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Chapter 13: Q. 16 (page 353)

What is the escape speed from Jupiter?

Short Answer

Expert verified

The escape speed from Jupiter is 59.5km/s.

Step by step solution

01

Given information

We know, mass of the planet = 1.898×1027kg., radius of the planet =71492km.

02

Calculation

Escape speed is only possible at the condition when the kinetic energy exceeds the gravitational potential energy at the surface.

The kinetic energy is given by : K.E=12mv2.

Where, 'v' is the escape velocity.

'm' is the mass of a planet.

03

Continuation of calculation

The potential energy is given by : P.E=GMmR.

Where, 'G' is the gravitational constant=6.67×10-11m3/kg·s2.

'M' is the mass of the planet =1.898×1027kg.

'R' is the radius of the planet =71492km.

Equating potential energy to kinetic energy :

12mv2=GMmRv=2GMR.

04

Continuation of calculation

Substituting the values ofG,M,Rwe get,

v=2GMRv=2×(6.67×10-11m3/kgs2)(1.898×1027kg)(71.492×103m)v=5.95×104m/sv=59.5km/s.

05

Final answer

Escape speed from Jupiter is 59.5km/s.

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Most popular questions from this chapter

A new planet is discovered orbiting the star Vega in a circular orbit. The planet takes 55earth years to complete one orbit around the star. Vega’s mass is 2.1times the sun’s mass. What is the radius of the planet’s orbit? Give your answer as a multiple of the radius of the earth’s orbit.

The escape speed from Planet X is 10,000 m/s. Planet Y has the same radius as Planet X but is twice as dense. What is the escape speed from Planet Y?

A moon lander is orbiting the moon at an altitude of 1000 km. By what percentage must it decrease its speed so as to just graze the moon’s surface one-half period later?

A satellite in a circular orbit of radius r has period T. A satellite in a nearby orbit with radius r + Δr, where Δr << r , has the very slightly different period T+ ΔT.

a) Show that ΔTT=32Δrr

b) Two earth satellites are in parallel orbits with radii 6700 km and 6701 km. One day they pass each other, 1 km apart, along a line radially outward from the earth. How long will it be until they are again 1 km apart?

In 2014, the European Space Agency placed a satellite in orbit around comet 67P/Churyumov-Gerasimenko and then landed a probe on the surface. The actual orbit was elliptical, but we’ll approximate it as a 50-km-diameter circular orbit with a period of 11 days.
a. What was the satellite’s orbital speed around the comet? (Both the comet and the satellite are orbiting the sun at a much higher speed.)

b. What is the mass of the comet?
c. The lander was pushed from the satellite, toward the comet, at a speed of 70 cm/s, and it then fell—taking about 7 hours—to the surface. What was its landing speed? The comet’s shape is
irregular, but on average it has a diameter of 3.6 km.
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