a) Consider an astronaut with a mass of 78 kg floating some distance directly between two planets, one with mass M and one with mass m. Denote the distance between these planets by d. There is a point in between these planets where this astronaut feels an equal and opposite pull of gravity from the two planets. Come up with a general formula for this point depending on the two masses (M and m) and the distance (d). Show why the astronaut's mass does not matter. b) Use the formula you derived in part a) to find this point when the masses of the two planets are equal. c) Plug in the numbers for the Earth and Moon to solve for the distance using the following data: Mgarth = 5.98 x 10²ª kg, MMoon = 7.35 x 1022 kg, , d = 3.84 x 105 km.
a) Consider an astronaut with a mass of 78 kg floating some distance directly between two planets, one with mass M and one with mass m. Denote the distance between these planets by d. There is a point in between these planets where this astronaut feels an equal and opposite pull of gravity from the two planets. Come up with a general formula for this point depending on the two masses (M and m) and the distance (d). Show why the astronaut's mass does not matter. b) Use the formula you derived in part a) to find this point when the masses of the two planets are equal. c) Plug in the numbers for the Earth and Moon to solve for the distance using the following data: Mgarth = 5.98 x 10²ª kg, MMoon = 7.35 x 1022 kg, , d = 3.84 x 105 km.
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Transcribed Image Text:a) Consider an astronaut with a mass of 78 kg floating some distance directly between two planets, one with
mass M and one with mass m. Denote the distance between these planets by d. There is a point in
between these planets where this astronaut feels an equal and opposite pull of gravity from the two
planets. Come up with a general formula for this point depending on the two masses (M and m) and the
distance (d). Show why the astronaut's mass does not matter.
b) Use the formula you derived in part a) to find this point when the masses of the two planets are equal.
c) Plug in the numbers for the Earth and Moon to solve for the distance using the following data:
Mgarth = 5.98 x 1024 kg, Mmoon = 7.35 x 102 kg, , d = 3.84 x 10° km.
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