Question

a) Your cosmic journey brought you into the vicinity of a neutron star. In fact, you are orbiting this neutron star at an orbital distance of 2,184 kilometers. The neutron star has mass of 1.6 solar masses (M_Sun = 1.99 × 10³⁰ kg).
What is the local acceleration due to gravity that you experience in your spaceship? Express your answer in m/s²; use scientific notation and round the coefficient to two decimals.

b) What is the escape velocity from Earth’s gravity for a spacecraft launched from the orbit at an altitude of 3,445 kilometers above the Earth surface? Earth’s mean radius is R_E = 6.37 ×10⁶ m; Earth's mass is M_E = 5.97×10²⁴kg. Express your answer in km/s and round it to two decimals.

c) What is the escape velocity from Sun’s gravity for a spacecraft with mass 6,970 kilograms launched from a distance equal to the Jupiter’s average orbital distance from the Sun i.e. 5.2 AU (1AU = 1.5× 10⁸ km)? M_Sun = 1.99 × 10³⁰ kg. Express your answer in km/s and round it to two decimals.

d) A comet orbits the Sun in 2,356 years. What is its average orbital distance from the Sun? Express your answer in AU (enter "AU" for units) and round it to the nearest integer.

Answer 1

PLEASE DO NOT POST THESE MANY QUESTIONS AT ONCE....ONE QUESTION AT A TIME

(a) g = GM / r²

g = 6.67e-11 * 1.6 * 1.99e30 / (2184000)²

g = 4.45e7 m/s²

g = 4.5e7 m/s²

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(b) v (escape) = sqrt (2GM/ r)

v (escape) = sqrt ( 2*6.67e-11 * 5.97e24 / 9815000

v (escape) = 9007.82 m/s

v (escape) = 9 km/s

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(c) same formula as above. use sun's mass not the spacecraft's

v (escape) = sqrt (2GM/ r)

here , M = 1.99 × 10³⁰

r = 5.2*1.5e11 m

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(d) Use kepler's third law

T² = 4*pi²*r³ / GM