pad in Florida. At what point above the Earth's surface will the force of gravity be reduced to ½ of its original value?
------------------

Prior to this question I was given the equations to calculate the Force of Gravity (Fg = GMm/R^2) and the Gravitational Field Strength (g = GM/R^2).

At first, I thought you would use the Force of Gravity equation due to what the question is asking but am I mistaken in thinking that the correct answer is gotten by using the Gravitational Field Strength equation?

I'm also not too sure about whether or not the original force of gravity would be 9.8m/s^2.

Using the given value G = (6.67 x 10^-11) and letting d = distance above the Earth's surface.. (0.5)g = GM/(R+d)^2, I just plugged the values in and ended up with a distance of (2.6 x 10^6) meters above the Earth's surface.

Please use the Homework Help Template in all of your schoolwork posts here. Thanks.

The force of gravity falls off as 1/r^2, so you only need the radius of the Earth to answer this question. Does that help?

Also, 9.8m/s^2 is the acceleration due to gravity at the surface of the Earth; it is not a force.

 

[Hannahj1]

Please use the Homework Help Template in all of your schoolwork posts here. Thanks.

The force of gravity falls off as 1/r^2, so you only need the radius of the Earth to answer this question. Does that help?

Also, 9.8m/s^2 is the acceleration due to gravity at the surface of the Earth; it is not a force.

Thank you! So should i do Fg1 = Fg2 and when i reduce it, it gives me 1/R^2 = 1/2R^2 but the second R is radius of Earth plus the distance of the satellite? I tried to solve for the distance and got a negative number.

 

[berkeman]

Thank you! So should i do Fg1 = Fg2 and when i reduce it, it gives me 1/R^2 = 1/2R^2 but the second R is radius of Earth plus the distance of the satellite? I tried to solve for the distance and got a negative number.

Try using Re and R2 for the two radii, and Fe and F2 as the two forces. Please post your full work so we can see it and correct any errors.

 

[Hannahj1]

Try using Re and R2 for the two radii, and Fe and F2 as the two forces. Please post your full work so we can see it and correct any errors.

OH I just realized my mistake! i was doing 0.5GMm/R^2 but i had to do 2GMm/R^2. Thank you for all the help!