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Консультация № 132540
16.04.2008, 23:07
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помогите пожалуйста!)Искусственный спутник Земли движется по круговой орбите в плоскости экватора с запада на восток.на какой высоте h над поверхностью должен находится спутник,чтобы быть неподвижным относительно земного наблюдателя?спасибо огромное!
Обсуждение
Неизвестный
16.04.2008, 23:40
общий
это ответ
Здравствуйте, Anyta111!
Раз спутник неподвижен для наблюдателя, значит, спутник вращается с такой же скоростью что и Земля и период его орбиты 24 часа
Сила, с которой он притягивается Землей, это сила гравитационного взаимодействия:
F=G*(m*M)/r^2
где G=6.673 * 10^-11 м^3 кг^-1 с^-2
m-масса спутника
M-масса земли = 5.9742 * 10^24 кг
r=R+h- расстояние от центра Земли до нашего спутника
Она складывается из радиуса Земли R=6300км=6.3 *10^6 м
и высоты h которую надо найти
так же есть центробежная сила:
F=m*V^2 /r (1)
V-скорость спутника на орбите
V=w*r (2)
w=2*pi/T => (2)=2*pi*r/T =>
(1)=m* (2*pi*r/T)^2 /r=m* (2*pi/T)^2 *r
обе силы равны для того чтобы спутник висел на одной высоте:
m* (2*pi/T)^2 *r = G*(m*M)/r^2
(2*pi/T)^2 *r = G*M/r^2
r^3=G*M*T^2/(2*pi)^2
r=sqrt3[G*M*T^2/(2*pi)^2]
R+h=sqrt3[G*M*T^2/(2*pi)^2]
h=sqrt3[G*M*T^2/(2*pi)^2] -R
учтем что T=24часа=24*3600=86400с
h=35.937*10^6 м
Раз спутник неподвижен для наблюдателя, значит, спутник вращается с такой же скоростью что и Земля и период его орбиты 24 часа
Сила, с которой он притягивается Землей, это сила гравитационного взаимодействия:
F=G*(m*M)/r^2
где G=6.673 * 10^-11 м^3 кг^-1 с^-2
m-масса спутника
M-масса земли = 5.9742 * 10^24 кг
r=R+h- расстояние от центра Земли до нашего спутника
Она складывается из радиуса Земли R=6300км=6.3 *10^6 м
и высоты h которую надо найти
так же есть центробежная сила:
F=m*V^2 /r (1)
V-скорость спутника на орбите
V=w*r (2)
w=2*pi/T => (2)=2*pi*r/T =>
(1)=m* (2*pi*r/T)^2 /r=m* (2*pi/T)^2 *r
обе силы равны для того чтобы спутник висел на одной высоте:
m* (2*pi/T)^2 *r = G*(m*M)/r^2
(2*pi/T)^2 *r = G*M/r^2
r^3=G*M*T^2/(2*pi)^2
r=sqrt3[G*M*T^2/(2*pi)^2]
R+h=sqrt3[G*M*T^2/(2*pi)^2]
h=sqrt3[G*M*T^2/(2*pi)^2] -R
учтем что T=24часа=24*3600=86400с
h=35.937*10^6 м
Форма ответа
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