Useful formulae: a₁ = w²R. ac F = mã ||=wR, 0(t) — 0(0) = wt. ; ac = v = R |F Gravity = G M1 M2 Newton's universal constant of gravitation: G: R² = 6.674 × 10-11 Nm² (kg)2 Units of work: 1 J = 1 m N Gravity acceleration near the surface of the Earth: g = 9.8 m/s² Problem 2: A small planet of mass Mp = 5 × 1021 kg orbits at a distance R = 1.5 × 10¹¹ m from a star. The star has mass Ms = 2 × 1030 kg (notice that the mass of the star is much greater than the mass of the planet). It is also known that the orbit is circular. Answer the following questions: a) Calculate the centripetal acceleration of the planet Option A: 0.0059 m/s² Option B: 9.8 m/s² Option C: 0.332 9.8 m/s² Option D: 0 m/s² b) Calculate the planet's speed as it travels its orbit Option A: 3,333 m/s Option B: 29,748 m/s Option C: 15,001 m/s Option D: 20 km/h c) Calculate what the centripetal acceleration of the planet would be if it had half the mass that it has. Option A: 0.332 9.8 m/s² Option B: 0.0059 m/s² Option C: 12.243 m/s² Option D: 122.43 m/s² d) If the radius R of the orbit is reduced by half (while the rest of the parameters remain the same), what would happen to the centripetal acceleration of the planet? It would ... Option A: ... be multiplied by 4. Option C: ... be multiplied by 0.5. Option B: ... be multiplied by 2. Option D: ... remain the same. e) If the radius of the orbit is reduced by half, what would happen to the "years" on that planet (i.e. the time required to complete an entire orbit)? The length of the year ... Option A:... would be shortened. Option C: ... would remain the same. Option B: ... would lengthen. Option D: ... depends on the mass of the planet, Mp.
Useful formulae: a₁ = w²R. ac F = mã ||=wR, 0(t) — 0(0) = wt. ; ac = v = R |F Gravity = G M1 M2 Newton's universal constant of gravitation: G: R² = 6.674 × 10-11 Nm² (kg)2 Units of work: 1 J = 1 m N Gravity acceleration near the surface of the Earth: g = 9.8 m/s² Problem 2: A small planet of mass Mp = 5 × 1021 kg orbits at a distance R = 1.5 × 10¹¹ m from a star. The star has mass Ms = 2 × 1030 kg (notice that the mass of the star is much greater than the mass of the planet). It is also known that the orbit is circular. Answer the following questions: a) Calculate the centripetal acceleration of the planet Option A: 0.0059 m/s² Option B: 9.8 m/s² Option C: 0.332 9.8 m/s² Option D: 0 m/s² b) Calculate the planet's speed as it travels its orbit Option A: 3,333 m/s Option B: 29,748 m/s Option C: 15,001 m/s Option D: 20 km/h c) Calculate what the centripetal acceleration of the planet would be if it had half the mass that it has. Option A: 0.332 9.8 m/s² Option B: 0.0059 m/s² Option C: 12.243 m/s² Option D: 122.43 m/s² d) If the radius R of the orbit is reduced by half (while the rest of the parameters remain the same), what would happen to the centripetal acceleration of the planet? It would ... Option A: ... be multiplied by 4. Option C: ... be multiplied by 0.5. Option B: ... be multiplied by 2. Option D: ... remain the same. e) If the radius of the orbit is reduced by half, what would happen to the "years" on that planet (i.e. the time required to complete an entire orbit)? The length of the year ... Option A:... would be shortened. Option C: ... would remain the same. Option B: ... would lengthen. Option D: ... depends on the mass of the planet, Mp.
Principles of Physics: A Calculus-Based Text
5th Edition
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter11: Gravity, Planetary Orbits, And The Hydrogen Atom
Section: Chapter Questions
Problem 30P
Related questions
Question
Transcribed Image Text:Useful formulae:
a₁ = w²R.
ac
F = mã
||=wR, 0(t) — 0(0) = wt.
;
ac =
v =
R
|F Gravity
=
G M1 M2
Newton's universal constant of gravitation: G:
R²
= 6.674 × 10-11 Nm²
(kg)2
Units of work: 1 J = 1 m N
Gravity acceleration near the surface of the Earth: g = 9.8 m/s²
Transcribed Image Text:Problem 2: A small planet of mass Mp = 5 × 1021 kg orbits at a distance R = 1.5 × 10¹¹ m from a star. The
star has mass Ms = 2 × 1030 kg (notice that the mass of the star is much greater than the mass of the planet).
It is also known that the orbit is circular. Answer the following questions:
a) Calculate the centripetal acceleration of the planet
Option A: 0.0059 m/s²
Option B: 9.8 m/s²
Option C: 0.332 9.8 m/s²
Option D: 0 m/s²
b) Calculate the planet's speed as it travels its orbit
Option A: 3,333 m/s
Option B: 29,748 m/s
Option C: 15,001 m/s
Option D: 20 km/h
c) Calculate what the centripetal acceleration of the planet would be if it had half the mass that it has.
Option A: 0.332 9.8 m/s²
Option B: 0.0059 m/s²
Option C: 12.243 m/s²
Option D: 122.43 m/s²
d) If the radius R of the orbit is reduced by half (while the rest of the parameters remain the same), what
would happen to the centripetal acceleration of the planet? It would ...
Option A: ... be multiplied by 4.
Option C: ... be multiplied by 0.5.
Option B: ... be multiplied by 2.
Option D: ... remain the same.
e) If the radius of the orbit is reduced by half, what would happen to the "years" on that planet (i.e. the time
required to complete an entire orbit)? The length of the year ...
Option A:... would be shortened.
Option C: ... would remain the same.
Option B: ... would lengthen.
Option D: ... depends on the mass of the planet, Mp.
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