Question

Analysis Model Tutorial As an astronaut, you observe a small planet to be spherical. After landing on the planet, you set off, walking always straight ahead, and find yourself returning to your spacecraft from the opposite side after completing a lap of 26.0 km. You hold a hammer and a falcon feather at a height of 1.76 m, release them, and observe that they fall together to the surface in 29.7 s. Determine the mass of the planet. Part 1 of 5 - Conceptualize: Imagine it is you standing on the planet releasing the feather and the hammer att = 0. The time t at which they strike the surface will depend on the gravitational field of the planet. The gravitational field will depend on the mass M of the planet and the radius R of the planet. The distance of the lap around the planet is the circumference of the planet and is also related to its radius. From these thoughts, we see that we can determine the mass of the planet from the information given. We expect a planet-sized mass, but much smaller than that of the Earth, due to the long time interval for the hammer and feather to reach the surface. Continue

Answer 1

1 2 2 tt (ircumference of the planet. The distance of lap = 2TR = e where R is the radius of the planet R = I= 26 km 4.138 n 4. 14 km. 3 = 4.14x10 m (GMm) Force on an object of Ma mais of planet a = acceleration. In Naw in the question given the variation gravity along the given length is negligible it be constant mall m. KAJ (4 m) = 0 of .. we assume

released at is o o ] Naw the objects are height h = 1.76m, s it reaches the ground. in t= 29.7 s.. [Note: initial aclocity h = 1 alt) from 2h - Gm gh- a t2 G =) 2hR² ) M t R? G t²

M- 2x1.76X (4.14x103)2 6.674x 10" (29.7)2 17 1615 ng 0.01 x lollo = 0.01 X10 of the planet. is the man