Determine g for each situation using the method shown in the example below: Example: Planet Moe has the same mass as Earth, but twice the radius. Calculate gMoe by using the fact that gE = 9.81 m/s2 on Earth. gE = GM / rE2 = 9.81 m/s2 gMoe = GMMoe / rMoe2 = GME / (2rE)2 = 1 GME / 4rE2 = ¼ x 9.81 m/s2 = 2.45 m/s2 a) Planet X has a mass 3 times that of the earth, but the same radius. What is the acceleration due to gravity near its surface? b) A distant planet has a radius half the size of Earth’s, but it has the same mass as Earth.What is the acceleration due to gravity near its surface? c) Neptune has a radius 3.9 times that of earth and a mass 17 times that of the earth.What is B at its surface?
Determine g for each situation using the method shown in the example below:
Example: Planet Moe has the same mass as Earth, but twice the radius.
Calculate gMoe by using the fact that gE = 9.81 m/s2 on Earth.
gE = GM / rE2 = 9.81 m/s2
gMoe = GMMoe / rMoe2 = GME / (2rE)2 = 1 GME / 4rE2 = ¼ x 9.81 m/s2 = 2.45 m/s2
a) Planet X has a mass 3 times that of the earth, but the same radius. What is the acceleration due to gravity near its surface?
b) A distant planet has a radius half the size of Earth’s, but it has the same mass as Earth.What is the acceleration due to gravity near its surface?
c) Neptune has a radius 3.9 times that of earth and a mass 17 times that of the earth.What is B at its surface?
d) A woman who weighs 800.0 N on Earth wants to lose weight, so she takes a trip to Planet Lite, which has twice the mass and three times the radius of earth.
- What is B on Planet Lite?
- What is her weight on Planet Lite?
e) What is g for a falling apple released from a distance of . . .
- earth radius above the earth's surface?
- earth radii from the center of the earth?
- 10 earth radii from the center of the earth?
f) What is the centripetal acceleration of a communication satellite orbiting at an altitude of 5.6 earth radii?
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