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10 Nov 2019

A NASA satellite has just observed an asteroid that is on a collision course with the Earth. The asteroid has an estimated mass, based on its size, of 5 × 109 kg. It is approaching the Earth on a head-on course with a velocity of 615 m/s relative to the Earth and is now 5.0 × 106 km away. With what speed will it hit the Earth's surface, neglecting friction with the atmosphere?

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Reid Wolff
Reid WolffLv2
1 Aug 2019

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Related textbook solutions

Physics: Principles with Applications
7th Edition, 2013
Giancoli
ISBN: 9780321625922

Related questions

Earth is rotating about the Sun in our solar system. The distance between the Earth and Sun
is 1.5 × 1011m. Consider the impact of an asteroid of mass 8.9 ×1015 kg and a speed of 90,000
km/h with respect to the Earth’s surface. The asteroid strikes the Earth at the equator as shown
in Figure. Consider the mass and radius of the Earth are ME = 5.97 × 1024 kg and RE = 6.38
×106 m, respectively. Assume that the axial and orbital axis of rotations are parallel to each
other.

(a) Calculate the axial and total angular momentum of the Earth. (4 marks)
(b) What is the change in the angular velocity of the Earth due to the collision? (6 marks)
(c) What is the maximum possible change in the length of a day due to the collision?
(3 marks)
(d) How much energy is needed to stop the Earth’s rotation about its axis after the collision?
(4 marks)
(e) What would be the moment of inertia of the Earth if the axis of rotation is parallelly
shifted so that it touches the equator?

In Example 34.6 (page 1111), we imagined equipping 1950DA, an asteroid on a collision course with the Earth, with a solar sail in hopes of ejecting it from the solar system. We found that the enormous size required for the solar sail makes the plan impossible at this time. Of course, there is no need to eject such an object from the solar system: we only need to change the orbit. A much more pressing problem is Apophis, a 300-m asteroid that may be on a collision course with the Earth and is due to come by on April 13, 2029. It is unlikely to hit the Earth on that pass, but it will return again in 2036. If Apophis passes through a 600-m keyhole on its 2029 pass, it is expected to hit the Earth in 2036. causing great damage. There are plans to deflect Apophis when it comes by in 2029. For example, we could hit it with a 10- to 150-kg impactor accelerated by a solar sail. The impactor is launched from the Earth to start orbiting the Sun in the same direction as the Earth and Apophis. The idea is to use a solar sail to accelerate the impactor so that it reverses direction and collides head-on with Apophis at 80–90 km/s and thereby keeps Apophis out of the keyhole. Consider the momentum in the impactor’s orbit (Fig. P34.75) when the solar sail makes an angle of θ = 60° with the tangent to its orbit. Current solar sails may be about 40 m on a side, but the hope is to construct some that are about 160 m on a side. Estimate the impactor’s tangential acceleration when it is about 1 AU from the Sun. Keep in mind that the sail is neither a perfect absorber nor a perfect reflector, and a heavier impactor would presumably be equipped with a larger sail. Don’t be surprised by what may seem like a very small acceleration.

Consider an Earth-like planet hit by an asteroid. The planet hasmass Mp = 3.59 × 1023 kg and radius Rp = 6.08 × 106 m, and you mayapproximate it as a solid ball of uniform
density. It rotates on its axis once every T = 35 hr. The asteroidhas mass Ma =2.01 × 1017 kg and speed va = 26900 m/s (relative tothe planet’s center); its velocity vector points = 54? below theEastward horizontal. The impact happens at an equatorial location.First, calculate the planet’s angular momentum (relative to itsspin axis) before the impact.
Answer in units of kgm2/s.

Part B) Calculate the asteroid’s angular momentum relative to theplanetary axis.
Answer in units of kgm2/s.

Part C)The impact is totally inelastic — the asteroid is stuck inthe planet’s crust. But thanks to the asteroid’s angular momentum,the planet rotates faster after the impact than it didbefore.
By how many seconds has the collision shortened the planetary day?For simplicity, ignore the effect of the asteroid’s mass on theplanet’s moment of inertia
and assume Iafter = Ibefore planet .
Warning: At intermediate stages of this calculation, do not roundoff intermediate results and keep at least 7 significantdigits.
Answer in units of s.

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