Swb123
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Hey can some one help me to solve this question please.
A satellite X is in a circular orbit of radius r about the centre of a spherical planet of mass M.
Which line, A to D, in the table gives correct expressions for the centripetal acceleration a and the speed v of the satellite?
Answer is
acceleration= GM/r*2 and speed = √GM/r
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kursk1896
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so the satellite experiences a gravitational force of GMm/r^2. This is the same as a centripetal force acting on the satellite as the satellite orbits around the planet with circular motion. Hence GMm/r^2 = mv^2/r (centripetal force acting on the satellite). Cancel out the mass of the satellite on both sides (little m) and rearrange to find v.
Centripetal acceleration is given by v^2/r. As you figured out v, you just need to substitute the expression for v you figured out into the equation for centripetal acceleration.
Last edited by kursk1896; 1 year ago
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Swb123
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okay got it. Thank you so much
(Original post by kursk1896)
so the satellite experiences a gravitational force of GMm/r^2. This is the same as a centripetal force acting on the satellite as the satellite orbits around the planet with circular motion. Hence GMm/r^2 = mv^2/r (centripetal force acting on the satellite). Cancel out the mass of the satellite on both sides (little m) and rearrange to find v.
Centripetal acceleration is given by v^2/r. As you figured out v, you just need to substitute the expression for v you figured out into the equation for centripetal acceleration.
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A Smart Guy
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(Original post by kursk1896)
so the satellite experiences a gravitational force of GMm/r^2. This is the same as a centripetal force acting on the satellite as the satellite orbits around the planet with circular motion. Hence GMm/r^2 = mv^2/r (centripetal force acting on the satellite). Cancel out the mass of the satellite on both sides (little m) and rearrange to find v.
Centripetal acceleration is given by v^2/r. As you figured out v, you just need to substitute the expression for v you figured out into the equation for centripetal acceleration.
i know this thread is old but where did you get the equation: GMm/r^2 from? I'm doing year 2 a level
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charlottefife
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(Original post by A Smart Guy)
i know this thread is old but where did you get the equation: GMm/r^2 from? I'm doing year 2 a level
formula sheet? F= gMm/r^2

When I did this question I used the formula sheet g=GM/r^2 for a at the start
then a = v^2 / r which is equal to GMm/r^2. Finally equalling v = square root of (GM/r)
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A Smart Guy
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(Original post by charlottefife)
formula sheet? F= gMm/r^2

When I did this question I used the formula sheet g=GM/r^2 for a at the start
then a = v^2 / r which is equal to GMm/r^2. Finally equalling v = square root of (GM/r)
My teacher gave us this question before we even went over gravitational fields, he probably assumed it only had to do with circular motion
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charlottefife
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(Original post by A Smart Guy)
My teacher gave us this question before we even went over gravitational fields, he probably assumed it only had to do with circular motion
ah fair enough
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